Multiple choice

Directions: The question given below is followed by two statements I and II. You are to determine whether the data given in the statement is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer according to the following codes: (a) If the question can be answered by using statement I alone but cannot be answered by using statement II alone. (b) If the question can be answered by using statement II alone but cannot be answered by using statement I alone. (c) If both statements I and II together are required to answer the question. (d) If the answer can be found by using any of the two statements alone. (e) If both the statements together are not sufficient to answer the question. A cart with front wheel smaller than rear wheel moves a distance of 800 ft. Find the revolutions made by the front wheel. I. The circumference of the front wheel is 25 ft and that of the rear wheel is 32 ft, which makes 7 more revolutions than that by the rear wheel. II. The circumference of the front wheel is 7 less than that of the rear wheel and makes 7 revolutions more than those made by the rear wheel.

  1. (a)

  2. (b)

  3. (c)

  4. (d)

  5. (e)

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A Correct answer
AI explanation

Statement I provides the circumference of the front wheel as 25 ft, so using the formula for revolutions equaling distance divided by circumference, the front wheel makes 800 divided by 25, or 32 revolutions. Statement II states the circumference of the front wheel is 7 less than that of the rear wheel and makes 7 more revolutions, which leads to the equation 800 divided by x equals 800 divided by (x + 7) plus 7, where x represents the circumference of the rear wheel; solving this complex equation without a calculator is impractical for determining the front wheel's exact revolutions. Therefore, the question can be answered by using statement I alone but cannot be answered by using statement II alone.