Vision IAS CSAT Test-5 2023 cse_updates(1)

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VISION IAS 
www.visionias.in 
 
 
 
TEST BOOKLET 
 
CSAT APTITUDE TEST– (4021) – 2023 
Time Allowed: Two Hours Maximum Marks: 200 
 
 
INSTRUCTIONS 
 
1. IMMEDIATELY AFTER THE COMMENCEMENT OF THE EXAMINATION, YOU SHOULD CHECK THAT THIS BOOKLET 
DOES NOT HAVE ANY UNPRINTED OR TORN OR MISSING PAGES OR ITEMS ETC. IF SO, GET IT REPLACED BY A 
COMPLETE TEST BOOKLET. 
 
2. ENCODE CLEARLY THE TEST BOOKLET SERIES A, B, C OR D AS THE CASE MAY BE IN THE APPROPRIATE PLACE IN 
THE ANSWER SHEET. 
 
3. You have to enter your Roll Number on the Test Booklet in 
the Box provided alongside. DO NOT write anything else on 
the Test Booklet. 
 
4. This Test Booklet contains 80 items (Questions). Each item is printed in English. Each item comprises four 
responses (answers). You will select the response which you want to mark on the Answer Sheet. In case you feel 
that there is more than one correct response, mark the response which you consider most appropriate. In any 
case, choose ONLY ONE response for each item. 
 
5. You have to mark all your responses ONLY on the separate Answer Sheet provided. See direction in the answers 
sheet. 
 
6. All items carry equal marks. Attempt all items. Your total marks will depend only on the number of correct 
responses marked by you in the answer sheet. For every incorrect response one-third of the allotted Marks will 
be deducted. 
 
7. Before you proceed to mark in the Answer sheet the response to various items in the Test booklet, you have to 
fill in some particulars in the answer sheets as per the instruction sent to you with your Admission Certificate. 
 
8. After you have completed filling in all responses on the answer sheet and the examination has concluded, you 
should hand over to Invigilator only the answer sheet. You are permitted to take away with you the Test 
Booklet. 
 
9. Sheets for rough work are appended in the Test Booklet at the end. 
 
DO NOT OPEN THIS BOOKLET UNTIL YOU ARE ASKED TO DO SO 
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1. First 50 consecutive odd numbers are written 
on a black board, 1, 3, 5, 7, …. in that order. 
Two persons Anurag and Bhawna are playing a 
game of putting ‘+’ and ‘–’ sign one by one 
between any two consecutive integers out of 
these 50 odd numbers. Both Anurag and 
Bhawna are free to put any sign (+ or –) 
anywhere, provided there is no sign already 
placed between the two odd numbers. At the 
end, when all the signs have been put between 
all such two consecutive odd numbers, result is 
to be calculated. If the result is even, Anurag 
wins and if the result is odd, Bhawna wins. 
Who will win? 
(a) Anurag 
(b) Bhawna 
(c) It’s a tie 
(d) Cannot be determined. 
 
2. Two statements S1 and S2 are given below 
followed by a question. 
S1: Unit digit of 9x (i.e. 9 multiplied by x) is 1. 
S2: x is a natural number. 
Question: What is the remainder when x is 
divided by 4? 
(a) S1 alone is sufficient to answer the 
Question. 
(b) S2 alone is sufficient to answer the 
Question. 
(c) Either S1 alone or S2 alone is sufficient to 
answer the question. 
(d) S1 and S2 together are not sufficient to 
answer the question. 
3. Ironite is a mixture of iron and zinc only. It is 
extracted from an ore that contains iron and 
zinc in a ratio of 3:2 by weight. In the process 
of extraction, the entire iron is retained, 
but some amount of zinc is lost. If ironite 
contains 10% zinc by weight, find the amount 
of ore needed to produce 5 tonnes of Ironite. 
(a) 8.5 tonnes 
(b) 6 tonnes 
(c) 7.5 tonnes 
(d) 7 tonnes 
 
4. If 17 < a < 67, how many positive integral pairs 
of (a, b) are possible satisfying the equation 
(3/a) + (2/b) = 1/18? 
(a) 7 
(b) 8 
(c) 9 
(d) 10 
 
5. When a ball is dropped, it bounces back to 3/4th 
of the height from which it was dropped from . 
If the ball is dropped from a height of 30 m, 
find the total vertical distance travelled by the 
ball before it comes to rest. (Neglect air 
resistance.) 
(a) 210 m 
(b) 240 m 
(c) 180 m 
(d) 200 m 
 
 
 
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6. A wooden box of thickness 0.5 cm, length 21 
cm, width 11 cm and height 6 cm is painted on 
the inside. The box is open on the top, i.e. there 
is no top surface/lid. The expense of painting is 
Rs. 70. What is the rate of painting per square 
centimeter? 
(a) Rs. 0.7 
(b) Rs. 0.5 
(c) Rs. 0.1 
(d) Rs. 0.2 
 
7. Two statements are given below followed by a 
question. 
S1: Age of A is a perfect square, and age of B 
is a perfect cube. 
S2: A and B are twins. 
Question: The ages of A and B are integers 
greater than 20 but less than 70. What are their 
individual ages? 
(a) S1 alone is sufficient to answer the 
Question. 
(b) S2 alone is sufficient to answer the 
Question. 
(c) Either S1 alone or S2 alone is sufficient to 
answer the question. 
(d) S1 and S2 together are sufficient to answer 
the question. 
Directions for the following 6 (six) items: 
Read the following five passages and answer the items 
that follow each passage. Your answers to these items 
should be based on the passages only. 
Passage – 1 
For most people, the climate crisis is no longer a future 
scenario. Floods, heat waves and wildfires have gripped 
our entire planet and will become stronger in years to 
come. Countries in the Global South are particularly 
hard hit, even though their citizens have been 
emitting the least CO2. Drastic reduction of carbon 
emissions is only one pillar in the fight against climate 
change. Many of its consequences can no longer be 
stopped. There is an urgent need for adaptation 
measures so people both in cities and in rural areas have 
the chance to cope with the effects of climate change. 
That's why several years ago rich nations committed to 
supporting low-income countries with $100 billion (€95 
billion) annually from 2020 to help them cut emissions 
and adapt to climate change. It was a central promise 
for more climate justice that has not been kept so far. 
8. Based on the above passage, the following 
assumptions have been made: 
1. Through proper adaptation mechanisms 
and funding climate change can be arrested. 
2. Countries from the global south are not 
responsible for climate change. 
3. UN could help make the rich countries 
accountable for funding the sum of $100 
billion for climate change. 
Which of the above assumptions is/are valid? 
(a) 1 and 2 only 
(b) 2 and 3 only 
(c) None of these 
(d) 1, 2 and 3 
 
 
 
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9. What is the crucial message conveyed by the 
above passage? 
(a) Controlling carbon emissions should be the 
prime focus in the fight against climate 
change. 
(b) The rich countries must be made 
accountable to low-income countries facing 
climate change. 
(c) Climate change not only affects the 
environment, but also threatens the very 
existence of human life. 
(d) Climate change cannot be reversed; the 
only solution is adaptation mechanisms. 
Passage – 2 
The globalization of the Indian economy has 
dramatically influenced social life in India. The 
expansion of the middle class is said to have occurred 
as a consequence of this process. Based on 
ethnographic research among lower-middle-class 
families in India, there seems to be an apparent paradox 
betweenwomen's positive perceptions of empowerment 
and the overall negative impact of structural adjustment 
policies on women. Many scholars argue that 
globalization has been detrimental to women due to 
growing structural gender inequalities, but many 
respondents identify greater opportunities to challenge 
preexisting patriarchal norms through the role models 
available in the globalized media. While there are 
increasing inequalities for households, women do not 
consider these to be gender disadvantages, emphasizing 
instead the opportunities for greater independence. 
10. Based on the above passage, the following 
assumptions have been made: 
1. Globalization has increased incomes 
resulting in a change in the social life of the 
people. 
2. The Indian middle class has obtained the 
most benefits out of globalization. 
3. The impact of globalization on women is 
not clear. 
Which of the above assumptions is/are valid? 
(a) 1 only 
(b) 3 only 
(c) 1 and 2 only 
(d) All 1, 2 and 3 
Passage – 3 
The digital divide is associated with negative outcomes. 
It is suggested that the digital divide may cause 
technological, immaterial, social, and educational types 
of inequality. Individuals who lack access to 
information technology are disadvantaged in 
knowledge-based societies and economies. Further, e-
government is an important means to break barriers and 
bring government assistance to all citizens. Digital 
media usage is a strong predictor of political 
participation which implies that a digital divide may 
result in political alienation of those who lack digital 
media access. 
11. Based on the above passage, the following 
assumptions have been made: 
1. Building cyber cafes could help reduce the 
digital divide. 
2. Bridging the digital divide could help 
empower citizens technologically as well as 
politically. 
Which of the above assumptions is/are valid? 
(a) 1 only 
(b) 2 only 
(c) Both 1 and 2 
(d) Neither 1 nor 2 
 
 
 
 
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Passage – 4 
Invasive species may be one of the worst environmental 
problems facing the conservation of natural areas, 
because of their role in changing ecosystem function. 
At the same time, invasive species cause much human 
suffering and economic loss. The approach to 
eliminating invasive species can be improved by a 
better understanding of the various types of invasive 
species, and the scientific hypotheses surrounding their 
ability to invade novel environments. Despite the 
billions of dollars spent each year, invasive species are 
difficult if not impossible to eliminate after they have 
been established. 
12. Based on the above passage, the following 
assumptions have been made: 
1. Invasive species, if not eliminated in future, 
could threaten the food security of people. 
2. If invasive species are not allowed to 
change the ecosystem function, natural 
areas can definitely be conserved. 
Which of the above assumptions is/are valid? 
(a) 1 only 
(b) 2 only 
(c) Both 1 and 2 
(d) Neither 1 nor 2 
Passage – 5 
With an inter-connected world, we might assume that 
today’s children have higher EQ as compared to their 
predecessors. But the truth might be different. With the 
boom in technology, many children are glued to their 
screens and don’t get to meet other children face-to-
face. Relating to others and relationship management is 
an important element that nurtures a high EQ in an 
individual. But technology and its addiction among 
children are a hindrance in attaining high EQ levels and 
this leads to many of them not being able to manage 
their emotions well. 
13. Based on the above passage, the following 
assumptions have been made: 
1. Technology directly impacts the EQ of 
children. 
2. Human relations have a positive impact on 
EQ as compared to technology. 
Which of the above assumptions is/are valid? 
(a) 1 only 
(b) 2 only 
(c) 1 and 2 
(d) None 
 
14. D is a positive integer, which is a product of 
two prime numbers. Which of the following 
cannot be a value of D? 
(a) 46 
(b) 91 
(c) 143 
(d) 153 
 
15. Ajay and Vijay are running towards each other 
at the same speed from points A and B 
respectively. After running for some time, Ajay 
sprains his ankle at point C and walks at half 
his earlier speed. They finally meet at a point 
D, such that AD = (4/10) AB. Find the ratio of 
AC/AD. 
(a) 1:2 
(b) 2:3 
(c) 2:5 
(d) 3:4 
 
 
 
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Directions for the following three items: 
Study the pie charts given below and answer the three 
questions that follow. 
Chart 1 shows the percentage distribution of 12 million 
tonnes of crude oil transported through different modes 
over a specific period of time. 
 
Chart 2 shows the percentage distribution of the cost of 
transporting this crude oil. The total cost was Rs. 30 
million. 
 
16. The per tonne transportation cost of oil via rail 
happens to be roughly 
(a) Rs. 3 
(b) Rs. 3.33 
(c) Rs. 4.5 
(d) Rs. 2.67 
 
17. As per the charts, it appears that the cheapest 
mode of transportation is 
(a) Road 
(b) Rail 
(c) Pipeline 
(d) Ship 
 
18. If the per tonne transportation costs by ship, air 
and road are represented by P, Q and R 
respectively, then which of the following is 
true? 
(a) R > Q > P 
(b) P > R > Q 
(c) P > Q > R 
(d) R > P > Q 
 
19. Ram and Shyam, who are standing 100 m away 
from each other, are throwing a Frisbee towards 
each other in a straight trajectory. Initially Ram 
has the Frisbee and as soon as he throws it 
towards Shyam, they both start moving towards 
each other. Shyam catches the Frisbee and 
throws it back to Ram and they keep throwing 
it until they meet each other. They both throw 
the frisbee at a speed of 20 m/s. If the frisbee 
travelled a total distance of 12 km and the 
speeds of Ram and Shyam are in the ratio of 
2:3 respectively, then find the speed of Shyam 
(in metres per min). (Assume that the time 
taken by Ram and Shyam to catch the frisbee 
and to throw it back again is negligible, and the 
frisbee travels at a uniform speed in the air). 
(a) 8 
(b) 6 
(c) 9 
(d) 10 
 
Pipeline, 
49%
Ship, 9%
Airfreight, 
11%
Road, 22%
Rail, 9%
Volume Transported
Pipeline ship
Pipeline, 
65%
Ship, 10%
Airfreight, 
7%
Road, 6% Rail, 12%
Cost of Transportation
Pipeline Ship Airfreight Road Rail
 
 
 
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20. Let ‘a’ and ‘b’ be two 2-digit numbers, such 
that b is obtained by reversing the digits of a. It 
is also known that they satisfy the relation a2 – 
b2 = k2, where k is some positive integer. What 
is the value of a + b + k? 
(a) 151 
(b) 115 
(c) 154 
(d) 153 
 
Directions for the following 3 (three) items: 
Read the following three passages and answer the items 
that follow each passage. Your answers to these items 
should be based on the passages only. 
Passage – 1 
Ecosystem services, defined as the benefits to human 
welfare provided by organisms interacting in 
ecosystems, are considered to be at risk. Pollination by 
wild animals is a key ecosystem service. Crop 
pollination is commonly cited as an example of an 
endangered ecosystem service as detailed studies of the 
crop pollination systems are incomplete or out of date. 
Animalpollination is important to the sexual 
reproduction of many crops and the majority of wild 
plants, which can also be important for providing 
calories and micronutrients for humans. Furthermore, 
the decline of pollinating species can lead to a parallel 
decline of plant species. 
21. Which of the following is/are the most rational 
and logical Inference/Inferences that can be 
made from the passage? 
1. To protect this ecosystem service, holistic 
contemporary research in crop pollination 
may help. 
2. Loss of pollinator species can have grave 
consequences for human nutrition. 
Select the correct answer from the code given 
below: 
(a) 1 only 
(b) 2 only 
(c) Both 1 and 2 
(d) Neither 1 nor 2 
 
Passage – 2 
One of the biggest problems that solar energy 
technology poses is that energy is only generated while 
the sun is shining. That means night time and overcast 
days can interrupt the supply. The shortage created by 
this interruption would not be a problem if there were 
low-cost ways of storing energy as extremely sunny 
periods can generate excess capacity. As the global 
capacity for solar power continues to rise, nations like 
Japan and other global leaders in solar energy 
technology are focusing on developing adequate energy 
storage to deal with this issue. 
22. Which of the following is/are the most rational 
and logical inference/inferences that can be 
drawn from the passage? 
1. Tropical countries with year-long 
availability of sunshine are less dependent 
on the storage of solar energy. 
2. In future, the cost of storage of solar energy 
may reduce due to the involvement of 
global leaders. 
Select the correct answer from the code given 
below: 
(a) 1 only 
(b) 2 only 
(c) 1 and 2 
(d) None 
Passage – 3 
New advancements in technologies ranging from 
robotics and drones to computer vision software have 
completely transformed modern agriculture. The 
primary goal of farm automation technology is to cover 
easier, mundane tasks. Some major technologies that 
are most commonly being utilized by farms include 
harvest automation, autonomous tractors, seeding and 
weeding, and drones. Farm automation technology 
addresses major issues like a rising global population, 
farm labour shortages, and changing consumer 
preferences. The benefits of automating traditional 
farming processes are monumental by tackling issues 
from consumer preferences, labour shortages, and the 
environmental footprint of farming. 
 
 
 
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23. Which one of the following statements best 
reflects the central idea of the passage? 
(a) The supply chain of agricultural produce 
will transform with evolving technologies. 
(b) Agricultural technology has the potential to 
solve socio-economic issues along with the 
environment. 
(c) There is a dire need for automation of 
agriculture in India to help alleviate the 
status of marginal farmers. 
(d) Application of modern technology will 
increase the input cost of farmers. 
 
24. Let x, y and z be distinct integers, wherein x 
and y are odd and positive, and z is even and 
positive. Which one of the following statements 
cannot be true? 
(a) y(x − z)2 is even 
(b) y2(x − z) is odd 
(c) y(x − z) is odd 
(d) z(x − y)2 is even 
 
25. Raman was asked to add first few natural 
numbers (i.e., 1 + 2 + 3 + …) as long as he 
wanted. When he stopped, he gave the sum as 
575. When the teacher declared the result was 
wrong, Raman discovered that he had missed 
one number in the sequence during addition. 
What was the number that he missed? 
(a) Less than 10 
(b) 10 
(c) 15 
(d) More than 15 
 
26. A number N gives a remainder of 7 when 
divided by D and a remainder of 20 when 
divided by 2D. What will be the remainder 
obtained when 2N is divided by D? 
(a) 0 
(b) 1 
(c) 6 
(d) 3 
 
27. There are 25 students in a class, and the number 
of students who scored 5, 7 and 3 marks in a 
test are 8, 10 and 7 respectively. The teacher 
can decide how many students should go to the 
remedial class, but can't pick specific students 
for it. Once the number is decided, the students 
are selected at random. The teacher wants every 
student in the class to have atleast three others 
who scored the same marks in the examination 
as him/her. What is the minimum number of 
students who should be sent to the remedial 
class for this to happen? 
(a) 19 
(b) 22 
(c) 18 
(d) 16 
 
28. If X and Y are multiples of 7 with X>Y>0, 
which of the following statements is not always 
true? 
(a) X3 – Y3 is divisible by 49. 
(b) HCF of X and Y is a multiple of 7. 
(c) LCM of X and Y is a multiple of 49. 
(d) X2 – Y2 is a multiple of 49. 
 
29. A six-digit number N is formed using the digits 
0, 3, 6 and 9 only. Each of the digits is used at 
least once. It was found that N is divisible by 
18. What is the ten’s digit of the smallest 
possible such six-digit number? 
(a) 0 
(b) 9 
(c) 6 
(d) 3 
 
 
 
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30. If the numerator of a fraction is increased by 
a% and denominator of the fraction is increased 
by b%, then what will be the ratio of original 
fraction to new fraction? 
(a) a/b 
(b) (a +1)/(b + 1) 
(c) (100 + b)/(100 + a) 
(d) b/a 
 
Directions for the following 3 (three) items: 
Read the following three passages and answer the items 
that follow each passage. Your answers to these items 
should be based on the passages only. 
Passage – 1 
Universal and affordable access to quality education 
and healthcare must be the focus of our attention. Rural 
India cannot be left behind in this mission. Improving 
rural infrastructure across the country must be fast-
tracked and integrated into the larger development 
narrative. Promotion of the mother tongue will 
revolutionize the educational landscape by making it 
more inclusive and equitable. 
With his unbounded greed, man has caused irreversible 
damage to the environment. Today, climate change is a 
global phenomenon. Conservation is our only hope for 
the survival of the planet and we must direct our 
collective energies toward this end with missionary 
zeal. Our scriptures mirror the cosmic vision of our 
ancient culture. They are replete with examples of the 
worship of the divine in the elements — rivers, 
mountains, holy plants and trees. We only have to go 
back to our moorings to draw inspiration and strive to 
secure the future of succeeding generations. 
 
31. Consider the following: 
1. Pollution 
2. Non-discriminatory education 
3. Irrigation 
4. Quality healthcare 
5. Human Survival 
6. Avariciousness 
Which of the above issues have been 
highlighted by the passage? 
(a) 1, 2, 4 and 5 only 
(b) 1, 2, 4, 5 and 6 only 
(c) 3, 4, 5 and 6 only 
(d) 2, 4 and 5 only 
Passage – 2 
In cities, in high-rises, not many of us know our 
neighbors anyway. Parents might not like cricket. 
Friends might not share our interest in sports. The 
intrusion of others is probably not welcomed by all. 
Especially, for this generation which has grown up in 
bubbles for most things — entertainment, online 
studies, social media — even if, paradoxically, the 
surfeit of lonely pursuits has reduced the quality of 
solitude. 
32. Which one of the following statements best 
reflects the suggestion conveyed by the 
passage given above? 
(a) People should avoid living in cities. 
(b) In cities, people should become more 
socialized. 
(c) In search of loneliness, we have shortenedthe quality of solitude. 
(d) Cities have become a breeding ground for 
loneliness. 
Passage—3 
Earlier, the rural always existed in Hindi films. It was a 
regular narrative trope: characters from rural areas 
would always be arriving in the city. Those films 
created a split between the rural and the urban: the rural 
was seen as pure and the urban as impure, the rural as 
innocent and the urban as corrupt. They created a 
binary between the village and the city. 
 
 
 
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33. According to the passage, which of the 
following is correct about Hindi films? 
(a) Now, Hindi films portray only ‘the urban’. 
(b) It is solely because of Hindi films that there 
exists a split between ‘the rural’ and ‘the 
urban’. 
(c) Earlier, Hindi films portrayed the rural as 
‘good’ and the urban as ‘bad’. 
(d) Both (b) and (c) 
 
34. The sum of the areas of two circles, which 
touch each other externally is 153π. If the sum 
of their radii is 15, find the ratio of the larger to 
the smaller radius. 
(a) 4 
(b) 2 
(c) 3 
(d) None of these 
 
35. Two statements are given below followed by a 
question. 
S1: The cost of three caramel pops, five toffee 
bites and seven mango pops is Rs. 68. 
S2: The cost of two caramel pops, three toffee 
bites and four mango pops is Rs. 41. 
Question: Priya went to a candy shop to buy 
some caramel pops, toffee bites and mango 
pops. What is the total price of one caramel 
pop, one mango pop and one toffee bite? 
Which one of the following is correct in respect 
of the Statements and the Question? 
(a) S1 alone is sufficient to answer the 
Question. 
(b) S2 alone is sufficient to answer the 
Question. 
(c) S1 and S2 together are sufficient to answer 
the question. 
(d) S1 and S2 together are not sufficient to 
answer the Question. 
 
Directions for the following 2 (two) items: 
Study the graph given below carefully and answer the 
questions that follow. 
The bar graph given below shows the data of the 
production of paper (in lakh tonnes) by three different 
companies X, Y and Z. 
 
36. For which of the following years, is the 
percentage rise/fall in production from the 
previous year the maximum for Company Y? 
(a) 2007 
(b) 2008 
(c) 2009 
(d) 2010 
 
37. What is the ratio of the average production of 
Company X in the period 2008-2010 to the 
average production of Company Y in the same 
period? 
(a) 1:1 
(b) 15:17 
(c) 23:25 
(d) 27:29 
 
30
45
25
50
40
25
35 35
40
50
35
40
45
35 35
0
5
10
15
20
25
30
35
40
45
50
55
2006 2007 2008 2009 2010
Production of Paper (in lakh tonnes) by 
Three Companies X, Y and Z
x Y Z
 
 
 
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38. If value of a is between – 6 and – 3 and value 
of b is between – 3 and 3, then the value of 
(a2 – b2) must be in between which of the 
following ranges? 
(a) – 36 and 9 
(b) – 36 and – 9 
(c) 0 and 9 
(d) 0 and 36 
 
39. Ramesh bought some articles at a price which 
was 10% lower than its marked price. He then 
sold 50% of the articles at a price 10% above 
the marked price. After this he sold the next 
25% articles at a price which was 20% lower 
than the marked price. If Ramesh wants to earn 
a profit of 10% in the entire transaction, then at 
what price should he sell the remaining 25% 
articles? 
(a) 4% above the marked price 
(b) 4% below the marked price 
(c) 6% above the marked price 
(d) 6% below the marked price 
 
40. A shopkeeper sells 1 kg rice to two customers 
Rani and Vani. For Rani he charges exactly the 
cost price but under weighs the quantity by 
10%. For Vani he sells at 20% more than the 
cost price but over weighs the quantity by 10%. 
What is his overall profit/ loss percentage? 
(a) 10% loss 
(b) 10% profit 
(c) 9.1% loss 
(d) 9.1% profit 
Directions for the following 3 (three) items: 
Read the following two passages and answer the items 
that follow each passage. Your answers to these items 
should be based on the passages only. 
Passage – 1 
Scientists might have a solution to growing concerns of 
climate change hampering crop productivity. 
Researchers have identified genes in Africa’s local food 
crops that can improve resistance to drought. 
Incorporating these genes through hybridisation might 
improve crop yield that is affected by increasing global 
temperatures and heatwaves. Countries like India and 
Pakistan are also likely to be affected by the prolonged 
heatwaves, the United Nations Environment 
Programme (UNEP) estimated. The UN body is 
responsible for coordinating responses to environmental 
issues. Orphan crops are nutritious local food crops that 
could play a crucial role in combating hunger. These 
crops are not traded internationally but have adapted 
themselves to grow in harsh weather conditions. 
Africa’s arid environment is not suited for crops like 
rice and maize. Orphan crops like finger millets, little 
millet, African yam bean, jojoba and jatropha are 
commonly found on the continent. 
41. Based on the above passage, the following 
assumptions have been made: 
1. Africa has the potential to fight hunger 
without dependence on other countries. 
2. UNEP should promote the trade of orphan 
crops from Africa to other hunger-affected 
continents. 
Which of the above assumptions is/are valid? 
(a) 1 only 
(b) 2 only 
(c) Both 1 and 2 
(d) Neither 1 nor 2 
 
 
 
 
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Passage – 2 
India would reduce fossil fuels, generate more 
renewable energy, reduce carbon emissions and 
intensity, and eventually become a net-zero emitter by 
2070. The goals are ambitious. They are built around 
the levers which, at the policy level, are most likely to 
create a positive impact on climate. Can policy 
initiatives alone fulfil India’s commitments toward 
arresting climate change? Actions that are driven top-
down, via government policy, no doubt set the stage for 
change. But unless people shift their attitude and 
behaviour in tune with the policy initiatives, change 
will not be able to retain its momentum. 
42. Based on the above passage, the following 
suggestions may be made: 
1. India, with the help of renewable energy, 
would be able to control carbon emissions 
completely by 2070. 
2. Government may involve citizens in 
policymaking and execution for achieving 
the target of net-zero emission. 
Which of the above suggestions is/are valid? 
(a) 1 only 
(b) 2 only 
(c) Both 1 and 2 
(d) Neither 1 nor 2 
 
43. What is the crucial message conveyed by the 
above passage? 
(a) Climate change cannot be reversed only 
with the commitments of India. 
(b) Climate change is a global issue, and 
people across countries must change their 
attitude towards it. 
(c) Indian government should consult 
specialised global agencies in the 
formulation of climate change policy. 
(d) Policy framework along with targets should 
prescribe citizens' behaviour for 
contributing to meeting net-zero emission 
targets by 2070. 
 
44. There is a circle of radius 5 cm that 
circumscribes a quadrilateral. It is further 
known that 2 of the adjacent sides of the 
quadrilateral are 6 cm and 8 cm. Determine the 
maximum possible area of the quadrilateral. 
(a) 38 cm2 
(b) 52 cm2 
(c) 64 cm2 
(d) 49 cm2 
 
45.In a polygon, all the interior angles are either 
90 degrees or 270 degrees. If the number of 
interior angles which are 90 degrees is 31, find 
the number of angles which are 270 degrees? 
(a) 31 
(b) 35 
(c) 27 
(d) Cannot be determined 
 
46. In a school, 90% of the students faced problems 
in Mathematics, 80% of the students faced 
problems in Computers, 75% of the students 
faced problems in Sciences, and 70% of the 
students faced problems in Social Sciences. 
Find the minimum possible percent of the 
students who faced problems in all the four 
subjects. 
(a) 15% 
(b) 25% 
(c) 26% 
(d) 32% 
 
 
 
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47. If two letters are taken at random from the 
word HOME, what is the probability that none 
of the letters would be vowels? 
(a) 1/6 
(b) 1/2 
(c) 1/3 
(d) 1/4 
 
Direction for the following 2 (two) items. 
Study the table given below carefully and answer the 
questions that follow. 
The following table gives the percentage distribution of 
population of five states, P, Q, R, S and T on the basis 
of poverty line and also on the basis of gender. 
State Percentage of 
Population 
below the 
Poverty Line 
Proportion of Males and Females 
Below poverty 
line 
Above 
Poverty Line 
M F M F 
P 35 5 6 6 7 
Q 25 3 5 4 5 
R 24 1 2 2 3 
S 19 3 2 4 3 
T 15 5 3 3 2 
48. If the male population above poverty line for 
State R is 1.9 million, then the total population 
of State R is 
(a) 4.5 million 
(b) 4.85 million 
(c) 5.35 million 
(d) 6.25 million 
 
49. What will be the number of females above the 
poverty line in the State S if it is known that the 
population of State S is 7 million? 
(a) 3 million 
(b) 2.43 million 
(c) 1.33 million 
(d) 5.7 million 
50. P is a prime number > 71. If N = (P + 2) 
(P − 1)(P + 1)(P − 2), then which of the 
following will definitely divide N for all the 
values of P? 
(1) 120 
(2) 240 
(3) 360 
(4) 480 
(a) 1 and 2 only 
(b) 1 and 3 only 
(c) 2 and 4 only 
(d) 1, 2 and 3 only 
 
Directions for the following 3 (three) items: 
Read the following two passages and answer the items 
that follow each passage. Your answers to these items 
should be based on the passages only. 
Passage – 1 
India which will soon have twice the number of Internet 
users as the U.S. is a large market for all kinds of new 
technologies. While this presents a huge opportunity, 
the domestic industry has not yet managed to derive the 
benefits. For instance, the country is operating far 
below its potential in electronic manufacturing. 
Electronic goods and components are the second largest 
item, after oil, in India’s import bill. Also, the country’s 
imports are almost five times its exports in this industry 
(based on 2020-21 data). High-value electronic 
components needed in the manufacture of, say, mobile 
phones are technology and design-intensive. Big 
multinational companies control these technologies and 
corner the bulk of the revenues. China has used its large 
market size as a bargaining chip in negotiations with 
foreign firms: stay in our markets only if you localize 
production and share technologies with the local firms. 
 
 
 
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51. Based on the above passage, the following 
assumptions and suggestions have been made: 
1. Indians have a high rate of consumption of 
electronics. 
2. India may use its large market size as a 
bargaining chip for the promotion of its 
electronics industry. 
Which of the above assumptions and 
suggestions is/are valid? 
(a) 1 only 
(b) 2 only 
(c) 1 and 2 
(d) None 
 
52. Which one of the following statements best 
reflects the crux of the passage? 
(a) Union government should trade with the 
USA not only in products but also in 
services like technology. 
(b) Domestic companies should invest in 
human resources to excel in the 
technologies of the electronic industry. 
(c) Despite a large user base, India is not able 
to scale electronics production due to 
technological limitations. 
(d) Big multinational companies should shift 
their manufacturing base from China to 
India. 
Passage – 2 
While governance is often equated with government, it 
involves much more. Governance occurs at all levels 
and encompasses the ways that formal government, 
non-governmental groups, community organizations 
and the private sector manage resources and affairs. 
Three factors that largely determine the efficacy of any 
system of governance are the quality of leadership, the 
characteristics of the governed, and the nature of the 
structures and processes employed to exercise authority 
and meet human needs. The capacity of any institution 
to effect and manage change, and to respond creatively 
to challenges that lie before it, increases with the 
development of several critical skills. These include the 
ability to maintain a clear perception of social reality 
and the forces operating in it; to properly assess the 
resources of the community; and to implement 
decisions with an openness and flexibility that avoid all 
traces of dictatorial behaviour, among others. This 
constellation of skills must draw on both intellectual 
and moral resources. 
53. Based on the above passage, the following 
assumptions have been made: 
1. Not only the government but citizens are 
also responsible for governance outcomes. 
2. Rigid and closed implementation of 
decisions reduces the capacity of governing 
institutions. 
Which of the above assumptions is/are valid? 
(a) 1 only 
(b) 2 only 
(c) 1 and 2 
(d) None 
 
 
 
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54. A super lotto has all the two-digit numbers 
written on various balls, which have been kept 
in a bag. Number on each ball is different. If 
two balls are chosen at random without 
replacement, then what is the probability that 
their numbers have the same units digit and the 
product of these numbers also has the same 
units digit? 
(a) 2/5 
(b) 2/25 
(c) 1/25 
(d) None of the above 
 
55. There are 100 people in a group. Each person, 
while working individually, can complete a 
piece of work in 100 days. One person starts 
working on the project. On the second day, 
another person joins him, on the third day, one 
more person joins the first two and this process 
goes on till the work is completed. On which 
day will the work get completed? 
(a) 13th day 
(b) 14th day 
(c) 12th day 
(d) 15th day 
 
56. If x + y = 36, then which of the following must 
be true? 
1. Both x and y must be positive. 
2. If x is positive, y must be negative. 
3. If x is negative, y must be positive. 
Select the correct answer using the code given 
below. 
(a) 1 only 
(b) 3 only 
(c) 2 only 
(d) Neither 1 nor 2 nor 3 
 
57. From the first 25 natural numbers, how many 
arithmetic progressions (APs) of 6 terms can be 
formed such that the common difference of the 
AP is a factor of the 6th term? 
(a) 31 
(b) 32 
(c) 30 
(d) 28 
 
58. The ratio of incomes of Anil and Ajit is 5:7. 
The ratio of their expenditures is 3:4. Which of 
the following is a possible ratio of their 
savings? (Savings = Income - Expenditure) 
(a) 4:5 
(b) 3:4 
(c) 1:1 
(d) 12:17 
 
59. 29 paintings are displayed in an art exhibition, 
which are made by using eitheroil colours or 
water colours or both. Oil and water colours 
have been used in making 16 and 19 of these 
paintings respectively. What is the number of 
paintings in which both types of colours have 
been used? 
(a) 5 
(b) 6 
(c) 3 
(d) 8 
 
60. How many pairs of integers exist such that the 
difference between their product and sum is 
72? 
(a) 6 
(b) 4 
(c) 2 
(d) 13 
 
 
 
 
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Directions for the following 3 (three) items: 
Read the following three passages and answer the items 
that follow each passage. Your answers to these items 
should be based on the passages only. 
Passage – 1 
The ignorance of class differences that are necessitated 
in democracy’s pursuit of equality makes it vulnerable 
to class conflict. By institutionalizing class disparities 
into a balanced representative structure, republicanism 
attempts to preserve order between distinctive 
subdivisions of society. Also, the pursuit of complete 
‘negative liberty’ in pure democracies is susceptible to 
anarchic disorder, as it disregards the law. The 
responsibility to uphold the law, typically maintained in 
the form of a constitution, by both the government and 
the individual is essential in a republic for the 
preservation of societal order. 
61. Which one of the following statements best 
reflects the crux of the passage? 
(a) Limitations of democracy regarding social 
order can be handled through the 
constitution. 
(b) Democracy due to inherent flaws is not the 
best political model for governance. 
(c) Only governments following a constitution 
can guarantee the preservation of social 
order. 
(d) The pursuit of equality in a democracy is 
the bedrock for preventing class conflicts. 
Passage – 2 
Hyperconsumption is a curse of our modern times. 
Humans generate monumental amounts of waste, a 
sizeable portion of which is disposed of in landfills and 
through waste-to-energy incinerators. However, billions 
of tonnes of garbage, including microplastics, never 
make it to landfills or incinerators and end up in the 
oceans. This garbage chokes marine life and disturbs 
zooplankton, which is vital to the elimination of carbon 
dioxide from the atmosphere. In India, nearly 60% of 
the household waste is wet organic waste, with low 
calorific value. This makes options such as waste-to-
energy incinerators inefficient. 
62. Which one of the following statements best 
reflects the crux of the passage? 
(a) Incineration is not the best technological 
solution for waste processing in India. 
(b) Reducing consumption will solve the issue 
of waste generation. 
(c) Incinerators shall be established in and 
around the landfills for faster processing of 
waste. 
(d) India should develop customized 
incinerators to ensure the processing of 
organic waste. 
Passage – 3 
Especially in the last century, most Western countries 
have experienced significant demographic changes with 
a continuing increase in the number of older people 
who face medical and functional challenges, as well as 
diseases that are age-specific but have often originated 
in people’s younger years. Most of these diseases 
including obesity, cardiovascular heart diseases (CHD) 
or type 2 diabetes mellitus are caused by civilisation. 
Most NCDs primarily result from unhealthy lifestyles 
including the consumption of too much or unhealthy 
food, too much alcohol and excessive smoking habits, 
combined with physical inactivity. More specifically, 
inactivity and unhealthy eating habits are associated 
with weight gain. Overweight and obesity are the major 
underlying causes of modern diseases such as CHD or 
type 2 diabetes mellitus. 
 
 
 
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63. Which one of the following statements best 
reflects the practical implication of the 
passage? 
(a) Prevention of NCDs can be done through 
physical activity and making healthy food 
choices. 
(b) Indians should learn from western countries 
about the importance of physical activity 
for good health. 
(c) Due to physical inactivity, any kind of non-
communicable disease can develop at any 
age of life. 
(d) Unhealthy food, alcohol, and smoking 
causes CHD or type 2 diabetes mellitus. 
 
64. Two statements S1 and S2 are given below 
followed by a question. 
S1: Price of mixture A is Rs. 40 per litre and 
price of mixture of B is Rs. 32 per litre. 
S2: Price of mixture C is Rs. 50 per litre. 
There are three different mixtures of milk and 
water—mixture A, mixture B, and mixture C. 
In what ratio should mixtures A and B be 
mixed with mixture C to get the average price 
Rs. 35 per litre? 
(a) S1 alone is sufficient to answer the 
Question. 
(b) S2 alone is sufficient to answer the 
Question. 
(c) Either S1 alone or S2 alone is sufficient to 
answer the question. 
(d) S1 and S2 together are NOT sufficient to 
answer the question. 
 
65. If we have two different prime numbers x and 
y, both greater than 2, then which of the 
following must be true? 
(a) x − y = 23 
(b) x + y ≠ 87 
(c) Both (a) and (b) 
(d) None of these 
 
66. Two statements S1 and S2 are given below 
with regard to two numbers followed by 
question. 
S1: a > b3 
S2: a > b6 
Question: If the product of a and b is a positive 
number, is (a + b) > 0? 
Which one of the following is correct in respect 
of the Statements and the Question? 
(a) S1 alone is sufficient to answer the 
Question. 
(b) S2 alone is sufficient to answer the 
Question. 
(c) Either S1 alone or S2 alone is sufficient to 
answer the question. 
(d) S1 and S2 together are sufficient to answer 
the question. 
 
67. How many distinct natural numbers 'n' are there 
such that, amongst all its divisors, greater than 
1 and less than 'n', the largest divisor is 21 
times the smallest divisor? 
(a) 0 
(b) 1 
(c) 2 
(d) Infinite 
 
68. It takes 10 men and 20 women to complete a 
project in 48 days. After the first day, a woman 
was replaced by a man and it took them 45 
more days to complete the work. If 10 men and 
20 women had worked on the same project, and 
after 2 days, if 2 of the women had been 
replaced by 2 men, how many more days would 
it have taken to finish the project? (Round up to 
the nearest integer) 
(a) 43 
(b) 44 
(c) 40 
(d) 42 
 
 
 
 
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69. A certain number of people take 40 hours to 
process a fixed quantity of a substance. The 
substance is priced at Rs x per unit which is 
determined by the labour costs and other 
costs. After a new technology is developed, the 
same number of people take 20 hours to 
process the same amount of the substance. If 
the cost of technology is negligible, how much 
would the new price of the processed substance 
per unit quantity be? (Assume that the other 
costs remain the same.) 
(a) > x 
(b) < x/2 
(c) x/2 
(d) > x/2 
 
70. The cost of 4 pencils, 2 erasers and a sharpener 
together is Rs. 80, whereas the cost of 1 pencil, 
2 erasers and a sharpener together is Rs. 35. 
Find the combined cost of 2 pencils, 2 erasers 
and 1 sharpener. 
(a) Rs. 60 
(b) Rs. 50 
(c) Rs. 40 
(d) Cannot be determined 
 
Directions for the following 4 (four) items: 
Read the following three passages and answer the items 
that follow eachpassage. Your answers to these items 
should be based on the passages only. 
Passage – 1 
India’s structural transformation, particularly since 
1991, has been slow and unique. Despite abundant low-
skilled labour, our growth trajectory has mostly skipped 
manufacturing, growing instead on the back of a far 
smaller, high-skilled services sector. Consequently, the 
bulk of jobs our economy generated even in its peak 
growth years was in the largely informal, low-value add 
construction sector. The distributional consequences of 
this have been significant. Under-employment and low 
inter-generational mobility have been persistent 
features of the Indian economy resulting in deep 
inequalities. Most of India continues to live in 
extremely precarious economic conditions with limited 
opportunity. Growth lifted a large population out of 
poverty. However, as the World Bank data show, most 
of those (40 per cent of the population) who escaped 
poverty between 2005-2012 moved into what they call 
the vulnerable group — one income shock away from 
falling below the poverty line. 
71. Based on the above passage, the following 
assumptions have been made: 
1. Availability of low skilled labor may 
promote the development of manufacturing 
sector. 
2. Service sector can thrive even on a small 
workforce. 
3. The peak growth year of 2005-2012 helped 
the service sector grow faster. 
Which of the above assumptions is/are valid? 
(a) 1 and 2 only 
(b) 2 and 3 only 
(c) 1 and 3 only 
(d) 1, 2 and 3 
 
 
 
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72. According to the passage given above, India’s 
unique structural transformation has led to 
which of the following? 
1. A category of people just outside the 
bounds of poverty. 
2. Decline in the share of agriculture in the 
overall economic growth. 
Select the correct answer using the code given 
below. 
(a) 1 only 
(b) 2 only 
(c) Both 1 and 2 
(d) Neither 1 nor 2 
Passage – 2 
The debate around how the matters of the ‘mind’ are 
associated with the male and the ‘body’ invariably 
linked to the woman is not new. And of course, the 
mind is superior to the body. In this regard, the feminist 
critique of French philosopher René Descartes’s 
Cartesian duality is an important intervention. The 
mind-body dualism has led to gender inequality by 
privileging the ‘rational’ mind over the ‘irrational’ or 
emotional body. Women’s voices have been suppressed 
and their silence has been treated as ‘golden’. What we 
need to understand, and question is the politics behind 
recognizing the domain of intellect as essentially a male 
prerogative. 
73. Which of the following is/are the most rational 
and logical Inference/Inferences that can be 
made from the passage? 
1. Women should be treated equally with men 
even in aspects of intellect. 
2. Descartes may be said to be responsible for 
gender inequality in society to some extent. 
3. Gender equality cannot be achieved 
without social change. 
Select the correct answer from the code given 
below: 
(a) 1 and 2 only 
(b) 2 only 
(c) None of the above 
(d) 1, 2 and 3 
 
Passage – 3 
Education is a journey, which gives the art of living, not 
just the livelihood. It makes us learn how to nurture our 
life and be more creative. Education makes us 
understand our conflicts. Thus, education is not merely 
learning facts but is training our minds to think. 
Education systems must provide opportunities to every 
individual to learn through experience and should help 
to develop critical thinking and problem-solving skills. 
However, in India, the education system has evolved in 
a completely different manner. Instead of focusing on 
critical thinking, expressing new ideas and debating and 
writing critically on any issue, our students are forced 
to learn through the rote route. 
74. Which of the following is/are the most rational 
and logical Inference/Inferences that can be 
made from the passage? 
1. Indians cannot think critically and be 
creative. 
2. One way to improve the outcome of 
education is to include learning by 
experience and reduce rote learning. 
Select the correct answer using the code given 
below: 
(a) 1 only 
(b) 2 only 
(c) Both 1 and 2 
(d) Neither 1 nor 2 
 
75. In a class consisting of 150 students, one more 
student is added and as a result the average 
weight of class increases by 0.05 units. 
Thereafter, from this class one student is taken 
out and the average weight of the class is 
reduced by 0.02 units. If the sum of the weights 
of the two students mentioned is 2x+b, where x 
is the original average weight of the class of 
150 students, then find the value of b. 
(a) 7.50 
(b) 3.05 
(c) 10.60 
(d) 11.10 
 
 
 
 
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76. A, B and C are 3 varieties of beer which 
contain starch, hops and water in varying 
proportions. A contains x% starch and y% 
hops. B contains y% starch and y% water. C 
contains x% hops and y% water. When A, B 
and C are mixed in the ratio 2:3:5, the final 
mixture has 38% starch and 28% hops. Find the 
sum of x and y. 
(a) 50 
(b) 26 
(c) 13 
(d) 65 
 
77. A cricket team of 11 is to be selected from 7 
batsmen and 6 bowlers which are available. 
The team must have at least 5 bowlers. In how 
many ways can it be done? 
(a) 21 
(b) 42 
(c) 84 
(d) 63 
 
Directions for the following 2 (two) items: 
The following graph shows the percentage share of 
small, medium and large establishments in total 
employment provided by manufacturing sector. Study 
the graph carefully and answer the items that follow. 
 
78. In 1981 and 1987, 50 million and 60 million 
people were employed in manufacturing sector 
respectively. What was the difference between 
the number of employees employed in small 
establishments in 1981 and 1987? 
(a) 8 million 
(b) 12 million 
(c) 6 million 
(d) 4 million 
 
79. In 1996 there were a total of 100,000 
employees in manufacturing sector and 750 
medium establishments. What was the average 
number of employed persons per medium 
establishment unit in that year? 
(a) 100 
(b) 75 
(c) 125 
(d) 1000 
 
80. A book contains 57 stories, each with fewer 
than 58 pages. The first story starts on the 2nd 
page and each story thereafter, starts on a fresh 
page. What is the largest possible number of 
stories than can begin on an odd numbered 
page? 
(a) 29 
(b) 56 
(c) 55 
(d) 28 
0
10
20
30
40
50
60
70
80
Percentage share of small, medium 
and large establishments in jobs in 
manufacturing sector 
Small establishments Medium establishments
Large establishments
 
 
 
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ANSWERS & EXPLANATION 
APTITUDE TEST–Test (4021) – 2023 
 
 
1.(a) 
Whatever sign we put between two odd numbers, resultant of 50 odd numbers = Even 
Hence, Anurag will win. 
Hence, option (a) is correct. 
 
2.(d) 
Using S1 alone: 
Unit digit of 9x is 1. 
x can be 9 or 19 or 29, …. So, remainder obtained when x is divided by 4 can be 1 or 3. 
Hence S1 alone is NOT sufficient. 
Using S2 alone: 
x is a natural number. 
Value of x can be any natural number. As a result, remainder obtained when x is divided by 4 will NOT 
have a unique value. Hence S2 alone is NOT sufficient. 
Both statements togetherare not sufficient either. 
Hence, option (d) is correct. 
 
3.(c) 
Zinc present in 5 tonnes of Ironite = 0.5 tonnes and 
Iron present in 5 tonnes of Ironite = 4.5 tonnes. 
Since the ratio given in ore is 3:2, the weight of iron = 3x and the weight of zinc = 2x 
Some zinc is lost, but the amount of iron will remain the same in both. 
Hence, 4.5 = 3x 
or x = 1.5 
Total weight = 3x + 2x = 5x = 5 × 1.5 = 7.5 tonnes 
Thus, 7.5 tonnes of ore is needed to produce 5 tonnes of Ironite. 
Hence, option (c) is correct. 
 
4.(b) 
Given equation: 
(3/a) + (2/b) = 1/18 
The given equation can be rewritten as 3b + 2a = (ab/18) 
Or 54b + 36a = ab 
Or ab - 36a - 54b = 0 
In order to factorize, we add 36×54 = 1944 to both sides. 
ab - 36a - 54b + 1944 = 1944 
Or a(b – 36) – 54(b – 36) = 1944 
Or (a - 54) (b - 36) = 1944. 
This equation can be written as (a - 54) (b - 36) = 1944 = 2
3
×3
5
 
For 17 < a < 67, the following ordered pairs satisfy the given equation.: 
(55, 1980), (56, 1008), (57, 684), (58, 522), (60, 360), (62, 279), (63, 252), (66, 198), i.e., 8 pairs. 
Hence, option (b) is correct. 
 
 
 
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5.(a) 
Here, when the ball is dropped, it bounces back to 3/4 of the height it was dropped from, and then falls 
again. So, in other words it covers 3/4 of its original drop-height 2 times - going up and then down. The 
same will happen every time. 
Initial height is 30 m and in each bounce, it rebounds to 3/4
th
 of the distance it fell. 
After the first bounce, the height reached is (3/4)×(30). 
After the second bounce, the height reached = (3/4)×[(3/4)×(30)] = 30×(3/4)
2
 
After the third bounce, the height reached = (3/4)×[(3/4)×(3/4)×(30)] = 30×(3/4)
3
 
So, Total distance travelled = 30 + 2×(30)×(3/4) + 2×30×(3/4)
2
 + 2×30×(3/4)
3
 + …….. 
= 30 + 2 × [(30)×(3/4) +(30)× (3/4)
2
 + (30)×(3/4)
3
 + ……..] 
The given series is in the form of a geometric progression. 
 
So, total distance covered = Distance travelled first time + 2 × {a ÷ (1 - r)} 
Here a = 30×(3/4), common ratio (r) = 3/4 
So, total distance covered = 30 + 2 × [30×(3/4)/[(1 – 3/4)] = 30 + 2 × [30×(3/4)×4] = 30 + 180 = 210 m 
 
6.(c) 
Inside dimensions of cube are as follows: 
Length = 21 - 2 × 0.5 = 20 cm 
Width = 11 - 2 × 0.5 = 10 cm 
Height = 6 – 0.5 = 5.5 cm (as top is open) 
So total painted area = 2 (20 × 5.5) + 2 (10 × 5.5) + (10 × 20) 
= 220 + 110 + 200 
= 530 cm
2
 
Cost of painting 530 cm
2
 is Rs. 70 
So, cost per cm
2
 = 70/530 = 0.1 
 
7.(d) 
Using both the statements individually, we can't solve for the ages of A and B. 
However, using both the statements together, we can conclude that A = B and the required number is both 
a perfect square and a perfect cube. 
So, A = B = x
6
 for some x. 
Only 64 satisfies this condition for x = 2. 
So, we can answer the question using both the Statements together, but not by using any of the two 
statements individually. 
Hence, option (d) is correct. 
 
8.(c) 
Assumption 1 is incorrect. The statement mentions arresting climate change with the help of funding and 
adaptation mechanisms. However, the lines “Drastic reduction of carbon emissions is only one pillar in 
the fight against climate change. Many of its consequences can no longer be stopped”, show that climate 
change has, now, reached a point where it cannot be arrested or stopped. Therefore, it is an incorrect 
assumption. 
Assumption 2 is incorrect. The only line regarding countries from the global south is “Countries in the 
Global South are particularly hard hit, even though their citizens have been emitting the least CO2.” It 
shows that they too have been emitting carbon dioxide. “Least amount” is only a relative connotation and 
can be very high in absolute terms. Therefore, we cannot assume that they are not responsible for climate 
change. As per the passage, certainly, the major emissions have been from rich countries, but the 
assumption mentioned completely absolves the countries from the global south, which is incorrect. 
Assumption 3 is incorrect. The statement is beyond the scope of the passage because the passage does 
not discuss the role of the UN in making rich countries accountable for the failed promise of funding for 
addressing the impacts of climate change. Thus, it is an incorrect assumption. 
 
 
 
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9.(d) 
Option (a) is incorrect. This option is not correct because the line “Drastic reduction of carbon 
emissions is only one pillar in the fight against climate change”, reflects that we have reached a point 
where only controlling carbon emissions will not address the adverse impacts of climate change. Rather, 
focussing on “adaptation measures” needs focus, “so people both in cities and in rural areas have the 
chance to cope with the effects of climate change.” 
Option (b) is incorrect. This option seems to be correct, but it is not the crucial message because the core 
theme of the passage is not about making the rich countries accountable, but that climate change is 
irreversible and needs the world population to urgently adapt to it. 
Also, as the rich countries have not fulfilled their promise of funding $100 billion, this option could be a 
rational implication but not a crucial message. 
Option (c) is incorrect. The given option is very broad but beyond the scope of the passage, as it is not 
inspired by the information given in the passage. The passage does not discuss climate change threatening 
the very existence of human life. Therefore, this cannot be the crucial message of the passage. 
Option (d) is correct. This option captures the real essence of the passage. The lines “Many of its 
consequences can no longer be stopped. There is an urgent need for adaptation measures so people both 
in cities and in rural areas have the chance to cope with the effects of climate change” reflect that climate 
change cannot be reversed and that adaptation is a must for coping with climate change. Therefore, the 
message in this option is the crucial message of the passage. 
 
10.(b) 
Assumption 1 is incorrect. The statement is beyond the scope of the passage because the passage does 
not mention or discuss anything regarding income or increased incomes. So, this is not a correct 
assumption. The passage instead discusses the increased opportunities for women in the globalised world. 
Assumption 2 is incorrect. The line “The expansion of the middle class is said to have occurred as a 
consequence of this process” reflects that there has been a considerable impact of globalization on the 
Indian middle class, but does not compare it with middle classes of other countries. Also, the passage does 
not compare the impact of globalization on different classes in India. 
Assumption 3 is correct. This statement is correct because of the following lines from the passage, 
“Many scholars argue that globalization has been detrimental to women due to growing structural gender 
inequalities, but many respondents identify greater opportunities to challenge preexisting patriarchal 
norms through the role models available in the globalized media”. These lines represent two contrasting 
opinions about the impact of globalization on women. Scholars say that it has been detrimental, but 
respondents say that it has benefitted as it provides opportunities to challenge the patriarchal norms. 
Therefore, it is correct to say that impact of globalization on women is not clear as per the information 
provided in the passage. 
 
11.(b) 
Assumption1 is incorrect. This assumption might be true in general, but is not based on the information 
given in the passage and is beyond the scope of the passage. The passage nowhere discusses cyber cafes 
or their impact on minimizing the digital divide. Hence, this assumption is not correct. 
Assumption 2 is correct. The lines “It is suggested that the digital divide may cause technological, 
immaterial, social, and educational types of inequality” and “Digital media usage is a strong predictor of 
political participation which implies that a digital divide may result in political alienation of those who 
lack digital media access” suggest that since digital divide causes technological inequality and results in 
political alienation, therefore, bridging it (the digital divide) will lead to technological and political 
empowerment. 
 
 
 
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12.(d) 
Statement 1 is incorrect. This is not a correct assumption because it is beyond the scope of the passage. 
The passage nowhere discusses the food security aspect of the future. 
Statement 2 is incorrect. This statement might seem to be a correct assumption. However, the lines 
“Invasive species may be one of the worst environmental problems facing the conservation of natural 
areas, because of their role in changing ecosystem function” suggest that invasive species change the 
ecosystem functioning and therefore are one of the worst environmental problems. However, this does not 
imply/ guarantee that natural areas can definitely be conserved by keeping a check on the invasive 
species. As the lines of the passage clearly suggest invasive species are probably “one of the worst 
environmental problems”, it implies that there are other causative factors degrading our environment, 
which could also be addressed in order to conserve natural areas. 
 
13.(c) 
Statement 1 is correct. The passage mentions, "But technology and its addiction among children are a 
hindrance in attaining high EQ level and this leads to many of them not being able to manage their 
emotions well”. This line confirms statement 1, that technology acts as a hindrance to the development of 
EQ in children. 
Statement 2 is correct. The passage mentions, “Relating to others and relationship management is an 
important element that nurtures a high EQ in an individual. But technology and its addiction among 
children are a hindrance in attaining high EQ level and this leads to many of them not being able to 
manage their emotions well". This line also is in line with the given option statement that human relations 
have a positive effect on EQ as compared to technology. So, this is the correct assumption. 
 
14.(d) 
Prime numbers: A prime number is a positive integer which has no factors other than 1 and itself. The 
first few prime numbers are 2, 3, 5, 7, 11, 13, 17 … 
Therefore, 2 is the only even prime number. 
Now, 46 = 23 × 2; 91 = 13 × 7; 143 = 13 × 11; 153 = 17 × 9 
9 is not a prime number. 
Hence, option (d) is correct. 
 
15.(a) 
Let the length of AB be 100 metres. 
Ajay and Vijay are running towards each other at the same speed from points A and B respectively. After 
running for some time, Ajay sprains his ankle at point C and walks at half his earlier speed. 
Suppose by the time Ajay reaches C, Vijay reaches E and let AC = X. 
Thus BE must also be equal to X, as speed of Ajay and Vijay was the same during that interval. 
Let, CD = Y 
Thus, ED = 2Y as the speed of Vijay from E to D is twice that of Ajay's from C to D. 
Hence, Total distance, AB = AC + CD + DE + BE = X + Y + 2Y + X = 2X + 3Y = 100 ……… (i) and 
Now, AD = (4/10) AB = (4/10) × 100 = 40 m 
AD = AC + CD = X + Y = 40 …………… (ii) 
Equation (i) – 2 × equation (ii), we get: 
So, X = 20 and Y = 20. 
Ratio AC/AD = X:(X + Y) = 20:(20 + 20) = 20:40 = 1:2 
Hence, option (a) is correct. 
 
16.(b) 
Volume of oil transported by rail = 12 × (9/100) = 1.08 million tonnes 
Cost incurred = 30 × (12/100) = 3.6 . 
Hence, required answer = 3.6/1.08 = Rs. 3.33 per ton 
 
 
 
 
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17.(a) 
Cheapest mode of transportation will be the one which will have the highest transport volume and 
comparatively lower cost. We can figure this out from the graphs. But let‟s calculate for the sake of solid 
proof. 
For Road, Cost = 6/22 
For Rail, Cost = 12/9 
For Pipeline, = 65/49 
For Ship, Cost = 10/9 
Lowest per ton cost is for road. 
 
18.(c) 
P = 10/9 
Q = 7/11 
R = 6/22 
We can see that P > Q > R. 
Hence option (c) is correct. 
 
19.(b) 
Ram and Shyam, who are standing 100 m away from each other, are throwing a Frisbee towards each 
other in a straight trajectory. The frisbee travels in the air until Ram and Shyam meet. 
Let‟s assume that the speeds of Ram and Shyam are a m/s and b m/s respectively. 
So, they will meet after [100/(a + b)] seconds. 
The frisbee travels throughout this time. The frisbee travelled a total distance of 12 km. They both throw 
the frisbee at a speed of 20 m/s. 
So, Distance travelled by Frisbee = Time × Speed = [100/(a + b)] × 20 = 12000 
or a + b = 1/6 m/s = 10 m/minute 
Speeds of Ram and Shyam are in the ratio of 2:3 respectively. 
So, a:b = 2:3 
Thus, a = 4 m/min and b = 6 m/min 
Hence, speed of Shyam is 6 m/min. 
Hence, option (b) is correct. 
 
20.(c) 
Let a = 10m + n 
So, b = 10n + m 
It is given that, a
2
 – b
2
 = k
2
 
So we have, (10m + n)
2
 – (10n + m)
2
 = k
2
 
or 100m
2
 + n
2
 + 20mn – (100n
2
 + m
2
 + 20mn) = k
2
 
or 99m
2
 – 99n
2
 = k
2
 
or 99(m + n)(m – n) = k
2 
or 11 × 9 × (m + n)(m – n) = k
2
 
9 is already a perfect square, so k
2
 can be of the form 99×11. 
So, k = 33 and (m + n)(m - n) = 11 
So, m = 6 and n = 5 
a = 10m + n = 10×6 + 5 = 65 
So, required numbers are 65 and 56. 
Hence, a + b + k = 65 + 56 + 33 = 154 
Hence, option (c) is correct. 
 
 
 
 
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21.(c) 
Statement 1 is correct. The lines “Crop pollination is commonly cited as an example of an endangered 
ecosystem service as detailed studies of the crop pollination systems are incomplete or out of date”, show 
that due to incomplete or out of date studies of crop pollination systems this ecosystem service is 
endangered. Therefore, the inference given in the statement is correct. 
Statement 2 is correct. The passage mentions “Animal pollination is important to the sexual 
reproduction of many crops and the majority of wild plants, which can also be important for providing 
calories and micronutrients for humans. Furthermore, the decline of pollinating species can lead to a 
parallel decline of plant species”. These lines show that pollination of plants has a direct bearing on 
human nutrition in terms of the calories and micronutrients available for human beings. If the pollinator 
species decline, it will also lead to a reduction in the number of plant species, which in turn provide 
nutrition to humans. Hence, this inference is correct. 
 
22.(b) 
Statement 1 is incorrect. The passage mentions, “…night time and overcast days can interrupt the 
supply”. This indicates that even tropical countries would need to develop storage of solar energy. 
Therefore, to infer that they are less dependent on storage will not be correct. 
Statement 2 is correct. The passage mentions “As the global capacity for solar power continuesto rise, 
nations like Japan and other global leaders in solar energy technology are focusing on developing 
adequate energy storage to deal with this issue”. This indicates that global leaders in solar energy 
technology have started investing in developing adequate energy storage. Therefore, we may infer that, in 
the future, the cost of storing solar power would probably decrease. 
 
23.(b) 
Option (a) is incorrect. This option is beyond the scope of the passage because there is no discussion on 
the supply chain of agricultural produce. So, it is not the central idea. 
Option (b) is correct. The lines “Farm automation technology addresses major issues like a rising global 
population, farm labour shortages, and changing consumer preferences. The benefits of automating 
traditional farming processes are monumental by tackling issues from consumer preferences, labour 
shortages, and the environmental footprint of farming”, show that technology will help address the social 
(rising global population), economic (farm labour shortages) and environmental issues. So, this captures 
the essence of the passage. 
Option (c) is incorrect. This statement, in general, would be correct but the passage does not mention 
India. So, to extrapolate the benefits of agricultural technology to India without any such clear indication 
in the passage would be incorrect. 
Option (d) is incorrect. This statement seems to be correct as it would increase the input cost due to the 
application of technology. However, this consequence of increased cost due to technology is not covered 
in the passage. So, this is not the correct central idea. 
 
24.(a) 
Answer can be verified by assuming the values x = 1, y = 3, z = 2. 
Let us verify the options: 
(a) Since, y is odd and (x – z) = -1, y(x − z)
2
 is also odd. 
Hence option (a) is not true. 
(b) Since y and (x − z) both are odd, y
2
(x − z) is odd. 
So, option (b) is true. 
(c) Since y and (x − z) both are odd, y(x − z) is odd. 
So, option (c) is true. 
(d) Since z and (x − y) both are even, z(x − y)
2
 is even. 
So, option (d) is true. 
Hence, option (a) is correct. 
 
 
 
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25.(d) 
Net summation from 1 to 30 = 465. So we are required to add some more numbers. 
Summation from 1 to 34 = 595. 
Hence, the missed out number = 595 − 575 = 20. 
Hence, option (d) is correct. 
 
26.(b) 
A number N gives a remainder of 7 when divided by D and a remainder of 20 when divided by 2D. 
N = DQ + 7 (where Q = Quotient, and D = Divisor) ………….(1) 
N = 2D × K + 20 (where K = Quotient and 2D = Divisor) ……………… (2) 
We can say that when N = 2D × K + 20 is divided by D, remainder obtained = 7. 
(2DK + 20)/D = (2DK/D) + (20/D) 
Remainder obtained from 2DK/D = 0. 
Hence, remainder obtained from 20/D = 7 
When 20 is divided by 13, then remainder will be 7. 
So, D = 13 
Now, 2N = 2 (DQ + 7) = 4DQ + 14. 
Remainder obtained from 2N/D = Remainder obtained from (4DQ + 14)/D = 14/D = 14/13 = 1. 
Hence, the remainder obtained will be 1. 
Hence, option (b) is correct. 
 
27.(b) 
If there are 22 students in the remedial class, then there will be at least four students with n marks each. 
Thus, the minimum number of students who should be sent to the remedial class is 22. 
Hence, option (b) is correct. 
 
28.(c) 
X and Y are multiples of 7 with X>Y>0. 
Let Y = 14 and X = 21 
Y = 2×7 and X = 3×7 
We will check each option one by one. 
Option (a): 
X
3
 – Y
3 
= 21
3
 – 14
3 
= (7×3)
3
 – (7×2)
3 
= 7
3
[3
3
 – 2
3
] 
It is divisible by 49. Hence, it is true. 
Option (b): 
HCF of X and Y = 7. Hence, it is true. 
Option (d): 
X
2
 – Y
2 
= 21
2
 – 14
2 
= (7×3)
2
 – (7×2)
2 
= 7
2
[3
2
 – 2
2
] 
It is divisible by 49. Hence, it is true. 
Option (c): 
LCM of X and Y = 7×2×3 = 42 
LCM of X and Y is a multiple of 7, but not necessarily a multiple of 49. 
Hence, it is not necessarily true. 
Hence, option (c) is correct. 
 
29.(b) 
Given that a six-digit number N is formed using the digits 0, 3, 6 and 9 only, and each of the digits is used 
at least once. 
The number is divisible by 18. Therefore, the number has to be divisible by both 2 and 9. 
Sum of the digits of the number should be divisible by 9, and the unit‟s digit of the number should be 
either 0 or 6. 
Smallest possible such number is 300096. 
Therefore, the digit at the ten‟s place is 9. 
Hence, option (b) is correct. 
 
 
 
 
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30.(c) 
Let the numerator of the fraction be x and the denominator be y. 
Hence, the original fraction = x/y 
New numerator = x + a% of x = x(100 + a)/100 
New denominator = y + b% of y = y(100 + b)/100 
Hence, new fraction = {x(100 + a)/100}/ {y(100 + b)/100} = (x/y){ (100 + a)/ (100 + b)} 
Ratio of original fraction to new fraction = (x/y) / [(x/y){ (100 + a)/ (100 + b)}] = (100 + b)/ (100 + a) 
Thus, the required ratio = (100 + b)/ (100 + a) 
Hence, option (c) is the correct answer. 
 
31.(b) 
Statement 1 is correct. The passage mentions, “With his unbounded greed, man has caused irreversible 
damage to the environment. Today, climate change is a global phenomenon.” Here the author highlights 
the issue of pollution which is damaging the environment and the reason behind climate change. 
Statement 2 is correct. The passage mentions, “Promotion of the mother tongue will revolutionize the 
educational landscape by making it more inclusive and equitable.” Here equitable education implies non-
discriminatory education. 
Statement 3 is incorrect. The passage mentions, “Rural India cannot be left behind in this mission. 
Improving rural infrastructure across the country must be fast-tracked and integrated into the larger 
development narrative.” It highlights the issue of rural infrastructure, however, it does not explicitly 
highlight the need for irrigation. 
Statement 4 is correct. The passage mentions, “Universal and affordable access to quality education and 
healthcare must be the focus of our attention.” It implies universal and affordable access to healthcare. 
Statement 5 is correct. The passage mentions, “Today, climate change is a global phenomenon. 
Conservation is our only hope for the survival of the planet.” It highlights the issue of the survival of the 
planet. If the survival of the planet is in danger, then it is an obvious threat to the survival of human 
beings. 
Statement 6 is correct. The passage mentions, “With his unbounded greed, man has caused irreversible 
damage to the environment.” It highlights the issue of human greed which shows his avariciousness 
nature. 
 
32.(b) 
Option (a) is incorrect. The passage highlights the issue of loneliness in the cities, but it nowhere 
prohibits living in cities. 
Option (b) is correct. The passage lists out issues of loneliness like people rarely talking to their 
neighbours; children do not play cricket; friends may not play together; and friends or relatives are not 
generally welcomed. We spend time on online studies or social media. Here, the author criticizes this life 
of cities and wants to convey the message of becoming a more socialized person. So, this option best 
reflects the suggestion conveyed by the passage. 
Option (c) is incorrect. The passage mentions, “…even if, paradoxically, the surfeit of lonely pursuits 
has reduced the quality of solitude.” Based on the passage, we cannot say that people are “Searching for 
loneliness” – it may be imposed based on the urban cultural setting. Also, this statement can be an 
inference but nota suggestion. 
Option (d) is incorrect. The passage mentions the problem of loneliness in the cities, so this statement is 
correct as the cities have become a ground for loneliness. But this is the problem cited by the author. 
While the demand of the question is the suggestion that author wants to convey. 
 
33.(c) 
Option (a) is incorrect. The passage talks about „rural‟ being always present in Hindi films, in the past. It 
nowhere says that now rural characters are not shown at all. 
Option (b) is incorrect. It is true that films affect society and vice versa. But, the existence of a split 
between rural and urban being a result of Hindi films ALONE is not conclusively proven in this passage. 
Option (c) is correct as the passage does talk about portrayal of „the rural‟ in Hindi films as good, and „the 
urban‟ as something evil. This is clear from the 3
rd
 sentence of the passage. 
Option (d) is incorrect due to option (b) being incorrect. 
 
 
 
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34.(a) 
π (r1
2
 + r2
2
) = 153 π 
Or (r1
2
 + r2
2
) = 153 
Or (r1 + r2)
2
 – 2r1r2 = 153 
Now, r1 + r2 = 15 
So, r1 r2 = 36 
On solving, we get: 
r1 = 12 
r2 = 3 
Required Ratio = 4 
 
35.(c) 
Let the cost of a caramel pop, a toffee bites and a mango pop be x, y and z respectively. 
Using S1: 
3x + 5y + 7z = 68 …………….(i) 
Using S2: 
2x + 3y + 4z = 41 ………….(ii) 
We cannot determine the answer from either of the two statements alone. 
Using both the statements: 
Multiplying equation (ii) by 2 and subtracting it by equation (i), we get: 
(4x + 6y + 8z) - (3x + 5y + 7z) = 2 × 41 – 68 = 14 
Or x + y + z = 14 
So, we can answer the question using both the Statements together, but not by using any of the two 
statements individually. 
Hence, option (c) is correct. 
 
36.(a) 
Percentage changes (rise/fall) in the production of Company Y in comparison to the previous year, for 
different years are: 
For 2007 = 
 
(35 - 25) 
x 100 
 
% = 40%. 
25 
For 2008 = 
 
(35 - 35) 
x 100 
 
% = 0%. 
35 
For 2009 = 
 
(40 - 35) 
x 100 
 
% = 14.29%. 
35 
For 2010 = 
 
(50 - 40) 
x 100 
 
% = 25%. 
40 
Hence, the maximum percentage rise/fall in the production of Company Y was in the year 2007. 
 
37.(c) 
Average production of Company X in the period 2008-2010 
 = 
 
1 
x (25 + 50 + 40) 
 
= 
 
115 
 
lakh tonnes. 
3 3 
Average production of Company Y in the period 2008-2010 
 = 
 
1 
x (35 + 40 + 50) 
 
= 
 
125 
 
lakh tonnes. 
3 3 
 
 Required ratio = 23:25 
 
 
 
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38.(d) 
Since value of a lies between – 6 and – 3, so value of a
2
 must lie between 36 and 9. 
And value of b lies between – 3 and 3, so value of b
2
 must lie between 9 and 0. 
To get the upper value of the required range, we will take maximum value of a and minimum value of b: 
a
2
 – b
2
 = 36 – 0 = 36 
To get the lower value of the required range, we will take minimum value of a and maximum value of b: 
a
2
 – b
2
 = 9 – 9 = 0 
∴ Value of (a
2
 – b
2
) will lie between 0 and 36. 
Hence, option (d) is correct. 
 
39.(b) 
Let‟s say that Ramesh bought 100 articles and marked price of each article is Rs. 10. 
So, total marked price = 100 × 10 = Rs. 1000 
But Ramesh got it for 10% less. So, the amount paid by Ramesh = 0.9 × 1000 = Rs. 900 
Now, Ramesh wants to earn a profit of 10%, so he must get 900 ×1.1 = Rs. 990 after selling the articles. 
Now, he sold 50% of the articles at a price 10% above the marked price. 
Thus, he sold first 50 articles for Rs. 11 each. So amount earned by him = 50 × 11 = Rs. 550 
After this he sold the next 25% articles at a price which was 20% lower than the marked price. 
Thus, he sold the next 25 articles at Rs. 8 each. So the amount earned by him by selling these articles = 25 
× 8 = Rs. 200 
So, total amount earned by him by selling 75articles = 550 + 200 = Rs. 750 
To earn a profit of 10% in the entire transaction, he needs to sell the remaining 25 articles at 990 – 750 = 
Rs. 240. 
So, selling price of each of the remaining articles = 240/25 = Rs. 9.6 
Marked price is less than the selling price by 10 – 9.6 = Rs. 0.4 
Required percentage = (0.4/10) × 100 = 4% 
Thus, remaining 25% articles must be sold at 4% below the marked price. 
Hence, option (b) is correct. 
 
40.(b) 
Let the cost price of 1 kg of rice be C. 
For Rani he sells at Rs. C but only sells 0.9 kg instead of 1 kg. 
For Vani he sells at Rs. 1.2C but sells 1.1 kg instead of 1 kg. 
Overall, he sold 2 kg rice and the cost price for it is Rs. 2C. 
His net revenue after both the transactions = C + 1.2C = Rs. 2.2C 
Profit = 2.2C – 2C = Rs. 0.2C 
Profit percentage = (0.2C /2C)× 100 = 10% profit 
Hence, option (b) is correct. 
 
41.(d) 
Statement 1 is incorrect. Refer to the lines “Orphan crops are nutritious local food crops that could play 
a crucial role in combating hunger. These crops are not traded internationally but have adapted 
themselves to grow in harsh weather conditions. Africa‟s arid environment is not suited for crops like rice 
and maize. Orphan crops like finger millets, little millet, African yam bean, jojoba and jatropha are 
commonly found on the continent.” This shows that orphan crops are nutritious and help in combating 
hunger, and they are not traded internationally. However, it does not mean that Africa is not dependent on 
any other country. The passage just lays down a few good aspects regarding resistance crops found in 
Africa. We cannot draw wide assumptions based on such a narrow premise. Thus, it is an incorrect 
assumption. 
Statement 2 is incorrect. The lines “Countries like India and Pakistan are also likely to be affected by 
the prolonged heatwaves, the United Nations Environment Programme (UNEP) estimated. The UN body 
is responsible for coordinating responses to environmental issues”, show that UNEP is responsible for 
environment-related issues. But to say that it should promote the trade of orphan crops from Africa to 
other hunger-struck countries would not be correct because the UNEP's limited role in the passage is not 
about promoting trade. The focus of the passage is more on adoption of drought-resistant genes, rather 
than on the trade of such crops. So, this option is not correct as an assumption. 
 
 
 
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42.(b) 
Statement 1 is incorrect. The statement mentions about completely controlling carbon emissions by 2070 
which is an extreme scenario. Net-zero emitter means that there would not be any addition of carbon 
emissions to the environment. The passage only talks about goals, but is rather shacky regarding their 
achievement. So, to say that with help of renewable energy carbon emissions can be completely controlled 
is saying too much too soon. Moreover, it‟s more in the nature of inference than a suggestion. Thus, it is 
an incorrect suggestion. 
Statement 2 is correct. The lines “But unless people shift their attitude and behaviour in tune with the 
policy initiatives, change will not be able to retain its momentum”, reflect that people at individual levels 
must change their behaviour and attitude (in line with the policy initiatives) towards climate change. The 
option however mentions about government involving citizens in policy formulation and execution, which 
may be a valid suggestion in line with the passage. So,this suggestion is correct. 
 
43.(d) 
Option (a) is incorrect. This option is beyond the scope of the passage because there is no information 
about other countries' contributions to climate change through their commitments. Although, the given 
statement is generally correct, to say that climate change cannot be controlled only with India‟s 
commitments is not the crucial message of the given passage. 
Option (b) is incorrect. This option is also a general option which seems to be correct, but it is not based 
on the information given in the passage. The passage is focused on India, its commitment and the need for 
policy and people‟s attitudes. Talking about global citizens would not be correct as it is not a part of the 
passage. Therefore, this is not the correct crucial message of the passage. 
Option (c) is incorrect. The given option is beyond the scope of the passage because there is no mention 
of any kind of support from specialised global agencies in the formulation of Indian policy for climate 
change. So, this is also not the crucial message. 
Option (d) is correct. This option captures the real essence of the passage. The lines “Actions that are 
driven top-down, via government policy, no doubt set the stage for change. But unless people shift their 
attitude and behaviour in tune with the policy initiatives, change will not be able to retain its 
momentum”. These lines reflect that only policy initiatives are not enough to maintain the momentum. 
The people should also change their attitude and behaviour towards climate change following the policy 
directives. Therefore, the message in this option is the crucial message of the passage. 
 
44.(d) 
There are two parts of the quadrilateral: the first one is a right-angled triangle with sides 6, 8 and 10; and 
another part is a isosceles triangle with the diameter of the circle as the base and radius as the height. 
Area of right-angled triangle = (1/2) × 8 × 6 = 24 cm
2
 
Area of isosceles triangle = (1/2) × 10 × 5 = 25 cm
2
 
So, Maximum possible area of the quadrilateral = 24 + 25 = 49 cm
2
 
 
Hence, option (d) is correct. 
 
 
 
 
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45.(c) 
Let the total number of angles of the polygon be n. 
Hence, the sum of the interior angles = 180 × (n - 2) 
We know that the number of angles which are 90 degrees is 31. 
Hence, the number of angles which are 270 degrees is (n – 31). 
Hence, the sum of the interior angles = 90 × 31 + 270 × (n - 31) = 180(n - 2). 
 Or, 90 × 31 + 270n – 270 × 31 = 180n - 360 
Or, 90n = 180 × 31 - 360 
Or, n = 2 × 31 - 4 = 58 
Hence, the number of angles which are 270 degrees = n – 31 = 58 - 31 = 27 
Hence, option (c) is correct. 
 
46.(a) 
We know that 30% of the students did not face problems in Social Sciences, 25% of the students did not 
face problems in Sciences, 20% students did not face problems in Computers and 10% students did not 
face problems in Mathematics. 
If each of these students were separate from each other, we would have 30 + 25 + 20 + 10 = 85% people 
who did not face a problem in at least one of the four subjects. 
Naturally, the remaining 15% would be the students who faced problems in all the four subjects. 
Thus, minimum possible percent of the students who faced problems in all the four subjects is 15%. 
Hence, option (a) is correct. 
 
47.(a) 
There are 4 letters in the word HOME, in which there are two vowels and 2 consonants. 
P(first letter is not vowel) = 2/4 
P(second letter is not vowel) = 1/3 
So, probability that none of letters would be vowels = (2/4) × (1/3) = 1/6 
Hence, option (a) is correct. 
 
48.(d) 
Let the total population of State R be x million. 
Then, population of State R above poverty line 
 = [(100 - 24)% of x] million 
 = 
 
76 
x x 
 
million 
100 
And so, male population of State R above poverty line 
 = 
 
2 
x 
 
76 
x x 
 
million 
5 100 
But, it is given that male population of State R above poverty line = 1.9 million. 
 
2 
x 
 
76 
x x 
 
= 1.9 x = 
5 x 100 x 1.9 
= 6.25. 
5 100 76 x 2 
 Total population of State R = 6.25 million. 
 
49.(b) 
Total population of State S = 7 million. 
 Population above poverty line 
 = [(100 - 19)% of 7] million 
 = (81% of 7) million 
 = 5.67 million. 
And so, the number of females above poverty line in State S 
 = 
 
3 
x 5.67 
 
million 
7 
 = 2.43 million. 
 
 
 
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50.(b) 
P is a prime number > 71, hence P is an odd number. 
(P − 1) and (P + 1) are two consecutive even natural numbers, hence, one of these two numbers will be 
divisible by 4 and other by 2. 
Also P will be of the format 6K ± 1, hence, one of (P − 1) or (P + 1) = 6K [if 6K + 1, then P − 1 = 6K and 
if 6K−1, then P + 1 = 6K]. 
Since we have already considered these two numbers to be even numbers, hence (P − 1)(P + 1) will be 
divisible by 24 (= 2 × 4 × 3)……….. (1) 
Now, as P is of the format 6K ± 1, so one of (P + 2) or (P - 2) will be a multiple of 3 ……….(2) 
Also, since P is an odd prime number, so unit digit of P = 1 or 3 or 7 or 9. 
If unit digit = 3 or 7, then one of (P − 2) or (P + 2) will be a multiple of 5. Or 
If unit digit = 1 or 9, then one of (P − 1) or (P + 1) will be a multiple of 5 
……………………………….(3) 
Combining (1), (2) and (3), N is a multiple of 24 × 3 × 5 = 360. 
Hence, N is definitely divisible by 120 and 360. It may or may not be divisible by 240. 
Hence, option (b) is correct. 
 
51.(c) 
Statement 1 is correct. The passage mentions “Electronic goods and components are the second largest 
item, after oil, in India‟s import bill”. So, it is correct to assume that the Indians consume a lot of 
electronic goods. 
Statement 2 is correct. The passage has made use of the China example to make this suggestion. 
 
52.(c) 
Option (a) is incorrect. The passage merely mentions “India which will soon have twice the number of 
Internet users as in the U.S. is a large market for all kinds of new technologies”. There is no information 
about any kind of electronics or technological services trade between the USA and India. Hence, this 
option is beyond the scope of the passage. So, this is not the crux of the passage. 
Option (b) is incorrect. This option is also not correct because there is no information about issues of 
human resources which hampers the functioning of domestic industry. Hence, it is not the crux of the 
passage. 
Option (c) is correct. The lines “India which will soon have twice the number of Internet users as in the 
U.S. is a large market for all kinds of new technologies”, “For instance, the country is operating far 
below its potential in electronic manufacturing” and “High-value electronic components needed in the 
manufacture of, say, mobile phones are technology and design-intensive. Big multinational companies 
control these technologies and corner the bulk of the revenues”, show that despite a large user base, 
India is not able to exploit the potential of the electronic industry which is mostly controlled by big 
multinational companies. Therefore, this is the crux of the passage. 
Option (d) is incorrect. The given option is beyond the scope of the passage because there is no 
discussion on the aspect of manufacturing bases of big multinational companies. Hence, this is not the 
crux of the passage. 
 
53.(c) 
Statement 1 is correct. Refer to the lines "Three factors that largely determine the efficacy of any system 
of governance are the quality of leadership, the characteristics of the governed, and the nature of thestructures and processes employed to exercise authority and meet human needs”. The characteristics of 
the governed is reflecting the citizens of the country. Thus, the given assumption in the statement is 
correct because governance depends on three factors: the quality of leadership, the characteristics of the 
governed, and the nature of the structures and processes employed to exercise authority and meet human 
needs. So, citizens are also responsible for efficient outcomes of governance. 
Statement 2 is correct. The passage mentions, “The capacity of any institution to effect and manage 
change, and to respond creatively to challenges that lie before it, increases the development of several 
critical skills. These include the ability to maintain a clear perception of social reality and the forces 
operating in it; to properly assess the resources of the community; and to implement decisions with an 
openness and flexibility that avoid all traces of dictatorial behaviour, among others". So, the capacity of 
the institution increases if the implementation of decisions is done with openness and flexibility. 
Therefore, it would be correct to say that capacity will reduce if the implementation is done in a rigid and 
closed manner. So, this is the correct assumption. 
 
 
 
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54.(d) 
Total number of balls = 90 
The numbers that give the same units digit on being squared are 0, 1, 5, 6. Hence the chance of getting 
such a number in units digit is 4/10 = 2/5. 
After the first ball is chosen, there would be 9 – 1 = 8 balls remaining with that unit digit (out of 89). 
Hence, the probability that the second number has the same units digit = 8/89 
Required probability = (2/5) × (8/89) = 16/445 
Hence, option (d) is correct. 
 
55.(b) 
Let the efficiency of each person be 1 unit of work per day. 
So, number of units of work to be done in total = 100 units 
Work done on the first day = 1 unit 
Work done on the second day = 2 units 
Work done on the third day = 3 units and so on 
Let the work be completed in „n‟ days 
Total Work = 1 + 2 + 3 +…+ n = n(n+1)/2 units 
So, n(n+1)/2 = 100 
or n(n+1) = 200 
or 14×15 ≥ 200 
So, minimum numerical value of n is 14 days. 
So, the work gets completed on the 14th day. 
Hence, option (b) is correct. 
 
56.(b) 
Given: x + y = 36 
Statement 1: Taking x = 37 and y = – 1 
x + y = 37 + (– 1) = 36 
Hence, statement 1 is not true because one of x or y can be negative. 
Statement 2: Taking x = 35 and y = 1 
x + y = 35 + 1 = 36 
Hence, statement 2 is not true because y can be positive even if x is positive. 
Statement 3: It must be true because y has to be positive if x is negative. Only then their summation can 
be positive. 
For example, taking x = – 12 and y = 48 
x + y = – 12 + 48 = 36 
Hence, option (b) is correct. 
 
57.(a) 
Let the first term of the AP be „a‟ and the common difference be „d‟. 
The sixth term of the series will be a + 5d. 
Given that, „d‟ should be a factor of „a + 5d‟. That is, a + 5d is divisible by d. 
So, a should be divisible by d. 
So the required cases are 
d = 1, a = 1, 2, 3.......20 → Number of cases = 20 
d = 2, a = 2, 4, 6.......14 → Number of cases = 7 
d = 3, a = 3, 6, 9 → Number of cases = 3 
d = 4, a = 4 → Number of case = 1 
So, the required number of AP‟s = 20 + 7 + 3 + 1 = 31. 
Hence, option (a) is correct. 
 
 
 
 
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58.(d) 
Ratio of incomes of Anil and Ajit is 5:7 and the ratio of their expenditures is 3:4. 
Let the incomes be 5k and 7k and expenditures be 3t and 4t. 
Savings = Income - Expenditure 
Ratio of savings = (5k-3t)/(7k-4t). 
Let us assume that (5k-3t)/(7k-4t) = 4/5 (Option a). 
25k - 15t = 28k -16t 
Or t = 3k. 
Now, substituting this relationship in the equation (5k-3t)/(7k-4t), we get -4k/-5k = 4/5. Though the 
overall ratio is 4/5, the numerator is -4k. Which means that, 3t > 5k in this case. Same is the case with 
denominator. However, we know that expenditure cannot be greater than income and therefore, we can 
eliminate this case. Checking similarly, we can eliminate options (b) and (c). 
Option (d): 
(5k - 3t)/(7k - 4t) = 12/17 
Or 85k - 51t = 84k - 48t 
Or k = 3t 
Substituting this relationship in (5k - 3t)/(7k - 4t), we get the ratio as 12t/17t. 
Both the numerator and denominator are positive and hence, option (d) is a possible solution. 
Hence, option (d) is correct. 
 
59.(b) 
Let the number of paintings in which both kind of colours have been used be x. With the help of Venn 
diagram, the given information can be represented as follows: 
 
So, (16 – x) + x + (19 – x) = 29 
or 35 – x = 29 
or x = 35 – 29 = 6 
Hence, number of paintings in which both type of colours have been used = 6 
Hence, option (b) is correct. 
 
60.(b) 
Let the two numbers be „a‟ and „b‟ respectively. 
There are 2 possibilities: 
Case 1: ab - a - b = 72 
or ab - a - b + 1 = 73 
or (a - 1)(b - 1) = 1 × 73 = (-1) × (-73) 
a = 2, b = 74 and a = 0, b = - 72 are the solutions. 
Case 2: a + b - ab = 72 
or ab - a - b + 1 = -71 
or (a - 1)(b - 1) = 1 × (-71) = (-1) × 71 
a = 2, b = -70 and a = 0 and b = 72 are the solutions. 
Thus, there are 4 pairs of such integers. 
 Hence, option (b) is correct. 
 
 
 
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61.(a) 
Option (a) is correct. The passage mentions, “The ignorance of class differences that are necessitated in 
democracy‟s pursuit of equality makes it vulnerable to the class conflict” and “The responsibility to 
uphold the law, typically maintained in the form of a constitution, by both the government and the 
individual is essential in a republic for the preservation of societal order”. These lines show that 
democracy has some limitations, but a constitution which helps the government and its citizens to uphold 
the law eventually helps in maintaining social order. So, this is the crux of the passage. 
Option (b) is incorrect. This option seems to be correct due to the following lines “The ignorance of 
class differences that are necessitated in democracy‟s pursuit of equality makes it vulnerable to class 
conflict. By institutionalizing class disparities into a balanced representative structure, republicanism 
attempts to preserve order between distinctive subdivisions of society. Also, the pursuit of complete 
„negative liberty‟ in pure democracies is susceptible to the anarchic disorder, as it disregards law”. 
However, there is no comparison of democracy as a governance model with any other model in the 
passage to conclude whether democracy is the best model or not. Hence, it is not the crux of the passage. 
Option (c) is incorrect. This option is beyond the scope of the passage because there is no information in 
the passage that only the governments following a constitution guarantees the preservation of social order. 
Therefore, this cannot be the crux of the passage. 
Option (d) is incorrect. The given option is contradictory to the lines of the passage “The ignorance of 
class differences that are necessitated in democracy‟s pursuit of equality makes it vulnerable to the class 
conflict” where the pursuit of equality is the reason for class conflicts. Hence, this is not the crux of the 
passage. 
 
62.(a) 
Option (a) is correct. The passage mentions “In India, nearly 60% of the household waste is wet organic 
waste, with lowcalorific value. This makes options such as waste-to-energy incinerators inefficient”. It 
reflects that incineration in India is not the best way to dispose of organic waste. So, this is the crux of the 
passage. 
Option (b) is incorrect. This option can be an inference but not the crux as it does not tell the main theme 
(Incineration of waste in India) of the passage. Reducing consumption can be a solution in general but that 
is not suggested in the passage. Hence, it is not the crux of the passage. 
Option (c) is incorrect. There is no discussion on the location of incinerators being done in the passage. 
So, this option is beyond the scope of the passage. Therefore, this cannot be the crux of the passage. 
Option (d) is incorrect. The given option could be a fair suggestion. However, the passage does not 
mention the development of customized incinerators. The crux is about the given information and not 
about possible implications from the given passage. Hence, this is not the crux of the passage. 
 
63.(a) 
Option (a) is correct. This is the correct option because it builds on the core idea of the passage. The 
lines “Most NCDs primarily result from unhealthy lifestyles including the consumption of too much or 
unhealthy food, too much alcohol and excessive smoking habits, combined with physical inactivity”, show 
that NCDs result from unhealthy lifestyles like physical inactivity and unhealthy food. So, prevention of 
NCDs can be done through physical activity and healthy food choices. 
Option (b) is incorrect. There is no lesson for India in the given passage because there is no data to 
reflect India‟s situation. Also, there is no discussion about India in the passage. 
Option (c) is incorrect. This statement is incorrect. The passage mentions, “Especially in the last century, 
most Western countries have experienced significant demographic changes with a continuing increase in 
the number of older people who face medical and functional challenges, as well as diseases that are age-
specific but have often originated in people‟s younger years”. It merely shows that some age-specific 
diseases can even develop early. So, the option is incorrect because it talks about the development of any 
kind of disease at any stage of life. 
Option (d) is incorrect. This statement is incorrect. The passage mentions, “More specifically, inactivity 
and unhealthy eating habits are associated with weight gain, overweight and obesity are the major 
underlying causes for modern diseases such as CHD or type 2 diabetes mellitus.” The option given could 
be correct in general, but the passage mentions that weight gain, overweight and obesity are the major 
causes of CHD, and diabetes and not unhealthy food, alcohol, or smoking. Moreover, this is just a fact 
stated in the passage; it cannot be called a practical implication. 
 
 
 
 
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64.(d) 
Using S1 alone: 
It does not provide the answer as the price of mixture C is not known. 
Using S2 alone: 
It does not provide the answer as the price of mixtures A and B are not known. 
Using S1 and S2 both: 
It can be observed that mixing A and B will get any price between Rs. 32 and Rs. 40. For example, Rs. 33 
per litre, or Rs. 34 per litre, or Rs. 35 per litre, etc. Mixing it with C will make the average price of the 
mixture as Rs. 35 per litre. But ratio of A : B : C in each of these mixtures will be different. 
Thus, S1 and S2 together are NOT sufficient to answer the question. 
Hence, option (d) is correct. 
 
65.(b) 
Prime numbers x and y are greater than 2, hence they must be odd. Difference of two odd numbers is 
even. So, option (a) is definitely false. 
The sum of two odd numbers is even. So, option (b) must be true. 
Hence, option (b) is correct. 
 
66.(b) 
If the product a and b is greater than 0, i.e. ab > 0, then both a and b must have the same sign. 
It means either a > 0, b > 0 OR a < 0, b < 0. 
Using S1 alone: 
a > b
3
 ⇒ a > b 
Now, there are two possibilities: 
Either (i) both a and b are positive. In that case, a + b > 0; 
(ii) Both a and b are negative. 
Assume a = −5 and b = −10. 
So, a + b = −15 < 0 
Hence, S1 alone is not sufficient. 
Using S2 alone: 
Given that a > b
6
 
So, b
6
 is positive and a is greater than it. So, a > 0 
It will be possible when both a and b will be positive, because their product is a positive number. 
So, a + b > 0. 
Hence, question can be answered by using S2 alone. 
Hence, option (b) is correct. 
 
67.(c) 
21 divides the number n. 
So, the smallest divisor of n is either 2 or 3 (as 3 divides 21) 
So, the largest divisor of n is either 21×2 = 42 or 21×3 = 63 
Hence, n = 84 (21×2 = 42) or n = 189 (21×3=63) 
So, number of possible values of n is 2. 
Hence, option (c) is correct. 
 
68.(a) 
Let the work done together by 10 men and 20 women in a day be W. 
10 men and 20 women together complete a project in 48 days. 
Total work = 48W 
After the first day, work remaining = 47W. 
Because of the replacement, let the additional work that can be done be D. 
So, 47W = 45(W + D) 
Or D = 2W/45 
Similarly, number of extra days needed in the second case = 46W/[W + 2D] = 46W/[W + 2 × (2W/45)] = 
42.2 
So, the number of extra days taken to finish the project will be 43 days (round up to the nearest integer). 
Hence, option (a) is correct. 
 
 
 
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69.(d) 
Cost price of the substance = x 
Assuming the number of quantity processed as y, the labour cost as L and the other cost as m. 
Cost price of the substance = (Labour cost + Other cost)/Quantity of the substance processed = x 
So, (L + m)/y = x 
Here, L = 40 hours 
or, a + b = x, (Assuming L/y = a and m/y = b) 
Since y and m remain the same. Only L is reduced to half (i.e. L becomes 20 from 40). 
Then, a/2 + b = a/2 + b/2 + b/2 = [(a + b)/2] + b/2 = x/2 + b/2 
From the above equation, it is clear that the new price of the processed substance per unit quantity will be 
greater than x/2. 
Hence, option (d) is correct. 
 
70.(b) 
Let the cost of a pencil, a eraser and a sharpener be a, b and c respectively. 
The cost of 4 pencils, 2 erasers and a sharpener together is Rs. 80. 
So, 4a + 2b + c = 80 ---(i) 
The cost of 1 pencil, 2 erasers and a sharpener together is Rs. 35. 
a +2b + c = 35 ---(ii) 
Subtracting equation (i) and (ii), we get: 
3a = 45 
or a = 15 
Now, the cost of 2 pencils, 2 erasers and 1 sharpener will be 2a + 2b + c. 
Adding “a” to equation (ii), we will get: 
a + a + 2b + c = 35 + 15 
or 2a + 2b + c = 50 
Thus, the combined cost of 2 pencils, 2 erasers and 1 sharpener is Rs. 50. 
Hence, option (b) is correct. 
 
71.(a) 
Assumption 1 is correct. The passage mentions, “Despite abundant low-skilled labour, our growth 
trajectory has mostly skipped manufacturing.” It clearly implies that availability of low-skilled labours 
would encourage the growth of manufacturing sector. 
Assumption 2 is correct. The passage mentions, “Growing instead on the back of a far smaller, high-
skilled services sector.” It implies that the service sector is thriving on a small workforce. 
Assumption 3 is incorrect. The passage mentions, “Growing instead on the back of a far smaller, high-
skilled services sector. Consequently, the bulk of jobs our economy generated even in its peak growth 
years was in the largely informal, low value add construction sector.” It implies that the economy post-
1991 is growing on the back of the service sector. But the passage does not mention the peak growth 
years, so we cannotassume whether it was the period from 2005-2012 or not. 
 
72.(a) 
Statement 1 is correct. The passage mentions, “However, as the World Bank data show, most of those 
(40 per cent of the population) who escaped poverty between 2005-2012 moved into what they call the 
vulnerable group — one income shock away from falling below the poverty line.” It implies that there is a 
group of people who are on the border of poverty line. These people are working in the informal, low-
value adding construction sector. So, any income shock can push them back into poverty. 
Statement 2 is incorrect. Although the lines, “Despite abundant low-skilled labour, our growth 
trajectory has mostly skipped manufacturing, growing instead on the back of a far smaller, high-skilled 
services sector” highlight the growth of services sector, they do not mention how the agriculture sector 
has performed in India during the same period. Therefore, no conclusive remarks can be made with regard 
to status of the agricultural sector. 
 
 
 
 
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73.(a) 
Statement 1 is correct. The lines “What we need to understand, and question is the politics behind 
recognizing the domain of intellect as essentially a male prerogative”, show that intellect has been a male 
forte which created inequality, and that is why we need to change it to give women equal importance in 
the area of intellect. Therefore, this inference is correct. 
Statement 2 is correct. The passage mentions “And of course, the mind is superior to the body. In this 
regard, the feminist critique of French philosopher René Descartes‟s Cartesian duality is an important 
intervention. The mind-body dualism has led to gender inequality for privileging the ‘rational’ mind 
over the ‘irrational’ or emotional body.” This establishes that due to the mind-body dualism of Descartes 
there has been a division in society which led to the belief of men being superior to women. Thus, this 
statement as inference is correct. 
Statement 3 is incorrect. This inference is incorrect because the passage does not discuss the social 
dimension of gender inequality anywhere. It might be correct in general, but we need to answer within the 
context of the given passage. Therefore, this inference is not correct. 
 
74.(b) 
Statement 1 is incorrect. The given option is not correct because the statement is extreme. 
Statement 2 is correct. The passage mentions “Thus, education is not merely learning of facts but is to 
train our mind to think. Education systems must provide opportunities to every individual to learn through 
experience and should help to develop critical thinking and problem-solving skills” and “Instead of 
focusing on critical thinking, expressing new ideas and debating and writing critically on any issue, our 
students are forced to learn through the rote route”. These lines show that to develop critical thinking 
(outcome of education) one should resort to experienced-based learning and reduce rote learning. 
 
75.(c) 
Let the initial average weight of 150 students be x. 
Sum of the weights of 150 students = 150x 
Let the new student, who is added, has weight m. 
The average weight of the new class becomes x + 0.05 
Therefore, [150x + m]/151 = x + 0.05 
Or 150x + m = 151x + 7.55 
Or m = x + 7.55 
Let the weight of the student who is removed be k. Then the new average becomes x + 0.05 - 0.02 = x + 
0.03 
According to the question, 
Or [150x + m - k]/150 = x + 0.03 
Or m - k = 150 × 0.03 = 4.5 
Or k = m - 4.5 = x + 7.55 - 4.5 = x + 3.05 (Since, m = x + 7.55) 
Now sum of the weights = m + k = (x + 7.55) + (x + 3.05) = 2x + 10.6 
Sum of the weights of the two students mentioned is 2x + b. 
On comparing with the above equation, we get b = 10.6. 
Hence, option (c) is correct. 
 
76.(a) 
Each of the three varieties contain starch, hops and water in varying proportions 
A contains x% starch and y% hops. 
So, percentage of water in A = [100 - (x + y])%. 
B contains y% starch and y% water. 
So, percentage of hops in B = [100 - 2y]% 
C contains x% hops and y% water. 
So, percentage of starch in C = [100 - (x + y)]% 
Concentration of starch in final mixture is 38%, so 
(2x/10) + (3y/10) + 5{100 - (x + y)}/10) = 38 
Or 3x + 2y = 120 ………………(i) 
Also, given concentration of hops in final mixture is 28%, so 
(2y/10) + 3(100 - 2y)/10 + (5x/10) = 28 
Or -5x + 4y = 20 …………….(ii) 
Solving (i) and (ii), we get: 
x = 20 and y = 30 
∴ x + y = 20 + 30 = 50 
Hence, option (a) is correct. 
 
 
 
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77.(d) 
Here we have to select, i.e. it's a question of combination (and not permutation), as the order of the players 
do not matter. 
As the team must have at least 5 bowlers, two cases emerge: 
Case I: Team has 5 bowlers and 6 batsmen. 
Number of ways of choosing such a team = Number of ways of choosing 5 bowlers out of 6 available and 
6 batsmen out of 7 available = 
6
C5 × 
7
C6 = 6 × 7 = 42. 
Case II: Team has 6 bowlers and 5 batsmen. 
Number of ways of choosing such a team = Number of ways of choosing 6 bowlers out of 6 available and 
5 batsmen out of 7 available = 
6
C6 × 
7
C5 = 1 × 21 = 21. 
Hence, total possible ways = 42 + 21 = 63. 
Hence, option (d) is correct. 
 
78.(a) 
Percentage share of small establishments in jobs in 1981 = 20% 
So, Number of jobs in small establishments in 1981 = (20/100) × 50 = 10 million 
And percentage share of small establishments in jobs in 1987 = 30% 
So, Number of jobs in small establishments in 1987 = (30/100) × 60 = 18 million 
Required difference = 18 – 10 = 8 million 
Hence, option (a) is the correct answer. 
 
79.(a) 
Percentage share of medium establishments in jobs in 1996 = 75% 
Total number of employees in manufacturing sector in 1996 = 100000 
So, Number of employees in medium establishments in 1996 = (75/100) × 100000 = 75000 
Now, Number of medium establishments in 1996 = 750 
Average number of employed persons per medium establishment unit in that year = 75000/750 = 100 
Hence, option (a) is the correct answer. 
 
80.(b) 
The first story starts on the 2nd page, i.e. from an even page number. 
We have to find the largest number of stories than can begin on an odd numbered page. Each story other 
than the first story (remaining 56 stories), starts on a fresh page. 
Thus, there could be a maximum of 56 stories starting on an odd-numbered page. 
Hence, option (b) is correct. 
 
 
 
 
 
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