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Source: — Data Sufficiency |

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by Rahul@gurome » Mon Nov 08, 2010 7:12 pm
First consider (1) alone.
It is given that QR is equal to RS.
We need to know x.
Obviously (1) alone is not sufficient because suppose we move point U more towards the right, S remaining the same, x will increase.
Next consider (2) alone.
It says ST is equal to TU.
Even (2) alone will not be sufficient because suppose we move point Q downwards, more towards point P, S remaining same, the value of x will decrease.
Next combine both statements together and check.
On combining, we have that QR = RS and ST = TU.
Let angle PTR be a.
So angle UST is (180 - a)/2 = 90 - a/2. (since triangle SUT is isosceles).
Angle PRT is 180 - (90 + a) = 90 - a.
So angle RSQ is {180 - (90 - a)}/2 = 45 + a/2.
Now 45 + a/2 + x + 90 - a/2 = 180.
Or x = 45.
So both statements together are sufficient to answer the question.

The correct answer is (C).
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by GMATMadeEasy » Thu Nov 11, 2010 12:35 pm
thanks. Makes sense.

What is the approach to hit such questions ,in general, ?
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by ajayrkp » Fri Nov 12, 2010 9:39 am
I have a little different approach, however, the same concept.

- Based on statement (1), I denote angles RQS=RSQ=a; We can not find angle x using this info. However, this gives us angle PRT=180-2a
- similarly, Based on statement (2), denote angles TUS=UST=b; and we get angle UTS=180-2b ... however, this statement along is not sufficient.

Combined together, we know angle PRT+PTR=90=180-2a+180-2b ==> a+b=135 ==> x=180-(a+b) = 45
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