Find the Sum of the Digit of x :

Let x be the smallest number, which when added to 2000 makes the resulting number divisible by 12,16,18 and 21. The sum of the digit of x is

  1. 5
  2. 7
  3. 4
  4. 6
Anurag Mishra Professor Asked on 26th October 2015 in Maths.
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1 Answer(s)

Answer is (2): 7

Explanation:-
Find the LCM of 12, 16, 18 and 21
Factors of 12 =  2 x 2 x 3
Factors of 16 = 2 x 2 x 2 x 2
Factors of 18 = 2 x 3 x 3
Factors of 21 =  3 x 7
Then, the LCM of 12, 16, 18 and 21 = 2 x 2 x 2 x 2 x 3  x 3  x 7
 =  1008
The second multiple of 1008 = 2 x 1008 
 = 2016

Then, the value of X = 2016 – 2000
 = 16

So, the of the digits 16 = 1 + 6 
 = 7

Hence, the answer is (2) 7. 

Monis Rasool Professor Answered on 28th October 2015.
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