Multiple choice

Mr. and Mrs. Clare invested \$24,000 in money market and index funds such that they earned the same amount of simple interest per annum from both investments. How many dollars did Mr. and Mrs. Clare invest in index funds? (1) Money market paid 6% simple interest, and index funds paid 12% simple interest per annum. (2) Mr. and Mrs. Clare invested less than \$12,000 in money market.

  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
A Correct answer
Explanation

Let M be money market and I be index funds. M + I = 24000. Interest: 0.06M = 0.12I, so M = 2I. Substituting: 2I + I = 24000 => 3I = 24000 => I = 8000. Statement 1 gives the rates, which is sufficient. Statement 2 is not needed.

AI explanation

Let the investment in money market be M and in index funds be I, so M plus I equals 24000. From statement (1), the simple interest from both are equal, meaning M times 0.06 equals I times 0.12. This simplifies to M equals 2I, and substituting this into the total investment gives 2I plus I equals 24000, so the index funds investment is $8000. Statement (2) provides an inequality rather than a specific rate, making it insufficient to solve for the amounts. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

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