McGraw-Hill Education GRE 2019

3. B To avoid working with fractions, cross-multiply and arrive at: 3a = bc. To
   make the columns look similar, substitute 3a for bc in Quantity B: 4(3a) = 12a.
   The comparison is 9a versus 12a. Since you are told that a is positive, you can
   divide both quantities by a. The comparison is thus:
   QUANTITY A QUANTITY B
   9 12 A B C D
   Quantity B is greater.


4. C
   Step 1: To simplify the comparison, add 8 to both quantities:
   Quantity A = 6x + 9y and Quantity B = 36.
   Step 2: To arrive at a value for Quantity A, manipulate the equation in
   the prompt to look similar to the expression in Quantity A:
   3(2x + 3y = 12)
   6 x + 9y = 36

Step 3: Substitute 36 for 6x + 9y in Quantity A

The two quantities are equal.

5. A
   Step 1: To make the two quantities look similar, factor the expression in
   Quantity A: ax + ay = a(x + y).
   Step 2: Divide both quantities by (x + y). Quantity A = a and Quantity B = b.
   Since you are told that a > b, the value in Quantity A is greater.

Exponents and Roots

Exponent Basics

In the term 5^3 , five is the base and 3 is the exponent. The exponent represents the

number of times you multiply the base by itself. So 5^3 comes out to 5 × 5 × 5. Both

the exponent and base can be any real number (not just positive integers).

Most GRE questions dealing with exponents will require you to use a few simple

rules and manipulate them in unorthodox situations. But before getting to these

rules, let’s look at some other properties of exponents:

An even exponent always yields a positive result.

The base of an exponential expression can be positive or negative, but when the

base is raised to an even exponent, the result will always be positive. Consider:

x^2 = 16

The most obvious solution to the preceding equation is 4. If you substitute 4 for x,

you arrive at 4^2 = 16, which is a true statement. But notice that –4 is also a solution

for x! If you substitute −4 back into the equation, you arrive at (−4)^2 = (−4)( −4) =

16, which is also true.

CHAPTER 11 ■ ALGEBRA 269

03-GRE-Test-2018_173-312.indd 269 12/05/17 11:54 am