What is the value of x? (1) {\m} \angle A C B=30^{\circ} (2) {\m} \angle A+\angle B=150^{\circ}

Correct Answer is : The problem can be solved using EITHER statement (1) only or statement (2) only.

Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself.

Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself.

The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2).

The problem can be solved using EITHER statement (1) only or statement (2) only.

The problem CANNOT be solved using statement (1) and statement (2) TOGETHER.

GMAT Quantitative Reasoning Practice Test 5

Question : 97 of 100

Marks: +1, -0

What is the value of x?

(1)

{\m} ∠ A C B=30^{∘}

(2)

{\m} ∠ A+∠ B=150^{∘}

Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself.
Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself.
The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2).
The problem can be solved using EITHER statement (1) only or statement (2) only.
The problem CANNOT be solved using statement (1) and statement (2) TOGETHER.

Validate

Solution:

In this problem, either statement is sufficient. Angle ACB is supplementary to x, so

180 − 30 = 150

degrees.
Statement (2) says that the sum of the two remote interior angle equal 150 degrees; this is equal to the exterior angle, x.
Note that the diagram is not drawn to scale so you should not rely on the diagram to calculate the answer.

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