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      Question

      Each question below is followed by two statements I and II. You have to decide whether the data given in the statements are sufficient to answer the question. What is the present age of Rahul? I. Rahul is 4 years older than twice the present age of his sister. The sum of their present ages is 34 years. II. Four years ago, the ratio of Rahul’s age to his sister’s age was 9 : 5.

      A If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient. Correct Answer Incorrect Answer
      B If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient. Correct Answer Incorrect Answer
      C If the data either in statement I alone or in statement II alone are sufficient to answer the question. Correct Answer Incorrect Answer
      D If the data in both statements I and II together are necessary to answer the question, but neither statement alone is sufficient. Correct Answer Incorrect Answer
      E If the data in both statements I and II together are not sufficient to answer the question. Correct Answer Incorrect Answer

      Solution

      ATQ, From I: Let Rahul’s age = R, sister’s age = S. R = 2S + 4 R + S = 34 Substitute R: (2S + 4) + S = 34 3S = 30 ⇒ S = 10, R = 24 Unique value for R ⇒ I alone is sufficient. From II: (R − 4) : (S − 4) = 9 : 5 ⇒ (R − 4)/(S − 4) = 9/5 ⇒ 5R − 20 = 9S − 36 ⇒ 5R − 9S = −16 Only one equation in two unknowns ⇒ infinitely many positive solutions. II alone is not sufficient.

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