Multiple choice

Reeve invests \$4,000 in two parts in two different investments at simple interest. How much more money will he invest at 5% simple interest than at 6% simple interest? (1) More money was invested at 6% simple interest than at 5% simple interest. (2) The yearly annual income from both the investments together is \$215.

  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
B Correct answer
Explanation

Let x be the amount at 5% and y be the amount at 6%. We have x + y = 4000. Statement 2 gives 0.05x + 0.06y = 215. This is a system of two linear equations with two variables, which is sufficient to solve for x and y, and thus the difference |x-y|. Statement 1 only gives a relationship between x and y without specific values, so it is insufficient.

AI explanation

The question asks for the difference between the two invested amounts, which equals the 5% investment minus the 6% investment. Statement 2 gives the equation 0.05x plus 0.06(4000 minus x) equals 215, which rearranges to 240 minus 0.01x equals 215, making 0.01x equal to 25. Solving for x gives \$2,500, so the other investment is \$1,500; this provides the exact numerical difference of $1,000. Statement 1 only provides a vague comparison without values, making statement 2 sufficient on its own to find the difference.

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