GMATPrep question about angles

[kiwitaker]

I couldnt figure out the answer to the question in the attachment.. Could someone please help.

[bubbliiiiiiii]

E

[bubbliiiiiiii]

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?

[kiwitaker]

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.

[bubbliiiiiiii]

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

[GMATGuruNY]

I posted a solution here:

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

[kiwitaker]

Thanks everyone for the replies..

PS: My GMAT is tomorrow!

[bubbliiiiiiii]

All the best and do share your story with us.