Question: What is the perimeter of quadrilateral Q?
(1) Q is a rectangle.
(2) The area of Q is 25.
- 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: 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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