Multiple choice

Passage

Directions: The following question is accompanied by three statements (I), (II), and (III). You have to determine which statement(s) is/are sufficient/necessary to answer the question.

Ratio of the age of A to the age of C is 3 : 5. What is the age of C? I. A is 3 years younger than B. II. Difference between the ages of A and C is 10 years. III. C is 7 years older than B.

  1. Only I and II

  2. Only III

  3. Only II alone or only I and III together

  4. Only III and either I or II

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

We have A/C = 3/5. To find C, we need the value of A or the difference between A and C. Statement II gives A-C = 10 (or C-A = 10), which allows solving for C. Statement I and III together give A = B-3 and C = B+7, so C-A = 10, which also allows solving for C. Thus, II alone or I and III together are sufficient.

AI explanation

Let the ages of A and C be 3x and 5x. Statement II gives the difference as 10 years, so 5x - 3x = 10, which means x = 5 and C is 25 years old. Using statements I and III, we know A is 3 years younger than B, and C is 7 years older than B, meaning C is 4 years older than A, which confirms the 10-year difference found in the ratio and solves the problem. Therefore, statement II alone or statements I and III together are sufficient.

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