If n is a positive integer, is n^3 + 4n^2 – 5n divisible by

Sure.

Factor out 2 from 4b+6: (4b+1)(4b)(4b+6)=(4b+1)(4b)(2)(2b+3)=(4b+1)(8b)(2b+3).

Hope it's clear.

The only things to point out or add if you will are the following

Question stem = Factorizing one gets (n)(n+5)(n-1)

Statement 1

n = 4b+1

Replacing (4b+1)(4b+6)(4b)

Now (4b) and (4b+1) are consecutive integers

Therefore one of them must be odd and one even, obviously 4b is the even one

So 4b is a multiple of 4 and 4b +6 is even so we have a multiple of 8

Statement 2

n(n-1) divisible by 24 means that either n or n-1 is divisible by 3 and that one of them, the even one, will be divisible by 8

Since we have both terms in our initial factorization then YES it is a multiple of 8

Hence D

Is this clear?

PS. The answer choice button tab in GMAT Club is awesome!

Cheers!
J

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