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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 two-digit number N?
      I. The sum of the digits of N is 11.
      II. The product of the digits of N is 24.

      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, Let tens digit = a, units digit = b. From I: a + b = 11 Possible (a, b) digit pairs: (2,9), (3,8), (4,7), (5,6), (6,5), (7,4), (8,3), (9,2) ⇒ Numbers: 29, 38, 47, 56, 65, 74, 83, 92 Not unique ⇒ I alone is not sufficient. From II: a × b = 24 Possible (a, b) digit pairs: (3,8), (8,3), (4,6), (6,4) ⇒ Numbers: 38, 83, 46, 64 Not unique ⇒ II alone is not sufficient. Using I and II together: We need (a, b) such that: a + b = 11 and a × b = 24 Check the pairs from product condition: (3,8) ⇒ sum = 11 (valid) ⇒ N = 38 (8,3) ⇒ sum = 11 (valid) ⇒ N = 83 (4,6) ⇒ sum = 10 (invalid) (6,4) ⇒ sum = 10 (invalid) There are two possible numbers (38 and 83) ⇒ not unique. Even together, the data are not sufficient.

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