What is the value of x – y

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Last Updated on May 10, 2023

GMAT OFFICIAL GUIDE DS

Solution:

We need to determine the value of x + y in the given figure. Let’s start by sketching the figure.

What is the value of x – y

In analyzing the angles in the figure, we must remember that the sum of the exterior angles of any polygon is 360°. Thus, we can say that x + y + w + z = 360 since these four angles represent the four exterior angles of the four-sided polygon in our diagram. Furthermore, since x + y = 360 – (w + z), if we can determine the value of w + z, we can determine x + y.

Statement One Alone: 

w = 95

Only knowing the value of w is not enough information to determine x + y. We can eliminate answer choices A and D.

Statement Two Alone: 

z = 125

Only knowing the value of z is not enough information to determine x + y. We can eliminate answer choice B.

Statements One and Two Together: 

Using statements one and two we see that z + w = 220.  Thus, x + y = 360 – 220 = 140.

Answer: C

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