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Official GMAT Prep Exam 5 Question

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by 800_or_bust » Fri Jun 17, 2016 12:24 pm
For the cube shown below, what is the degree measure of Angle PQR?

(a) 30
(b) 45
(c) 60
(d) 75
(e) 90

OA: C
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Last edited by 800_or_bust on Fri Jun 17, 2016 12:27 pm, edited 1 time in total.
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by 800_or_bust » Fri Jun 17, 2016 12:26 pm
So I got this as Question 37 (of 37). I can't recall having seen a similar question in my studies (i.e. one that asks for an angle measure in three dimensions), so I was kind of at loss. I guessed what might be the most obvious answer, but it was wrong. And I'm still having a difficult time conceptualizing the correct answer. Any insight?
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by Brent@GMATPrepNow » Fri Jun 17, 2016 12:33 pm
800_or_bust wrote:For the cube shown below, what is the degree measure of Angle PQR?

(a) 30
(b) 45
(c) 60
(d) 75
(e) 90

OA: C
If we draw a line connecting points P and R, we see we that triangle PQR must be an equilateral triangle, which means all 3 angles (including angle PQR) must be 60 degrees each.

Answer: C
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by [email protected] » Fri Jun 17, 2016 2:58 pm
Hi 800_or_bust,

Certain questions on Test Day are easier to solve if you 'play around' and do work in 'small pieces.'

In this prompt, you don't have much to work with, but you should notice that the two line segments are both DIAGONALS. Since we're dealing with a cube, those two diagonals would be the SAME length.

From there, you might think...since those two are the SAME length, if I formed a triangle with them, then that triangle would be ISOSCELES. That deduction, in and of itself, isn't that meaningful... BUT it should get you thinking about forming a triangle using those two line segments....

Drawing a quick sketch and including that new line segment across the "top" of the cube will help you to notice that that third line is ALSO a diagonal that has the SAME length as the other two line segments.

NOW you have a triangle with 3 equal sides... THAT is an EQUILATERAL triangle and determining the angle isn't very hard at all at that point.

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by Brent@GMATPrepNow » Fri Jun 17, 2016 3:04 pm
Rich makes a good point about playing around and doing work in small pieces.
Here are two videos with this and other strategies to consider when tackling geometry questions on the GMAT:

GMAT Geometry Strategies - Part I: https://www.gmatprepnow.com/module/gmat ... /video/864

GMAT Geometry Strategies - Part II: https://www.gmatprepnow.com/module/gmat ... /video/885

Cheers,
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by regor60 » Mon Jun 20, 2016 10:33 am
800_or_bust wrote:So I got this as Question 37 (of 37). I can't recall having seen a similar question in my studies (i.e. one that asks for an angle measure in three dimensions), so I was kind of at loss. I guessed what might be the most obvious answer, but it was wrong. And I'm still having a difficult time conceptualizing the correct answer. Any insight?
What the other guys said and you can view this as an equilateral triangle rotated 45 degrees about an axis parallel with PR going through point Q
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by Matt@VeritasPrep » Thu Jun 23, 2016 4:11 pm
Draw diagonal PR. Since each side of the triangle is a diagonal of the same length -- they each are diagonals of the same-sized square -- each of the triangle is the same, making it equilateral, with angles of 60°.

Neat Q, very typical GMAT: you can solve it in 5 seconds with the right approach (and minimal math!), but it can take an eternity if you don't think to draw the line.
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by evs.teja » Wed Jun 29, 2016 2:07 pm
Brent@GMATPrepNow wrote:
800_or_bust wrote: the cube shown below, what is the degree measure of Angle PQR?

(a) 30
(b) 45
(c) 60
(d) 75
(e) 90

OA: C
If we draw a line connecting points P R, we see we that triangle PQR must be an equilateral triangle, which means all 3 angles (including angle PQR) must be 60 degrees each.

Answer: C
Dear Brent,
I understood your solution but am in a dilemma, No matter whichever method I use I should get the same answer right ?
When I tried to solve this question via this method am getting 90 degrees , which is wrong but am not able to find out exactly where am I going in the wrong direction.
If I consider PQS as a triangle where S is corner between point P R.
I know a fact that it is an isosceles triangle
where angle PSR= 90
PS = SQ
therefore Angle SPQ = Angle SQP = 45
If I apply the same theory to triangle RSQ
Angle RQS = Angle SRQ = 45

Now Angle PQR = Angle PQS + Angle RQS = 90

Now I know this is wrong, sorry asking you such a dumb question :(.
But it will be really great if you help me out.

Regards
Teja.
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