In the figure shown, what is the value of x ?

[BrandenF768]

Data Sufficiency

Link to figure: http://s1038.photobucket.com/user/brand ... z.png.html

In the figure shown, what is the value of x ?

(1) The length of line segment QR is equal to the length of line segment RS
(2) The length of line segment ST is equal to the length of line segment TU

[End of Question]

I ultimately just could not arrive at an explicit number for x. I understand that the given both (1) and (2) together, we have isosceles triangles, but I don't understand how you jump from that piece of information to the actual value of x. Please advise.

[tim]

First, you don't actually need to calculate x to answer a DS problem. However, I'm not sure you could convince yourself that the statements together are sufficient without pretty much solving for x anyway, so let's take it from there.

Consider quadrilateral PQSU:
90 + PQS + x + SUP = 360

From the two triangles you've identified as isosceles:
RSQ = RQS = 180 - PQS
TSU = SUT = 180 - SUP

Now use this fact:
RSQ + x + TSU = 180

and sub in the information from the previous pair of equations:
180 - PQS + x + 180 - SUP = 180

Add this to the top equation:
90 + PQS + x + SUP + 180 - PQS + x + 180 - SUP = 360 + 180
2x + 450 = 540
2x = 90
x = 45

I'm not saying this is the fastest way to do it, but it works. If you're just looking for a fast way to realize x is calculable without calculating it, consider that x plus two angles is 180, and x plus the supplements of those two angles is 270. From here you may be able to see that you can solve for x, but if you don't, you HAVE to do something more concrete like what I did above.

[RonPurewal]

PLEASE search the forum before posting. thank you.

https://www.manhattanprep.com/gmat/foru ... tml#p10100