Source: Official Guide for the GMAT 12th Ed. Section 5.3 Problem Solving; #62

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# In the figure above, if PQRS is

In the figure above, if PQRS is a parallelogram, then y-x = 30, 35, 40, 70, 100

### 2 Explanations

1

Rustam Karshibaev

Pls, explain what is wrong with my calculations:

x=40. x/2 = 20. 2y+20=140. y=60. y-x=60-20=40.

Feb 3, 2014 • Comment

Kevin Rocci, Magoosh Tutor

Hi Rustam! I can help! :)

I think that you probably made this question more complicated than you needed to. When you found that x = 40, you were on the right path. But then you divided by 2. I am not sure why you did this. There is no reason to find half of x—all we need is to know what x equals.

Ultimately, we know this:

2y + x = 180

According to your calculations, it equals 140, which is not possible. The error comes from dividing x in half.

Also, we can find y fairly quickly if we recognize that 140 and 2y are congruent angles, meaning that they are equal. So,

2y = 140
y = 70

With our first equation, we can get all the information that we need.

2y + x = 180
140 + x = 180
x = 40

Thus,

y - x = ?
70 - 40 = 30

So I think that your calculations were thrown off when you divided x by 2. Does that make sense?