What is the area of quadrilateral ABCD?

A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D Statements (1) and (2) TOGETHER are NOT sufficient.

✓ Correct Answer: Option C

(1) ABCD is a rectangle, Perimeter = 2(L+W) = 40. L+W=20. Not sufficient as L and W are unknown. (2) Diagonal AC = 15. In a rectangle, L^2 + W^2 = (diagonal)^2, so L^2 + W^2 = 15^2 = 225. Not sufficient alone. Together: We have L+W=20 and L^2+W^2=225. Squaring (L+W)=20 gives L^2+2LW+W^2=400. Substitute L^2+W^2=225: 225+2LW=400, so 2LW=175. Area = LW = 175/2 = 87.5. Sufficient.

💡 Why is C) the correct answer?

The correct answer to the question "What is the area of quadrilateral ABCD?" is Option C: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient..

The other options — A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient., B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient., D) Statements (1) and (2) TOGETHER are NOT sufficient. — are incorrect for this GMAT Exam Prep question. As explained above: (1) ABCD is a rectangle, Perimeter = 2(L+W) = 40. L+W=20. Not sufficient as L and W are unknown. (2) Diagonal AC = 15. In a rectangle, L^2 + W^2 = (diagonal)^2, so L^2 + W^2 = 15^2 = 225. Not suffici…

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This 3-level GMAT Exam Prep question from the Data Insights topic is part of BrainForge Quiz's free exam preparation library. Each question includes the correct answer and a detailed explanation to help you understand the underlying concept, not just memorize the answer.

How to use this page: Read the question above, consider all four options (A through D), then check the highlighted correct answer and explanation. For active timed practice, start a free GMAT Exam Prep practice test or use flashcards for spaced repetition review.

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What is the area of quadrilateral ABCD?

✓ Correct Answer: Option C

📚 About This GMAT Exam Prep Practice Question

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