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      Question

      A number leaves a remainder 5 when divided by 8. If 3 is

      added to the number, the result becomes exactly divisible by both 12 and 16. What is the smallest such number?
      A 30 Correct Answer Incorrect Answer
      B 45 Correct Answer Incorrect Answer
      C 33 Correct Answer Incorrect Answer
      D 77 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      If 3 is added to the number, the result is divisible by both 12 and 16. LCM of 12 and 16 = 48 So, number + 3 = 48 Smallest such number = 48 - 3 = 45 Check: 45 divided by 8 leaves remainder 5 So, the condition is satisfied. Hence, the correct answer is 45.

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