McGraw-Hill Education GRE 2019

5. C Determining the number of thirds in 7 is the same thing as determining
   how many times^13 divides into 7. Written as a fraction, this becomes
   7
   1
   3

= ?. Dividing by a fraction is equivalent to multiplying by the reciprocal of

that fraction, so

7

1

3

= 7 × 31 = 21. The values in the columns are equal.

6. B Instead of calculating a value for Quantity A, look at how the two columns
   compare. Both fractions in Quantity A are smaller than the fraction in
   Quantity B. Multiplying two positive fractions will yield only a smaller
   fraction, so the product of the fractions in Quantity A must be less than 109.


7. B Since the two fractions have the same numerator, whichever fraction has
   the smaller denominator will be the greater fraction. 3^200 is greater than 2^200 ,
   so the denominator in Quantity A is greater, meaning that the fraction in
   Quantity A is smaller.


8. B Choose values for c. Since you are given a range, choose extremes. First
   choose 1. In this case, the value in Quantity B will be^89.^89 is greater than^78 , so
   in this case, the value in Quantity B is greater. Now choose a larger value for
   c: 100. 7 + 1008 + 100 = 108107 , which is greater than^78. Both values for c yielded a larger
   value in Quantity B than in Quantity A.


9. A Expressed algebraically, the prompt says that^12 k =^23 b, where k = Kathy’s
   salary and b = Bob’s salary. The quantities you are asked to compare are^23 k and
   1
   2 b.

2

3 k is greater than

1

2 k, and

1

2 b is less than

2

3 b. Thus if

1

2 k =

2

3 b, then

2

3 k must be

greater than^12 b.

This question can be done quickly if you identify what you are comparing

and how those values relate to the given information. Since^23 is greater than^12 ,

the value in Quantity A must be greater than half of Kathy’s salary. Since^12 is

less than^23 , the value in Column B must be less than^23 of Bob’s salary. If half of

Kathy’s salary equals^23 of Bob’s salary, then^23 of Kathy’s salary must be more

than^12 of Bob’s salary.

10. C You can use your calculator, but it is faster to express both quantities
    using powers of 10. In Quantity A, there are five digits total to the right of
    the decimal, so you can express Quantity A as 79 × 232 × 10 –5. In Quantity
    B, there are five digits total to the right of the decimal, so you can express
    Quantity B as 79 × 232 × 10 –5. The two quantities are equal.


11. A In each quantity, the same number of fractions is being added, and the
    numerators in Quantity A and Quantity B are the same. The difference is the
    denominators. The denominator of each of the values in Quantity B is greater
    than each corresponding denominator in Quantity A. If two positive fractions
    have the same numerator, the fraction with the smaller denominator is larger.
    Thus each fraction in Quantity A is greater than its corresponding fraction in
    Quantity B. Quantity A is greater.

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