McGraw-Hill Education GRE 2019

9. A Solution: a 4 = 3a 3 + 2a 2. Thus:
   35 = 3(7) + 2a 2
   14 = 2a 2
   7 = a 2


10. B To determine the 13th term, you will have to add 7 a certain number of
    times to the third term. How many times? To go from the 3rd to the 4th term,
    you add 7 once. To go from the 3rd to the 5th term, you add 7 twice. Thus to
    go from the 3rd to the 13th term, you should add 7 ten times. The 13th term
    thus equals 3rd term + 7(10) = 39 + 7(10) = 109.

Quantitative Comparison Questions

1. C Substitute the values in the quantities into the given formula:^12 +^13 =^13 +^12.
   The two quantities are equal.


2. C Because of the even exponent, (x − 3)^2 > 0. Thus the minimum value for
   2(x − 3)^2 = 0. The value of the function will be minimized when 2(x − 3)^2 =
   0. 7 + 0 = 7. The two quantities are equal.


3. B Since each unit represents a 5-pound increase, the difference in pounds
   between three units is 3(5) = 15.


4. D Without knowing the value of any of the terms in the sequence, you cannot
   determine anything about the value of a 4.


5. B a 3 = a 2 + 7. a 2 = a 1 + 7. Substitute a 1 + 7 for a 2 in the first equation:
   a 3 = (a 1 + 7) + 7 = a 1 + 14. Quantity B is greater.

Inequalities and Absolute Value

Inequalities look like the following:

5 > −2 y > 7 ab ≤ 15 3 < z < 9

Any time you see <, >, ≤, ≥, you are dealing with an inequality.

The following list translates inequalities:

Types of Inequalities

■ a > b means “a is greater than b”

■ a < b means “a is less than b”

■ a ≥ b means “the value of a is at least equal to the value of b”

■ a ≤ b means “the value of a is at most equal to the value of b”

■ 3 < a < 5 means “the value of a is between 3 and 5” (This is called a

compound inequality.)

300 PART 4 ■ MATH REVIEW

03-GRE-Test-2018_173-312.indd 300 12/05/17 11:56 am