GreenlightTestPrep wrote:

The width, length, and diagonal of a rectangle could be represented by which of the following groups of numbers?

I. 2, 3, \(\sqrt{13}\)

II. \(\sqrt{10}\), 4, 6

III. 3, 10, 11

A. I only

B. I and II only

C. I and III only

D. II and III only

E. I, II, and III

NOTE: The width, length, and diagonal create a RIGHT TRIANGLE, with the diagonal as the hypotenuse.

For these to be valid lengths, the

Pythagorean Theorem must apply.

That is, it MUST be the case that width² + length² = diagonal²

Let's check the 3 sets of values

BEGINNING WITH IIIIII. Does 3² + 10² = 11²? NO.

This means that 3, 10, 11 CANNOT represent the width, length, and diagonal of a rectangle.

This means we can ELIMINATE C, D and E

II. Does (√10)² + 4² = 6²? NO.

This means that √10, 4, 6 CANNOT represent the width, length, and diagonal of a rectangle.

This means we can ELIMINATE B

Answer: A

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Sign up for our free GRE Question of the Day emails