McGraw-Hill Education GRE 2019

Quantitative Comparison Questions

1. D Since the exponent on the variable is even, x = √ 16 = 4 or x = −√ 16 = −4.
   The relationship cannot be determined. The correct answer is D.


2. C If ab = 0, then a = 0 and/or b = 0. If bc = 3, then neither b nor c = 0. Since
   b does not equal zero, a must equal zero. The two quantities are equal. The
   correct answer is C.


3. A Add the given equations to solve for x: 2x + 14 → x = 7. Substitute x for 7 in
   the first equation to solve for y:
   7 + y = 9
   y = 2
   The value of Quantity A is 7^2 – 2^2 = 45. The value of Quantity B is 2^2 – 7^2 =
   4 – 49 = –45. Quantity A is greater.


4. B Set the quadratic equal to zero: x^2 + 7x + 12 = 0. Factor: (x + 3)(x + 4) = 0.
   There are two solutions:
   (x + 3) = 0
   x = –3 or (x + 4) = 0
   x = –4
   Since both solutions are negative, x < 0 and –x > 0. Quantity B is greater.


5. A First, solve for x by setting the first equation equal to zero:
   x^2 – 5x – 6 = 0
   (x – 6)(x + 1) = 0
   x = 6 or x = –1
   Next, solve for y by setting the second equation equal to zero:
   y^2 + 6y + 9 = 0
   (y + 3)(y + 3) = 0
   y = –3
   If x = 6, then Quantity A is greater. If x = –1, then Quantity A is greater.

Formulas, Functions, and Sequences

The next type of algebra question concerns situations where the question gives you

a formula to determine some value.

Formulas

In formula questions, the question will define a formula for you and will ask you

to substitute values or variables into the formula to arrive at an answer. A typical

question would be:

CHAPTER 11 ■ ALGEBRA 291

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