Multiple choice

An amount of money was invested by Sam. What is the rate percent per annum? (1) Simple interest for 3 years on the amount of money is \$240. (2) Compound interest on the sum of money for 2 years is \$170.

  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
C Correct answer
Explanation

Statement 1: SI = PRT/100 -> 240 = P*R*3/100 -> PR = 8000. Cannot find R without P. Statement 2: CI = P((1+R/100)^2 - 1) = 170. Cannot find R without P. Together: PR = 8000 -> P = 8000/R. Substitute into CI: (8000/R) * (2R/100 + R^2/10000) = 170. This allows solving for R.

AI explanation

Statement (1) provides the equation 240 = (P * R * 3) / 100, which has two unknowns and cannot be solved alone. Statement (2) provides the compound interest equation 170 = P(1 + R/100)^2 - P, which also has two unknowns and cannot be solved alone. When solved together, you can substitute P = 8000/R from the first equation into the second equation to find both P and R, meaning both statements together are sufficient.

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