GRE-Math-Questions-to-Know-by-Test-Day-2nd-Edition_pag212

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Answers ‹ 203
 In the second week, the student worked 40% more hours than in the first week, so write 
the following percent equation and solve for z, where z is the number of hours worked 
in the first week: = z28 140% . Thus, = = =z 28
140%
28
1.4
20 (the number of hours worked in 
the first week). Tip: Use the provided calculator wisely. Changing percents to decimals in 
this problem simplified the calculator computations. 
261. (C) =400 20, so choice C is the correct response because =( 20 ) 202 .
262. (D) In February, the electricity cost is −$1,420 0.025($1,420) = −($1,420)(1 0.025) = 
($1,420)(0.975). Thus, in March, the electricity cost is −($1,420)(0.975)(1 0.025) = 
($1,420)(0.975)(0.975).
263. (E) It is useful to know that, in general, if the prime factorization of a positive 
integer is p p pk k
n
k
1 2
n1 2 , where the p’s are distinct positive prime numbers and the k’s are 
their corresponding exponents, then the number of positive divisors of that integer is the 
product + + +k k k( 1)( 1) ( 1)n1 2 . Thus, the number of positive divisors of =m a b c d4 2 5 is 
+ + + +(4 1)(2 1)(5 1)(1 1) = (5)(3)(6)(2) = 180. Tip: Knowing simple tricks about integers 
such as how to quickly determine the number of positive divisors of a positive integer (as 
demonstrated in this question) can turn what, at first, looks like a difficult question into an 
easy computation exercise.
264. (B) Calculate the initial number of college students: × =
1
4
4,800 1,200. Calculate 1
3
 
of this number: × =
1
3
1,200 400. Calculate the number of college students remaining: 
− =1,200 400 800. Calculate the number of total residents remaining: − =4,800 400 4,400. 
Calculate the portion of the total remaining that are college students: =
800
4,400
2
11
.
265. (D) For convenience, suppose the investment is $100. In 10 years, its value will be 
⋅3 $100 = $300. In 20 years, its value will be ⋅3 $300 = $900. Finally, in 30 years, the value 
of the investment will be ⋅3 $900 = $2,700. Because $2,700 is 27 times $100, the invest-
ment increased by a factor of 27. Tip: Picking a convenient amount for the investment is a 
useful strategy in problems like this one.
266. (C) The total percent invested in stocks, the mutual fund, and bonds is 
+ + =50% 25% 20% 95%. Thus, the percent invested in certificates of deposit is 
− =100% 95% 5%. Write the following percent equation and solve for x, the total amount 
invested: =x5% $20,000. Hence,
 = = =x $20,000
5%
$20,000
0.05
$400,000 
267. (D)
Percent increase = − = − = = =New value Old value
Old value
$375 $300
$300
$75
$300
1
4
25% 
06_McCune_Answer.indd 203 2/21/22 4:49 PM