Exercise Answers
Discrete Quantitative Questions
- E First, convert the fractions in the question to improper fractions: 3^13 =^103
and 2^12 =^52. Now express the ratio as a fraction:10
3
5
2. Multiply the numerator by
the reciprocal of^52 :^103 × 25 =^43.
2. 45 First, express the ratio as a fraction: number of push-ups/number of
sit-ups = ps =^32 (Note: p = number of push-ups and s = number of sit-ups).
Next, set up a proportion: ps =^32 = 30 p. Now cross-multiply to solve for p:
90 = 2p
p = 45
3. E Remember that ratios specify relationships, not values. Let 4x = the original
number of sheep and 3x = the original number of horses. The new ratio will
be: number of sheep/number of horses =^43 xx + 5 + 5. Without knowing how many
horses or sheep there were originally, it is not possible to determine the new
ratio. Another option is to plug in numbers. If the ratio of sheep to horses
is 4:3, then there can be 4 sheep and 3 horses at the farm. In this case, the
new ratio will be 9:8. However, the original number of sheep can be 8 and
the original number of horses can be 6, in which case the new ratio would
be 8 + 56 + 5 =^1310. Multiple answers are possible, meaning that a value cannot be
determined.
4. D Express the ratio as a fraction: chimpanzees/bonobos =^4836. Reduce:
4(12)
3(12) =
48
36 =4
3- C Let the amount of water = 3x and the amount of alcohol = 1x. The sum of
water and alcohol is thus 3x + 1x = 4x. Since water and alcohol make up half of
the volume of the solution, the volume of the entire solution will be 2(4x) = 8x.
To determine water as a percentage of the entire solution’s volume, use the
percent formula:
(^) wholepart = percent 100
↓
38 xx = percent 100
38 xx × 100 = percent
38 × 100 = percent
percent = 37.5%
- C Represent the number of students algebraically:
number of freshmen = 3x
number of sophomores = 4x
number of juniors = 6x
number of seniors = 7x
The total number of students will be the sum of these four groups: 3x + 4x +
6 x + 7x = 20x. Since the number of students in the school must be an integer
252 PART 4 ■ MATH REVIEW03-GRE-Test-2018_173-312.indd 252 12/05/17 11:53 am