McGraw-Hill Education GRE 2019

The comparison is now:

Quantity A Quantity B

2 a + 3 b 3 a + 2 5 b

Cross-multiply: ↓

5(2a + b) 3(3a + 2b)

Distribute: ↓

10 a + 5b 9 a + 6b

Subtract 9a from both columns: ↓

a + 5b 6 b

Subtract 5b from both columns: ↓

a b

Since you are told that a > b, Quantity A is greater.

5. B To maximize the range, minimize the smallest value and maximize the
   greatest value. Since the terms are positive integers, the minimum value for an
   item in the set is 1. To maximize the greatest value, minimize the rest of the
   terms. In this case, that would mean making them all equal to 1. Therefore:
   1 + 1 + 1 + 1 + x = the sum of the set = 100
   4 + x = 100
   x = 96
   The maximum possible range is 96 – 1 = 95. Quantity B is greater.


6. A The difference between the two sets is the 0 in the second set. Since 0 is
   less than the average of 2,19, 34, and 60, the average of the second set must be
   smaller than the average of the first set. Quantity A is greater.


7. B Express Quantity A algebraically:
   1
   a +

1

b

2

=

b + a

ab

2

= b + a 2 ab

The numerators of the two quantities are the same. Since the denominator of

Quantity B is smaller, that fraction is larger.

8. B In Quantity B, each term in Quantity A is doubled. The spread of the set
   will thus be doubled. Since the spread in Quantity B is greater, the standard
   deviation of Quantity B is greater.

Rates

Rate questions always come in one of two forms: distance or work. In both cases,

there will be a constant relationship between the rate, time, and work or distance:

rate × time = distance

or

rate × time = work

CHAPTER 12 ■ FROM WORDS TO ALGEBRA 339

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