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InterviewSolution
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How many positive integers less than 1000 are 6 times the sum of their digits? (a) 0 (b) 1 (c) 2 (d) 3 |
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Answer» Answer: B. Number less than 1000 can write abc =100a + 10b +c where a, b, c ∈ {0,1 2 3....... 9 } and a+b+c > 0 The sum of digits of this number is ( a+b+c). . Given, 100a+10b+c= 6 (a+b+c) ∴ 94a+ 4b -5c = 0 Clearly, a > 0. No solution ∴ a = 0 then 4b = 5c This is possible only b = 5 and c = 4 ∴Number is 54. Hence, only one number i.e., 54. |
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