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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.
4. 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.
In each case, x=45.
Thus, the two statements combined are SUFFICIENT to determine the value of x.
The correct answer is C.
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.
4. 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.
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
