Latest CAT Aptitude Question SOLUTION: N is a positive integer ,which when divided by 16 ,17,18 giver remainders of 6,7,8 resp.find the rem when N^2+5N+6 is divided by 12

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N is a positive integer ,which when divided by 16 ,17,18 giver remainders of 6,7,8 resp.find the rem when N^2+5N+6 is divided by 12

Asked In CAT arjun (12 years ago)

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Bankim  (12 years ago)

N is 4886 .

4886^2 +5*4886 +6 = 358094940 + 24430 +6 = 358119396 which is fully divisible by 12.

so remainder is zero.

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ramani katakam  (9 years ago)

L.C.M of 16,17,18 is 2448.to get remainders of 6,7,8 subtract 10 from L.C.M which is 2438.
so required num is 2438.
factorizing equation we get (N+2)(N+3)
substituting we get 2440*2441
on simplification we get 610*2441/3=>1*1/3=>remainder=1
as we cancelled 4 times remainder is 4.

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PRADEEP KUMAR V B  (6 years ago)

There is a small mistake in Mr. Ramani answer. I have corrected it.

L.C.M of 16,17,18 is 2448.to get remainders of 6,7,8 subtract 10 from L.C.M which is 2438.
so required num is 2438.
factorizing equation we get (N+2)(N+3)
substituting we get 2440*2441
on simplification we get 610*2441/3=>1*2/3=>remainder=2
as we cancelled 4 times remainder is 2*4 = 8.

or..
Don't cancel the 4.
R [2440/12]* R [2441/12] = 4 * 5 = 20 => r [20/12] = 8 (Ans)

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