Exercise Answers
Discrete Quantitative Questions
- B Let the smallest integer = x. Therefore:
x + (x + 2) + (x + 4) + (x +6) = 44
4 x + 12 = 44
4 x = 32
x = 8
The second-largest integer is x + 4. Substitute 8 for x: 8 + 4 = 12. - E Use Property 2: The average (arithmetic mean) of an evenly spaced set =
the median of the set = the average of the endpoints. In this question, the
fastest way to determine the median is to take the average of the endpoints:
14 + 80
2 =
94
2 = 4 7.- 60 Use Property 3 to determine how many multiples of 3 there are from
1–120, inclusive. The lower bound is 3 and the upper bound is 120. Thus the
number of multiples of 3 = 120 –3 3 + 1 = 40. Now use Property 3 to determine
how many multiples of 4 there are from 1–120, inclusive. The lower bound is 4
and the upper bound is 120. Thus the number of multiples of 4 = 120 – 4 4 + 1 =
30 → 40 + 30 = 70. But there’s an issue: You have double-counted the multiples
of 12. You thus need to determine how many multiples of 12 there are from
1–120, inclusive, and subtract that value from 70. Use Property 3 again: The
number of multiples of 12 from 1–120, inclusive, is 120 – 12 12 + 1 = 10. Thus the
answer is 70 – 10 = 60. - A An even multiple of 9 is any number that has 9 and 2 as factors, in other
words, a multiple of 18. You are thus looking for the number of multiples of 18
from 1–1,000, inclusive. The smallest value in the set is 18. The largest value in
the set is 990. Substitute these values into the formula from Property 3:
990 –18
18 + 1 = 55 - C In an evenly spaced set, median = average, so the median of the first three
terms will equal number of itemssum =^933 = 31. Since each set has three terms, and
all the values are consecutive, the median of the next three terms will be 3
greater than the median of the first three terms: 31 + 3 = 34. Use Property 4 to
determine the sum of the last three terms:
average × number of items = sum
↓ ↓ ↓
34 × 3 = 102 - A Before using any of the relevant formulas, recognize that since the question
concerns multiples of 3, the endpoints are 12 and 108. Based on Property 4:
average × number of items = sum. From Property 2, you know that the average
of an evenly spaced set equals the average of the endpoints: 108 + 12 2 = 60.
Using Property 3, you can determine the number of items:
108 – 12
3 + 1 = 33
204 PART 4 ■ MATH REVIEW03-GRE-Test-2018_173-312.indd 204 12/05/17 11:51 am