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Expert replies
Source: — Problem Solving |

by Brent@GMATPrepNow » Sun Dec 14, 2008 9:45 am
You're right that neither statement (1) nor (2) are sufficient, so I'll jump to what happens when we combine both pieces of information.

From (1) we can conclude that angleRQS = angleRSQ
From (2) we can conclude that angleTUS = angleTSU

We also know that:
(angleRQS + angleRSQ + angleR) + (angleTUS + angleTSU + angleT) = 360

Here's the big part: angleR + angleT = 90 (since they must add to angleP to get 180 degrees)

So, we can conclude that (angleRQS + angleRSQ) + (angleTUS + angleTSU) = 270

Since angleRQS = angleRSQ and angleTUS = angleTSU, we can say that: angleRSQ + angleTSU = 135

Finally, since angleRSQ + angleTSU + angle X must add to be 180, we can conclude that angle x is 45

So the answer is E
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by ronniecoleman » Sun Dec 14, 2008 9:55 am
angle rqs = angle rsq = y

2y = 180 - angle prt

y = 90 - angle prt /2

Similarly

angle sut = angle ust = z

z= 90 - angle stu

y + z = 180- x

90 + 90 - ( prt + stu )

180- 90 = 90
x = 90

Hence both are together sufficient
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