Multiple choice

Directions: The given question is followed by two statements I and II. You have to determine which of the statements is/are necessary/sufficient to answer the question. A bakery sold a total of 5 cakes and 3 pies for \$37.50. What was the price of the 5 cakes? I. If the price of the 5 cakes had been reduced by 15 percent and the price of the 3 pies had been reduced by 10 percent, the total price would have been \$32.50. II. The price of the 5 cakes was $12.50 more than the price of the 3 pies.

  1. Statement I ALONE is sufficient, but statement II alone is not sufficient.

  2. Statement II ALONE is sufficient, but statement I alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements I and II TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let C be price of 5 cakes, P be price of 3 pies. C + P = 37.50. Statement I: 0.85C + 0.9P = 32.50. This is a system of 2 equations with 2 variables, solvable. Statement II: C = P + 12.50. Substituting into C + P = 37.50 gives P + 12.50 + P = 37.50, also solvable.

AI explanation

Let the price of the 5 cakes be x and the price of the 3 pies be y, establishing the base equation x plus y equals 37.50. Statement I provides the equation 0.85x plus 0.90y equals 32.50, which can be solved simultaneously with the base equation to find x. Statement II provides the equation x minus y equals 12.50, which can also be solved simultaneously with the base equation to find x. Therefore, each statement alone is sufficient.

Keep practicing — related questions