Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. Find the rate of interest per annum. (1) The amount invested by Payal is Rs. 8,000 and becomes Rs. 11,520 in 2 years at compound interest. (2) The amount invested by Payal is Rs. 8,000 and the difference between CI and SI at the same rate of interest in two years is Rs. 320.

  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 (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Both the statements alone are sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement 1: 11520 = 8000(1 + R/100)^2 leads to (1 + R/100)^2 = 1.44, so 1 + R/100 = 1.2, R = 20%. Statement 2: 320 = 8000(R/100)^2 leads to (R/100)^2 = 320/8000 = 0.04, R = 20%. Both are sufficient alone.

AI explanation

To find the rate from statement (1), use the compound interest formula Amount = Principal * (1 + r/100)^n. Substituting the values gives 11520 = 8000 * (1 + r/100)^2, which simplifies to (1 + r/100)^2 = 1.44, yielding a rate of 20%, so statement (1) is sufficient. From statement (2), the difference between compound interest and simple interest for two years is P * (r/100)^2. Substituting the known values gives 320 = 8000 * (r/100)^2, which simplifies to (r/100)^2 = 0.04, yielding a rate of 20%, so statement (2) is also sufficient. Both statements alone are sufficient.

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