- 5 First, get rid of the negative exponents by expressing each base as its
reciprocal:
1
x^3 ×
1
y^2 =1
72 → (x(^3) )(y (^2) ) = 72
Next, break 72 down into its prime factors: 72 = 3 × 3 × 2 × 2 × 2. x = 2
and y = 3. x + y =5.
- D Choose a value for the production cost: $1,000. The purchase price was thus
.7($1,000) = $700. The selling price was thus (^87 ) × 700 = $800. 800 is 80% of
1,000. - C Since the numerators of the fractions are the same, it must be true that
3 a < 100. The greatest integer, a, that satisfies this inequality is 4. - E The correct answer will be a value whose prime factors are not contained
within the prime factorization of 30!. The prime factors of 62 are 2 and 31. 31 is
not contained within the prime factorization of 30!. - A, B, and D Choose values that satisfy both constraints. Let x = −3 and y =
−2. For these values, choices A, B, and D all hold true. Now, choose new values
for x and y that satisfy the constraints: x = −^12 and y = −^13. For these values,
choices A, B, and D still hold true. - B Look at Diagram 1. In two of the sectors phone X was rated as the
preferred phone. The sum of these percentages is 15.3% + 18.7% = 34%. 34% of
1,000 is 340. In two of the sectors, phone Y was rated as the preferred phone.
The sum of these percentages is 9.8% + 6.2% = 16%. 16% of 1,000 is 160.
340 − 160 = 180. - B Since these ratings are averages, you may be inclined to get the sum of the
value ratings for each, and then use the percentage change formula. However,
we don’t need to get the sum, since the number of ratings is the same for both
groups. Instead, use the average rating in the percent change formula:
4.8 − 4.0
4.0 × 100 = 20% - C The preference YZX represents 9.8% of the entire circle. 9.8% × 360 degrees
= 35 degrees. - B Surface area of a cube = 6e^2. Plug in values. Let the original edge = 2. The
original surface area is thus 24. The new surface area is thus 96. The new
surface area is thus four times the original surface area. - B Plug in numbers. Let the original length = 10 and the original width = 10.
The new length is this 1.1(10) = 11, and the new width is thus .9(10) = 9. The
new area is thus 99. The original area was 100. 99 is 99% of 100. - B (probability of choosing r) × (probability of choosing r again) =
1
10 →^
r
5 ×r − 1
4 =1
10 →^r (r − 1)
20 =1
10 →^ r(r − 1) = 2 →^ r = 2514 PART 5 ■ GRE PRACTICE TESTS05-GRE-Test-2018_463-582.indd 514 12/05/17 12:14 pm