Multiple choice

Directions: Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer: Find the rate of interest. I. A sum of money becomes double of itself at simple interest in 12.5 years. II. 5000 becomes 5832 in 2 years at compound interest.

  1. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. The data in statements I alone or in statement II alone is sufficient to answer the question.

  4. The data in both the statements I and II is not sufficient to answer the question.

  5. The data in both the statements I and II together is necessary to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: A = 2P, so P(1 + r/100 * 12.5) = 2P, which allows solving for r. Statement II: 5832 = 5000(1 + r/100)^2, which also allows solving for r. Both are sufficient independently.

AI explanation

From statement I, a sum doubles in 12.5 years, meaning the interest earned equals the principal, so using the simple interest formula R equals 100 times time divided by years gives R equals 100 divided by 12.5 which is 8 percent. From statement II, 5000 becomes 5832 in 2 years at compound interest, so 5832 divided by 5000 gives the square of the growth factor as 1.1664, and taking the square root yields the annual factor of 1.08, which corresponds to an 8 percent rate. Because either statement independently provides the interest rate, the data in statement I alone or in statement II alone is sufficient to answer the question.

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