In Triangle PQR, if PQ = x, QR = x + 2, and PR = y GMAT Data Sufficiency

Question- In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of triangle PQR has the greatest degree measure?

(1) y = x+ 3
(2) x = 2

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.

“In triangle PQR, if PQ = x, QR = x + 2, and PR = y”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT 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 sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

It is asked In Δ PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of Δ PQR has the greatest degree measure?
Remember the rules
The triangle's key characteristics.
Always, the smallest angle is on the opposite side of the longest side.
Always, the greatest angle is on the longest side.
Any triangle side's length must be greater than the sum of the other two sides, but smaller than the positive difference of the other two sides.
Looking at statement 1
y = x + 3
PR is the longest side,
Therefore opposite the largest angle PQR.
This is Sufficient.
Looking at statement 2
x = 2
PQ=2 and QR=4
2 here, we cannot determine which side is the longest QR or PR.
This is insufficient
Statement 1 is sufficient and statement 2 is insufficient

Correct Answer: A

Approach Solution 2:

There is another approach to answering this question
The angle with the greatest degree measurement is the one we need to find. Keep in mind that the side with the greatest length is always opposite the angle with the greatest measure.
Statement One says:
y = x + 3
Knowing that y = x + 3 enables us to determine that PR is the triangle's longest side. As a result, we can conclude that angle PQR, which is opposite side PR, has the largest measure.
Therefore This is Sufficient.
Statement Two says:
x = 2
We don't know the value of y, so knowing the value of x alone is insufficient to provide an answer.
Statement 1 is sufficient and statement 2 is insufficient

Correct Answer: A

Approach Solution 3:

We need to determine the angle with the greatest degree measure. Remember that the angle with the greatest measure is always opposite the side of greatest length.

Statement One Alone:

y = x + 3

Since we know that y = x + 3, we know that PR is the longest side of the triangle. Thus, we know that angle PQR, the angle opposite side PR, is the angle with the largest measure. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

x = 2

Only knowing the value of x is not sufficient to answer the question because we don’t know the value of y.

Statement 1 is sufficient and statement 2 is insufficient

Correct Answer: A

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