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.
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- 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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