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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