Multiple choice

Directions: The question given below is followed by three statements numbered I, II and III. Read all the statements carefully and decide which of them is/are sufficient to answer the given question. Choose the correct alternative accordingly. Is the ratio of the present ages of P and Q greater than 5 : 6? I. The ratio of the ages of P and Q, 5 years ago, was 5 : 6. II. P is, at present, 30 years old. III. The ratio of the ages of P and Q, 5 years from now, will be 6 : 7.

  1. Only I

  2. Only II

  3. Only III

  4. Any two of the given three

  5. Even I, II and III together are not sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let P and Q be p and q. I: (p-5)/(q-5) = 5/6 => 6p-30 = 5q-25 => 6p-5q = 5. We want to know if p/q > 5/6. From 6p-5q=5, p/q = (5+5q)/6q = 5/6q + 5/6. Since 5/6q > 0, p/q > 5/6. Statement I is sufficient.

AI explanation

To determine if the present ratio of P and Q is greater than 5 to 6, we need to know if adding the same number to both parts of the ratio increases or decreases its value. Statement I says that 5 years ago their ratio was exactly 5 to 6, which means adding 5 years to both their ages will make their present ratio greater than 5 to 6. Statement III shows the ratio 5 years from now will be 6 to 7, which is less than 5 to 6, confirming the ratio is decreasing over time, but statement I alone directly proves the present ratio is greater. Therefore, only statement I is sufficient to answer the question.

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