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 amount at the end of the third year at compound interest. (1) At compound interest, the amount at the end of the first year is Rs. 2500 and the amount at the end of the second year is Rs. 3000. (2) The amount at the end of the second year is Rs. 3000 and the rate of interest is 20% compound interest.

  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. Each statement alone is 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 gives amounts at end of year 1 and 2, allowing calculation of rate (r = (3000-2500)/2500 = 20%) and principal, thus finding the amount at year 3. Statement 2 gives the amount at year 2 and the rate, which is sufficient to calculate the amount at year 3. Both are independently sufficient.

AI explanation

Using the first statement, the compound interest rate is calculated as the difference between the second and first year amounts divided by the first year amount, giving (3000 minus 2500) divided by 2500, which equals 20 percent. Multiplying the second year amount of 3000 by 1.20 gives the third year amount of 3600. Using the second statement, we already know the second year amount is 3000 and the rate is 20 percent, so multiplying 3000 by 1.20 also gives 3600. Since the amount can be found using either statement independently, each statement alone is sufficient.

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