Find the Sum of Digits of x :

Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves no remainder, The sum of digits of x is

  1. 18
  2. 21
  3. 22
  4. 24
Anurag Mishra Professor Asked on 26th October 2015 in Maths.
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  • 1 Answer(s)

    Answer is (1): 18

    Explanation:-
    Find the LCM of 5, 6, 7 and 8
    Factors of 5 = 1 x 5
    Factors of 6 = 2 x 3
    Factors of 7 = 1 x 7
    Factors of 8 = 2 x 2 x 2 

    Then, the LCM of 5, 6, 7 and 8 = 2 x 2 x 2 3 x 5 x 7
     = 840
    The second multiple of 840 = 2 x 840 
    = 1680

    Leaves a remainder 3 in each case.
    Then, the number = 1680 + 3
     = 1683,  which is divisible by 5, 6, 7 and 8 leaves a remainder 3 in case each but when divide by 9 leaves no remainder.

    Then, the sum of digits of 1683 = 1 + 6 + 8 + 3
     = 18

    Hence, the answer is (1) 18.

    Monis Rasool Professor Answered on 28th October 2015.
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