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stolyar
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N is a certain integer. When divided by 3, it leaves no remainer. When divided by 5, it leaves a remainer of 2. When divided by 11, it leaves a remainer of 8.

(A) Find the smallest N.
(B) Find the next N.



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Jasdeep
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The number should end with a unit digit of either 2 or 7. Therefore, the number when divided by 11 should end in 4 or 9 on which 8 should be added to get the number N. Such number is 162. The next number should be 162+165 and so on

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stolyar
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my approach

N+3 is div by 3
N+3 is div by 5
N+3 is div by 11

So, N=K*LCM(3, 5, 11)-3, where K is a positive integer.
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Jasdeep
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YOur approach is less time consuming. In such questions, observation is very much required like the one you have made out: N required 3 only to be divisible by 3,5,11. LCM comes handy here. I tried with LCM but then could not use your observation.Therefore, used the other method.



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