Multiple choice

Directions: The following problem consists of a question and two statements giving certain data. You have to decide whether the data given in the statements is sufficient for answering the question. Choose the appropriate option. Is the perimeter of square S greater than the perimeter of equilateral triangle T? (A) The ratio of the length of a side of S to the length of a side of T is 4 : 5. (B) The sum of the lengths of a side of S and a side of T is 18.

  1. Statement (A) alone is sufficient but statement (B) alone is not.

  2. Statement (B) alone is sufficient but statement (A) alone is not.

  3. Both (A) and (B) together are sufficient, but neither of them alone is sufficient.

  4. Both statements alone are sufficient.

  5. Both (A) and (B) together are not sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Perimeter of square S = 4s. Perimeter of triangle T = 3t. We want to know if 4s > 3t. Statement (A) gives s/t = 4/5, so s = 0.8t. Then 4s = 4(0.8t) = 3.2t. Since 3.2t > 3t, statement (A) is sufficient.

AI explanation

Let the side of the square be 4x and the side of the triangle be 5x based on the ratio in statement A. The perimeter of the square is 16x and the perimeter of the triangle is 15x. Since 16x is always greater than 15x for any positive side length, statement A alone is sufficient to answer the question.

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