GMATPrep question about angles

How much did you score in the quant section of this test?

The idea behind asking the question above is to when geometry questions appear in GMAT Prep?

Hey Pranay - I correct answer according to GMAT Prep is C.. I dont understand the reasoning behind this..

It was the 7th question on the exam.. I got a 47 for Quant on this particular test.

Yes the answer is C.

Here is how it is.

x=180-(Angle RSQ + Angle UST)

Option A:

QR=RS. We only know that Angle RQS and Angle RSQ are equal. Nothing can be deduced about Angle UST.
Also, Angle QRS = 180 - (Angle RQS + Angle RSQ).
Thus, Insufficient.

Option B:

ST = UT. We only know that Angle SUT and Angle UST are equal. Nothing can be deduced about Angle RSQ.
Also, Angle STU = 180 -(Angle SUT + Angle UST)
Thus, Insufficient.

A and B:

Now we know that,
Angle SUT and Angle UST are equal, and
Angle RQS and Angle RSQ are equal.

Moreover, consider the Triangle RPT, we know that Angle PRT + Angle PTR = 90 degrees.
since, triangle RPT is right angled triangle.

Synthesizing the information we have.

x=180-(Angle RSQ + Angle UST) ..... I

Angle PRT + Angle PTR = 90 degrees. ...... II
=> 180 - 2*RSQ + 180 - 2*UST = 90
on solving this we get,

Angle RSQ + Angle UST = 135.

Substituting this in I

we get x = 45 degrees.

Hope it helps

I posted a solution here:

https://www.beatthegmat.com/ds-geometry- ... 70380.html

Thanks everyone for the replies..

PS: My GMAT is tomorrow!

All the best and do share your story with us.