Multiple choice

Directions: In the following question, you have to find out which of the following statements is/are sufficient to find the answer. The ratio of the ages of A and B 8 years from now will be 8 : 7. What is the ratio of the present ages of A and B? I. Sum of the present ages of A and B is 44. II. A is 4 years older than B. III. Product of their ages 8 years before was 192.

  1. Only I

  2. Only I and III

  3. Only I and II

  4. Any one statement

  5. Any two statements
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the present ages be A and B. The ratio (A+8)/(B+8) = 8/7 implies 7A + 56 = 8B + 64, or 7A - 8B = 8. Statement I (A+B=44) provides a second equation, allowing us to solve for A and B. Statement II (A=B+4) also provides a second equation. Statement III (A-8)(B-8)=192 provides a quadratic relation that can also be solved. Since any one of these statements provides a unique solution, any one is sufficient.

AI explanation

Let the ages of A and B after 8 years be 8x and 7x, making their current ages 8x - 8 and 7x - 8. Statement I gives their sum as 44, allowing you to form an equation and find x. Statement II gives an age difference of 4, which also uniquely solves for x. Statement III provides a product equation for their ages 8 years ago, which when solved gives x, meaning any one statement alone is sufficient.

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