Section 5. Quantitative Reasoning
- D Consider values that satisfy the given information. Case 1: a = 2, b = 1. In
this case, a > b. Case 2: a = −2 , b = 1. In this case, a < b. A relationship cannot
be determined. - C Choose values. Let the diameter of the larger circle = 10. In this case, the
circumference of the larger circle is 10π. Let the diameter of the medium-
sized circle be 6 and the diameter of the smaller circle be 4. In this case, the
circumference of the smaller circle is 6π, and the circumference of the smaller
circle is 4π. 6π + 4π = 10π. The two quantities are equal. - D Test different numbers that would satisfy the prompt. If x =^12 , then 213 > 215.
Thus,^12 is a possible value for x. In this case, Quantity A is greater. What about
negative numbers? If x = −2 , t hen (−2)^3 > (−2)^5. Thus, −2 is a possible value
for x. In this case, Quantity B is greater. - B Deduce what you can from the given information. The first inequality:
b^2 must be positive because of the even exponent. Thus, if b^2 c < 0, then c < 0.
Now, for the second inequality: If c < 0, and abc > 0, then ab < 0. Thus,
Quantity B is greater. - C Since x and y are mutually exclusive, the sum of their probabilities must
be 1. - D Choose numbers. If q = 1 and n = 5, then the value of both quantities is 1. If
q = 2 and n = 10, then the value of quantity A is greater. A relationship cannot
be determined. - C Note that each side of the larger triangle is double the corresponding side of
the smaller triangle. These are thus similar triangles. One property of similar
triangles is that corresponding angles are equal. Since angles ABC and DEF
are opposite the largest side of their respective triangles, the measurement of
these angles must be equal. - B Choose values. Let y = 100, and let z = 20. Now, evaluate Quantity A. With
these values, a $5 increase will lead to a bookshelf that costs $105. After a
20% discount, the price of the bookshelf will be .8(105) = 84. Now, evaluate
Quantity B. With these values, a 20% reduction in the retail price will result in
a new price of .8(100) = 80. 80 + 5 = 85. Quantity B is greater. - C The expression in the question is in the form of x^2 − y^2 , where 4a^2
corresponds to x^2 and 4b^2 corresponds to y^2. Since x^2 − y^2 factors to (x + y)
(x − y), 4a^2 − 4b^2 factors to (2a)^2 − (2b)^2 = (2a + 2 b) (2a − 2b). - 4 Plug in numbers. Let the original side length of the square = 3. In this case,
the original area is 9. If the length of each side is doubled, then the length of
each side is 6 and the corresponding area is 6^2 = 36.^369 = 4 - E $2,600 was the salesman’s commission on the fourth sale. Since the average
of the four commissions is $2,000, the total must be $2,000 × 4 = $8,000.
Subtracting the total of the other three commissions from $8,000 gives the
commission on the fourth sale. - A First, isolate each variable. 2a < 6 → a < 3. 3b > 27 → b > 9. Now, assume
that a = 3 and b = 9. In this case, b − a = 9 − 3 = 6. Since a < 3 and b > 9, the
difference between the two must be greater than 6. Thus, 6 is not a possible
value for b − a.
CHAPTER 16 ■ PRACTICE TEST 2 56905-GRE-Test-2018_463-582.indd 569 12/05/17 12:14 pm