GMAT Quantitative Reasoning Practice Test 6

Question : 8 of 100

Marks: +1, -0

A rectangular courtyard with whole-number dimensions has an area of 60 square meters. Find the length of the courtyard.
(1) The width is two more than twice the length.
(2) The length of the diagonal of the courtyard is 13 meters.

Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself.
Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself.
The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2).
The problem can be solved using EITHER statement (1) only or statement (2) only.
The problem CANNOT be solved using statement (1) and statement (2) TOGETHER.

Validate

Solution:

Let

x =

the length of the courtyard. Statement (1) states that

2x + 2 =

the width of the courtyard. Using the formula area = length × width, we get the equation

60 = x(2x + 2)

, which can be solved for x. Statement (1) is sufficient. Using statement (2), the diagonal divides the courtyard into two congruent right triangles. If the diagonal is 13 meters, and the dimensions are whole numbers, this must be a

5-12-13

right triangle. The length is 5 meters, and statement (2) is also sufficient.

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