Multiple choice

In a family there are 5 members, A, B, C, D and E. Find the present age of E. I. The average age of five family members is 36 years. II. The total age of A, B and E is 75 years. III. The present age of E is 12 years more than the age of D.

  1. The data in statements I alone is sufficient to answer the question, while the data in statement II and II is not sufficient to answer the question.

  2. The data in statements II alone is sufficient to answer the question, while the data in statement II and III is not sufficient to answer the question.

  3. The data in statements I and II together or in statement III alone is sufficient to answer the question.

  4. The data in all the statements I, II and III is not sufficient to answer the question.

  5. The data in all the statements I, II and III together is necessary to answer the question.
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D Correct answer
Explanation

From I: Total age = 5 × 36 = 180 years. From II: A + B + E = 75. From III: E = D + 12. We have 5 variables (A,B,C,D,E) but only 3 equations: A+B+C+D+E=180, A+B+E=75, E=D+12. From A+B+E=75 and total=180, we get C+D=105. With E=D+12, we still can't find E's value uniquely without more information. Data is insufficient.

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