Scott Woodbury-Stewart

GMAT OFFICIAL GUIDE DS – In the parallelogram shown, what is…

In the parallelogram shown, what is…

Solution:

We are given a parallelogram with three given angles. Let’s sketch the diagram below.

Since we have a parallelogram we know that opposite angles are equal and that the angles sum to 360°.

Thus, x = z and

y + y + x + x = 360

2y + 2x = 360

y + x = 180

We must determine the value of x.

Statement One Alone: 

y = 2x

Using the information from statement one we can substitute 2x for y in the equation y + x = 180.  Thus we have:

2x + x = 180

3x = 180

x = 60

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone: 

x + z = 120

Since x = z, we know:

x + x = 120

2x = 120

x = 60

Statement two is sufficient to answer the question.

Answer: D 

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