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    Question

    β€˜Z’ is a two digit number in which the unit place

    digit is β€˜P’ and the tens place digit is β€˜Q’. The value of β€˜P’ is smaller than the value of β€˜Q’. The product of P and Q is the multiple of three. The unit place digit of (P) 2Β  ,(P) 3 and (P) 4 is the same. The difference between the values of P and Q is 4. If the unit and tens place digit of the number β€˜Z’ are interchanged with each other, then which of the following is the nearest prime number greater than the newly formed two digit number (after interchanging digits).
    A 59 Correct Answer Incorrect Answer
    B 43 Correct Answer Incorrect Answer
    C 47 Correct Answer Incorrect Answer
    D 61 Correct Answer Incorrect Answer
    E 83 Correct Answer Incorrect Answer

    Solution

    β€˜Z’ is a two digit number in which the unit place digit is β€˜P’ and the tens place digit is β€˜Q’. So the number is β€˜QP’.Β  Β  Eq.(i) The value of β€˜P’ is smaller than the value of β€˜Q’. The product of P and Q is the multiple of three. PxQ = multiple of threeΒ  Β  Eq.(iii) The unit place digit of (P) 2Β  ,(P) 3 and (P) 4 is the same. When P = 1, 5 and 9 , then only the above given condition will be true. The difference between the values of P and Q is 4. From Eq.(ii) and the above given condition, (Q-P) = 4 When P = 1, then (Q-1) = 4 Q = 4+1 = 5 When P = 5, then (Q-5) = 4 Q = 4+5 = 9 When P = 9, then (Q-9) = 4 [This is not possible. Because in this case β€˜Q’ will be a two digit number.] So Z = QP β‡’ 51 and 95 Because of Eq.(iii), (Z = 51) will not be possible. So Z = 95 If the unit and tens place digit of the number β€˜Z’ are interchanged with each other, then the newly formed number = 59 The nearest prime number greater than the newly formed two digit number (after interchanging digits) = 61

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