Multiple choice

David borrowed a total of \$12,000 from two moneylenders, Lender A and Lender B, at different simple annual interest rates. He agreed to repay both loans in one year, such that each lender earned the same amount of interest. How much did David borrow from Lender A? (1) Lender A charged 4% simple annual interest, and Lender B charged 8% simple annual interest. (2) David borrowed more than \$5,000 from Lender A.

  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 alone is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
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A Correct answer
Explanation

Let A be the amount borrowed from Lender A, and (12000-A) from Lender B. Interest: 0.04*A = 0.08*(12000-A). This is one equation with one variable, so statement (1) is sufficient. Statement (2) provides an inequality, which is not sufficient to find a unique value for A.

AI explanation

Let the amount borrowed from Lender A be A, so the amount from Lender B is 12000 - A. Using statement (1), the simple interest formula gives the equality of interest: A * 0.04 * 1 = (12000 - A) * 0.08 * 1. Solving 0.04A = 960 - 0.08A yields 0.12A = 960, so A = 8000. Statement (2) only says A > 5000, which is not enough to find a single value for A. Therefore, statement (1) alone is sufficient.

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