- C, D, and E If xy > 0, then x and y are both positive or both negative. If x and
y are both negative, then x + y < 0. The condition that x and y are both negative
does not satisfy the given information. Thus to satisfy the given information,
x and y must both be positive. If x and y are both positive, then choices C, D,
and E are true.
Quantitative Comparison Questions
- D Choose values: First, select an integer value for each variable. Let a = –1 and
b = –2. In this case, Quantity A = 1, and Quantity B = 16. In this case, Quantity B
is greater. Next, choose values that are likely to yield a relationship different than
the relationship that the first pair of numbers yielded. To do so, select “weird”
numbers. In this case, a good type of “weird” number is a fraction. Let a = 0.25
and let b = 0.5. In this case, Quantity A = 0.0625, and Quantity B = 0.0625. In this
case, both quantities are equal. Therefore, a relationship cannot be determined. - A Plugging in numbers is a good strategy here. Since the columns have even
exponents, the signs will not matter. So choose fractions and integers.
Case 1: x =^12 and y =^13. In this case, the value of column A is^14 and
the value of column B is^19. Quantity A is greater, so the answer is A or D.
Case 2: Plug in new values to prove D: x = 3 and y = 2. In this case, the
value of column A is 9, and the value of column B is 4. Quantity A is still
greater. - B Though it would appear that you do not have sufficient information about a
and b, keep in mind that the even exponents and the signs will help you make
inferences. In Quantity A, a^2 and b^4 must be positive (because of the even
exponents). Thus their product is positive. Multiply this product by –1, and
the result is negative. In Quantity B, –a^2 and –b^4 are both positive. Thus their
product is positive. The value in Column B is greater. - D Since ab equals a positive number, a and b must have the same sign.
However, you do not know what the signs are. If a = 8, then b = 2, and
Quantity A is greater. But if a = –8, then b = –2, and Quantity B is greater.
There is more than one relationship, so the answer is D. - A If ab > 0, then a and b must have the same sign. If a and b have the same sign,
then their product must be positive. Thus ab > 0, and the correct answer is A. - A Your first step should be to make inferences from the stem. Inequality 1:
you know that p^2 q^3 > 0. Because of the even exponent, p^2 must be positive.
Thus q^3 must be positive. If q^3 is positive, then q > 0 (remember, odd exponents
preserve the sign of the base). Inequality 2: you know that p^3 q^2 > 0. Because
of the even exponent, q^2 must be positive. Thus p^3 must be positive. If p^3 is
positive, then p > 0. Positive × positive = positive, so pq > 0. - B Your first step should be to make inferences from the stem. Inequality 1:
because of the even exponent, you know that a^2 > 0. Thus b^3 c^5 > 0. Because of
the odd exponents, b^3 and c^5 will have the same signs as b and c, respectively.
Thus bc > 0. Inequality 2: because of the even exponent, you know that b^4 > 0.
Thus a^3 c^5 < 0. Because of the odd exponents, a^3 and c^5 will have the same signs
as a and c, respectively. Thus ac < 0. Now you know that bc > 0 and ac < 0.
CHAPTER 9 ■ NUMBER PROPERTIES 19703-GRE-Test-2018_173-312.indd 197 12/05/17 11:51 am