Multiple choice

Alice lent \$1200 at simple interest for as many years as the rate of interest. What is the rate of interest? (1) She paid \$1632 by the end of the loan period. (2) She paid $432 as simple interest by the end of the loan period.

  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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple interest is calculated as I = (P * R * T) / 100. Given P = 1200 and T = R, the formula becomes I = (1200 * R * R) / 100 = 12 * R^2. Both statements provide the value of I (either directly or via the total amount), allowing for the calculation of R.

AI explanation

Statement (1) provides the total amount paid, meaning the interest earned is 1632 minus the 1200 principal, which equals 432. Statement (2) directly provides the same interest value of 432. Using the Simple Interest formula where time equals the rate, we set 432 = (1200 * r * r) / 100, which simplifies to 36 = r squared, giving a rate of 6 percent, so each statement alone is sufficient.

Keep practicing — related questions