What is the value of x? - OG prac test

[Kuros]

Another geometry question, I know my weakness isn't blatantly obvious or anything
:roll:

[spoiler]answer was c.

My thought process for this was: I needed to know or reduce some combination of equations to come up with ∠RSQ and ∠UST. 1) QR = QS means ∠RQS = ∠RSQ, but can't inform what ∠UST is, so insufficient. 2)ST = TU means ∠TUS = ∠TSU, but doesn't give me any information about ∠RSQ, so also insufficient. Both together, if I make ∠RSQ = y degrees, then ∠PRS = 180-2y, and therefore ∠UTS = 180-90-(180-2y) = 2y-90, and then TSU = (180-(2y-90))/2 = 135-y, since ∠RSQ is already y, then 180-(135-y+y)=x=45 [/spoiler]

My questions are: Is my process right? If it was, it took me at least 6-7 minutes to think about and work through it, are there better ways of approaching the problem where I can grasp whether this is solvable within a more reasonable time frame? Or do I just need more practice?

[GMATGuruNY]

I posted a solution here:
https://www.beatthegmat.com/geometry-ang ... 82540.html

[Jay@ManhattanReview]

Another geometry question, I know my weakness isn't blatantly obvious or anything
:roll:

[spoiler]answer was c.

My thought process for this was: I needed to know or reduce some combination of equations to come up with ∠RSQ and ∠UST. 1) QR = QS means ∠RQS = ∠RSQ, but can't inform what ∠UST is, so insufficient. 2)ST = TU means ∠TUS = ∠TSU, but doesn't give me any information about ∠RSQ, so also insufficient. Both together, if I make ∠RSQ = y degrees, then ∠PRS = 180-2y, and therefore ∠UTS = 180-90-(180-2y) = 2y-90, and then TSU = (180-(2y-90))/2 = 135-y, since ∠RSQ is already y, then 180-(135-y+y)=x=45 [/spoiler]

My questions are: Is my process right? If it was, it took me at least 6-7 minutes to think about and work through it, are there better ways of approaching the problem where I can grasp whether this is solvable within a more reasonable time frame? Or do I just need more practice?

Hi Kuros,

Your approach is fine. Regarding your timing is concerned, it can certainly be reduced significantly with more practice. Once you have seen many questions involving the properties of a right-angled triangle, isosceles triangle, and straight angle, you would certainly do similar questions in less than 2 minutes.

Relevant book: Manhattan Review GMAT Geometry Guide

Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Vienna | Kuala Lumpur | Sydney | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.