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by GMATGuruNY » Sat Sep 28, 2013 5:15 pm
Image

Neither statement alone is sufficient to determine the value of x.
When we combine the two statements, here's an efficient way to determine whether we have sufficient information to determine the value of x:

1. Plug in values for the angle measurements, satisfying the constraints in the problem and the rules of geometry.
2. Determine the value of x.
3. Plug in a different set of values, again satisfying the constraints in the problem and the rules of geometry.
3. Determine the value of x.

If the value of x is the same in each case, the two statements combined are SUFFICIENT.
If the value of x changes, the two statements combined are INSUFFICIENT.

Below are two sets of angle measurements that satisfy the rules of geometry and the constraints in the two statements:

∠PRT + ∠PTR = 90 because triangle PRT is a right triangle.
Since QR=RS, ∠RQS = ∠RSQ.
Since ST=TU, ∠UST = ∠SUT.
Since the sum of angles that form a straight line is 180, x = 180 - ∠RQS - ∠UST.

Image

In each case, x=45.
Thus, the two statements combined are SUFFICIENT to determine the value of x.

The correct answer is C.
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by Rohit.Singh » Mon Sep 30, 2013 10:23 am
How do we know angle RPT is 90 degree?
GMATGuruNY wrote:Image

Neither statement alone is sufficient to determine the value of x.
When we combine the two statements, here's an efficient way to determine whether we have sufficient information to determine the value of x:

1. Plug in values for the angle measurements, satisfying the constraints in the problem and the rules of geometry.
2. Determine the value of x.
3. Plug in a different set of values, again satisfying the constraints in the problem and the rules of geometry.
3. Determine the value of x.

If the value of x is the same in each case, the two statements combined are SUFFICIENT.
If the value of x changes, the two statements combined are INSUFFICIENT.

Below are two sets of angle measurements that satisfy the rules of geometry and the constraints in the two statements:

∠PRT + ∠PTR = 90 because triangle PRT is a right triangle.
Since QR=RS, ∠RQS = ∠RSQ.
Since ST=TU, ∠UST = ∠SUT.
Since the sum of angles that form a straight line is 180, x = 180 - ∠RQS - ∠UST.

Image

In each case, x=45.
Thus, the two statements combined are SUFFICIENT to determine the value of x.

The correct answer is C.
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