14. B and D Whenever a question provides multiple ratios with a common
element, manipulate the ratios so that the common element has the same value
in both ratios. In this case, the common element is teachers, so we should
manipulate the ratios so that the number of teachers is the least common
multiple of 2 and 5: 10. In the first ratio: students/teachers =^92 =^4510. In the
second ratio: teachers/administrators =^53 =^106. The ratio of students to teachers
to administrators is thus 45:10:6. The number of students must therefore be a
multiple of 45. Any choice that is a multiple of 45 is a potential value for the
number of students.- C Although the greatest number of Asian subscribers was in 2008, that is
not the answer, because Asians formed a smaller percentage of subscribers in
that year than they did in 2006. In 2008, there were roughly 15 million Asian
subscribers and roughly 72 million total subscribers. The percentage of Asians
in 2008 was therefore (^1572 ) × 100 = 20.8%. In contrast, in 2006, there were
roughly 10 million Asian subscribers and 42 million total subscribers.
(^1042 ) × 100 = 23.8%. - E Use the percent greater formula: percent greater = percent of − 100%. The
number of North American subscribers in 2008 was approximately 30 million.
The number of North American subscribers in 2006 was approximately 20
million. 30 million is 150% of 20 million. Thus, 30 million is 50% greater than
20 million. - 1,322 Use the weighted average formula: (average of 2007) × (weight of 2007)
- (average of 2008) × (weight of 2008). We are given the averages, so let’s find
the weights. The weight of 2007 is approximately (55 + 72)^55 = .43. The weight of
2008 is thus approximately .57. Now, use the formula: 1,210(.43) + 1,400(.57) =
524 + 798 = 1,322.
- (average of 2008) × (weight of 2008). We are given the averages, so let’s find
- B The first two factors form a difference of squares:
(√3 + √ 2 ) (√ 3 − √ 2 ) =
2
√3 −
2
√2 = 3 − 2 = 1
The last two factors form a difference of squares:
(√7 − √ 5 ) (√ 7 + √ 5 ) =
2
√7 −
2
√5= 7 − 5 = 2. Then multiply the 1 × 2 = 2 - 1 Notice that all the terms on the left side of the equation are equal. We can
thus combine like terms to arrive at: 5(5–x) = 1. Since 5 = 5^1 , we can rewrite the
equation as: 5^1 (5–x) = 1 → 5 (1–x) = 1. If 5(1–x) = 1, then 1 – x = 0 → x = 1. - E The easiest way to answer this question is to choose values for a and b.
Let a = .5 and b = 2. When we substitute these values into the choices, we
arrive at:
a) (.5)(2) = 1
b) (.5) 2 = .25
c) (^) .5^2 = 4
d) .5 4 = .125
e) (^) (.25)^2 = 8
Choice E yields the largest value.
516 PART 5 ■ GRE PRACTICE TESTS
05-GRE-Test-2018_463-582.indd 516 12/05/17 12:14 pm