McGraw-Hill Education GRE 2019

Section 6. Quantitative Reasoning

1. B x represents the number of times that 2 appears in the prime factorization
   of 1,000. So to determine possible values for x, let’s break 1,000 down into its
   prime factors and determine how many 2s appear. 1,000 = 4 × 250 = 4 × 2 ×
   125 = 2 × 2 × 2 × 5 × 5 × 5. So 1,000 has three 2s, which means the greatest
   value for x is 3.


2. B Don’t solve! Since quantity A is so ugly, we should manipulate the quantities
   to get rid of the radical.
   To eliminate the fourth-root, take both sides to the power of 4. Now, quantity
   A = 255, and quantity B = 44 = 256. Therefore, quantity B is larger.


3. D As a general rule, you should try to eliminate negative exponents within a
   fraction. To do so, we can use the following rule: a–x/b–x = bx/ax. Let’s apply this
   rule to each quantity.

Quantity A will come out to:^279 xx 24

Quantity B will come out to:^3612 xx

3

2

Now, let’s simplify both quantities further:

Divide Quantity A to arrive at^3 xx

4

2 →^3 x^2

Divide Quantity B to arrive at^3 xx

3

2 →^3 x

You may be tempted to choose Quantity A, since x is raised to a larger

exponent than in Quantity B, but don’t forget to consider “weird”

numbers!

If x = 1, then Quantity A = 3 and Quantity B = 3, in which case the quantities

are equal. If x = 2, then Quantity A = 12, and Quantity B = 6, in which case

Quantity A is greater. Since there is more than one relationship, the answer

is D.

4. B Don’t solve! Assume that the value of Quantity A is 75% and determine how
   that value would relate to the given information. Let’s use the weighted average
   formula to understand this relationship.
   If 75% of the company is female, then 25% is male, in which case the “weight”
   of the female employees is 0.75 and the weight of the male employees is 0.25.
   Plugging these values into the weighted average formula, we arrive at:
   0.25(24.7) + 0.75(25.9) = 25.6
   Since 25.6 > 25.5, we know that the actual percentage of female employees
   needs to be smaller. Therefore, Quantity B is greater.

68 PART 1 ■ GETTING STARTED

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