Comparação de Quantidades Matemáticas

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(the number of ways to select two × (the number of ways to select 
 of the five women) two of the four men)
= ×C C5 2 4 2 = 
−
×
−
5!
(5 2)!2!
4!
(4 2)!2!
 = ×5!
(3)!2!
4!
(2)!2!
 
 For Quantity B, the numerator is the number of ways to select three women and one 
man on the committee. Thus, Quantity B is the following product: (the number of ways 
to select three of the five women) × (the number of ways to select one of the four men) = 
×C C5 3 4 1 = 
−
×
−
5!
(5 3)!3!
4!
(4 1)!1!
 = ×5!
(2)!3!
4!
(3)!1!
 
 By inspection, the numerators of Quantity A and Quantity B have a common factor 
of 5!
(3)!2!
 = 5!
(2)!3!
, which you can divide out. Now, compare = ⋅ ⋅
⋅
=4!
(2)!2!
4 3 2!
(2 1)2!
6 and 
= ⋅ =4!
(3)!1!
4 3!
3!(1)
4. Because 6 > 4, Quantity A is greater.
107. (C) After the data are put in order (from least to greatest or greatest to least), the median 
is the middle value (for an odd number of data values) or the average of the two middle values 
(for an even number of data values). Quantity A is the median of 2,4,8,15,25 = 8. Quantity 
B is the median of −20,4,8,15,200 = 8. The two quantities are equal. Select (C).
108. (B) The mean = sum of data values
number of data values
 
 By inspection, the sum of the five numbers in Quantity A is less than the sum of the five 
numbers in Quantity B. Thus, Quantity B is greater.
109. (A) The standard deviation is a measure of the deviation of the data values from 
their mean. For both sets of data, the mean is 8. For Quantity B, the standard deviation 
is 0 because none of the data values deviate from 8. The data in Quantity A exhibit some 
deviation from the mean of 8. Thus, Quantity A is greater. Tip: For the GRE quantitative 
comparison questions, rather than trying to calculate a standard deviation by formula, sim-
ply look at the data. The standard deviation of data that cluster closely around the mean is 
less than the standard deviation of data that are spread out away from the mean.
110. (B) Let s = the standard deviation of the distribution. Then, = + s60 50 2 , = s10 2 , 
s = 5. Quantity B is greater.
111. (C) The number of workers who have $100,000 or more in total savings and 
investments is (6% 2%)(2,000)+ = 8%(2,000) 160= . The two quantities are equal. Select (C).
112. (B) The mode is the data value (or values) that occurs most often. Thus, Quantity A 
is 54. In an ordered set of n data values, the location of the median is the +n 1
2
 position. 
For the stem-and-leaf plot, n = 44, so +n 1
2
 = + =44 1
2
45
2
 = 22.5. Thus, the median is 
halfway between the 22nd and the 23rd data values. Hence, Quantity B is + =54 55
2
54.5. 
Quantity B is greater.
06_McCune_Answer.indd 171 2/21/22 4:45 PM