Problem Solving

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

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.

GMAT assassins aren't born, they're made,
Rich

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,
Brent