Question: In an isosceles triangle PQR, how many degrees is ∠ P

(1) The measurement of angle R is 100 degree.
(2) The measurement of angle Q is 40 degree.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: A

Solution and Explanation:
Approach Solution 1:
Statement 1

This has to be the solitary angle. There cannot be 2 angles of 100 degrees in a triangle.

So the two equal angles each will be 40 degrees.
Sufficient.

Statement 2

Now 40 can be one of the two equal base angles. Then angle P = 40 degrees

Or 40 can be the vertex angle. Other two angles are 70 degrees each. Then angle P will be 70 degrees
Not Sufficient

Approach Solution 2:
In terms of the condition
1) If R= 100, p= some degree and Q= 40. The answer is unique and the condition is sufficient.

In terms of the condition
2) If Q=40, both P= 40 and P= 50 are possible. The answer is not unique and the condition is not sufficient.

Approach Solution 3:
(1) The measurement of angle R is 100 degrees.

The 2 equal angles should be 40 each
Therefore ∠ P = 40
Sufficient

(2) The measurement of angle Q is 40 degrees.

∠ P can be equal to 40 if ∠ P= ∠ Q
else ∠ P can also be equal to 70
Not sufficient

“In an isosceles triangle PQR, how many degrees is ∠ P”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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