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

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