Multiple choice

Emily and Michael each invested in a bond that pays simple interest at an annual rate of 8% for one year. How many more dollars did Emily invest than Michael? (1) In one year, Emily earned \$18 more in interest than Michael. (2) If the annual simple interest rate had been 12%, Emily would have earned \$27 more in interest than Michael in one year.

  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

Let E and M be the investments. Interest = P * r * t. (1) 0.08E - 0.08M = 18 => E - M = 18/0.08 = 225. (2) 0.12E - 0.12M = 27 => E - M = 27/0.12 = 225. Both statements independently provide the difference E - M.

AI explanation

The difference in interest earned is calculated by multiplying the difference in their principal amounts by the interest rate. Using statement 1, Emily earns 18 dollars more at an 8 percent rate, so the difference in their investments is 18 divided by 0.08, which equals 225 dollars. Using statement 2, the difference would be 27 dollars at a 12 percent rate, so the difference in their investments is 27 divided by 0.12, which also equals 225 dollars. Since each statement independently provides enough information to find the exact difference in their investments, each statement alone is sufficient.

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