Question: What is the perimeter of quadrilateral Q?

(1) Q is a rectangle.
(2) The area of Q is 25.

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: E

Solution and Explanation:
Approach Solution 1:
Statement 1:
Insufficient

Statement 1:
If Q is square, P = 20
If Q is rectangle of 25x1, P=52
Insufficient

St1&2:
Same scenarios as statement 2
Insufficient

Approach Solution 2:
The key concept is to understand that the perimeter/area ratio decreases as the length and breadth of a rectangle converge: The minimum perimeter/area ratio is when the rectangle is a perfect square. Therefore, for a given area of a rectangle, its perimeter can be known only if the ratio of the length and breadth are known.

Statement (1) alone is insufficient, since we don't know the area nor its ratio;
Statement (2) alone is insufficient, since we don't know the type of quadrilateral, nor its perimeter, nor the ratio of the perimeter;
Both statements are insufficient also since we still don't know the ratio of the length and breadth.

Approach Solution 3:
Target question: What is the perimeter of quadrilateral Q?
If we recognize that each statement alone is not sufficient, we can jump straight to......

Statements 1 and 2 combined

There are several quadrilaterals that satisfy BOTH statements. Here are two:

Case a: Q is a rectangle with width 1 and length 25. In this case, the perimeter of quadrilateral Q is 1 + 1 + 25 + 25 = 52
Case b: Q is a rectangle with width 5 and length 5. In this case, the perimeter of quadrilateral Q is 5 + 5 + 5 + 5 = 20

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

“What is the perimeter of quadrilateral Q?”- is a topic of the GMAT Quantitative reasoning section of GMAT. 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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