KVPY 2019 SA Exam Previous Papers

Question : 7 of 80

Marks: +1, -0

Let N be the least positive integer such that whenever a non-zero digit c is written after the last digit of N, the resulting number is divisible by c. The sum of the digits of N is :

Validate

Solution:

Let the number be N
If we write c after the last digit now number is 10N + c
Now

c|10N + c ∀ c = 1, 2, ….., 9

⇒

c|10N ∀ c = 1, 2, ….., 9

⇒

c|N \for c = 4, 7, 9

Hence N is LCM of (4, 7, 9) = 252
so sum of digit = 9

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