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      Question

      Each question is followed by three statements I, II and

      III. You have to decide whether the data given in the statements are sufficient to answer the question. What is the present age of A? I. The present ages of A and B are in the ratio 5 : 3. Four years from now, the sum of their ages will be 64 years. II. B is 8 years younger than A. III. Six years ago, the ratio of the ages of A and B was 7 : 5.
      A If the data in statement I alone are sufficient, but the data in statements II and III alone are not sufficient. Correct Answer Incorrect Answer
      B If the data in statement II alone are sufficient, but the data in statements I and III alone are not sufficient. Correct Answer Incorrect Answer
      C If the data in statement III alone are sufficient, but the data in statements I and II alone are not sufficient. Correct Answer Incorrect Answer
      D If the data in any two of the three statements together are sufficient, but no single statement alone is sufficient. Correct Answer Incorrect Answer
      E If the data in all three statements together are necessary to answer the question; even any two statements together are not sufficient. Correct Answer Incorrect Answer

      Solution

      ATQ, Let present ages be A and B. Statement I: A : B = 5 : 3 ⇒ A = 5k, B = 3k Four years from now: A + 4 + B + 4 = 64 ⇒ (5k + 4) + (3k + 4) = 64 ⇒ 8k + 8 = 64 ⇒ 8k = 56 ⇒ k = 7 So A = 5k = 35, B = 21. A is uniquely determined. I alone is sufficient. Statement II: A = B + 8 Infinitely many (A, B) pairs ⇒ A not unique. II alone is not sufficient. Statement III: Six years ago: (A − 6) : (B − 6) = 7 : 5 ⇒ 5(A − 6) = 7(B − 6) ⇒ 5A − 30 = 7B − 42 ⇒ 5A − 7B = −12 Single linear equation in two variables ⇒ many solutions ⇒ A not unique. III alone is not sufficient. Thus, only statement I alone is sufficient.

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