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      Question

      How many numbers in the range from 50 to 500 are divisible

      by 3, 6, and 9?
      A 37 Correct Answer Incorrect Answer
      B 22 Correct Answer Incorrect Answer
      C 25 Correct Answer Incorrect Answer
      D 43 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ;

      If a number is a multiple of 3, 6, and 9, then the number is a multiple of the L.C.M of 3, 6, and 9.

      L.C.M of 3, 6, and 9 = 18

      Smallest multiple of 18 between 50 and 500 = 54

      Largest multiple of 18 between 50 and 500 = 486

      Common difference = 18

      Let the required number of terms be 'n'.

      So, 54 + (n - 1) Ă— 18 = 486

      Or, n - 1 = (486 - 54) Ă· 18 = 24

      So, n = 24 + 1 = 25

      So, there are 25 numbers between 50 and 500 which are multiples of 3, 6, and 9.

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