These are sample practice MCQs created for exam preparation. These are NOT official exam questions.
What is the length of the diagonal of rectangle R? (1) The area of rectangle R is 48 (2) The ratio of length to width is 3:2
Question:
What is the length of the diagonal of rectangle R? (1) The area of rectangle R is 48 (2) The ratio of length to width is 3:2
What is the length of the diagonal of rectangle R? (1) The area of rectangle R is 48 (2) The ratio of length to width is 3:2
Options
Answer: (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
Explanation:
Statement (1): Area = 48, but many length-width combinations possible. Insufficient. Statement (2): l/w = 3/2, so l = 1.5w, but no actual dimensions. Insufficient. Together: l × w = 48 and l = 1.5w. So 1.5w² = 48, w² = 32, w = 4√2, l = 6√2. Diagonal = √(l² + w²) = √(72 + 32) = √104 = 2√26. Sufficient.
Explanation:
Statement (1): Area = 48, but many length-width combinations possible. Insufficient. Statement (2): l/w = 3/2, so l = 1.5w, but no actual dimensions. Insufficient. Together: l × w = 48 and l = 1.5w. So 1.5w² = 48, w² = 32, w = 4√2, l = 6√2. Diagonal = √(l² + w²) = √(72 + 32) = √104 = 2√26. Sufficient.
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