GRE Question of the Week #2: Quantitative Comparison

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:

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A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Explanation

We begin by comparing the first terms. For quantity A, c+d a = c a + d a . Since both c and a are positive and c>a , c a >1 . Likewise, d a >1 and therefore, c+d a >2 . Using similar logic for the first term in quantity B, a+b d = a d + b d . Since a<d , a d <1 and likewise, b d <1 . Thus we know that a+b d <2 .

Next, compare the second terms. Note that both second terms have the same numerator: a−b . Since 0<a<b , we know that a−b<0 . The denominators are both positive, but since c<d , we know that | a−b d |<| a−b c | .

So, for quantity A, we start with a larger term, and add a negative term of smaller absolute value. For quantity B, we start with a smaller term, and add a negative term of greater absolute value. Therefore, quantity A is greater.

The correct answer is Choice (A).