GRE Question of the Week #2: Quantitative Comparison

Chalkboard

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:

0<a<b<c<d
Quantity A Quantity B
c+da+a−bd a+bd+a−bc

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.

Click here for the answer and explanation.
 

 

 

 

 

 

 

 

 

 

 

 

 

 

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).