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Could you pls help me to solve one doubt. It will be great help. I do not have question in formal format. But it is something like below.
Question
Variable X is positive integer. When X is divided by 4, 6, 7 & 9, in each case remainder is 3. When X is divided by 13 remainder is 0. Find smallest value of X.
Answer is 507.
Question
Variable X is positive integer. When X is divided by 4, 6, 7 & 9, in each case remainder is 3. When X is divided by 13 remainder is 0. Find smallest value of X.
Answer is 507.
What does "when X is divided by 4, 6, 7 & 9, in each case remainder is 3" imply?
It means, if we reduce X by 3, we should have a number which is divisible by all - 4, 6, 7 and 9.
Since we are looking for the smallest such number, let's find the LCM of these numbers.
LCM of 4, 6, 7 and 9 is 4*7*9 = 252
252 and all its multiples are completely divisible by 4, 6, 7 and 9. If we add 3 to 252 or any of its multiples, they will always leave a remainder of 3 when divided by 4, 6, 7 or 9.
So X should be of the form 252n + 3.
If n = 1, X = 255. But 255 is not divisible by 13.
If n = 2, X = 507. 507 is divisible by 13 so it is the smallest such number.
28 Dec 2019, 04:33
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