Using Numbers

For many Word Geometry Quantitative Comparison questions, using numbers is an effective technique.

This technique is most effective when the question references specific dimensions of a shape (e.g., length, width, radius) but provides no actual numbers. For example:

Rectangles R and S have equal
areas. Rectangle R’s length is
greater than Rectangle S’s width.
Quantity A Quantity B
The area of Rectangle R
if the length increases 30%		 The area of Rectangle S
if the width increases 30%

First, establish what you need to know. Both quantities have an unknown value, so you will have to judge their relative size.

The best way to judge the relative size of each quantity is to use numbers.

The common information states that the rectangles have equal areas. An easy number to use for the area is 10. The numbers chosen in this example are only one set of possibilities, but they were chosen because they are easy to use:

AreaR = AreaS = 10

Now, draw the picture. Make sure you include the numbers you chose.

Each rectangle has an area of 10, but the length of R is greater than the width of S:

Quantity A mentions the length of R and Quantity B mentions the width of S. Pick values for the length and width of R and S.

Make the length of R 10 and the width 1. Make the length of S 2 and the width 5:
Quantity A Quantity B
The area of Rectangle R if the
length increases 30%		 The area of Rectangle S if
the width increases 30%

Now, evaluate the quantities. Start with Quantity A. Increase the length of R by 30 percent:

130% of 10 = (1.3)(10) = 13

The new area of R is l × w = (13)(1) = 13:

Quantity A Quantity B
The area of Rectangle S if the width increases 30%

Now, evaluate Quantity B. Increase the width of S by 30 percent:

130% of 5 = (1.3)(5) = 6.5

Use the calculator for this computation, if need be.

The new area of S is l × w = (2)(6.5) = 13:

Quantity A Quantity B

The new areas are equal. This result will hold regardless of the precise length you choose. The correct answer is (C).