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

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If n is a positive integer, is n^3 + 4n^2 – 5n divisible by [#permalink] New post 14 Jan 2013, 06:40
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If n is a positive integer, is n^3 + 4n^2 - 5n divisible by 8 ?

(1) n = 4b + 1, where b is a positive integer.

(2) n^2 – n is divisible by 24.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 14 Jan 2013, 06:42, edited 1 time in total.
Edited the question.
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Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by [#permalink] New post 14 Jan 2013, 06:49
If n is a positive integer, is n^3 + 4n^2 - 5n divisible by 8 ?

n^3 + 4n^2 - 5n=n(n^2+4n-5)=n(n-1)(n+5)

(1) n = 4b + 1, where b is a positive integer --> n(n-1)(n+5)=(4b+1)(4b)(4b+6)=(4b+1)(8b)(2b+3). Sufficient.

(2) n^2 – n is divisible by 24 --> n(n-1) is divisible by 24, so its also divisible by 8. Thus n(n-1)(n+5) is also divisible by 8. Sufficient.

Answer: D.

Hope it's clear.
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Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by [#permalink] New post 15 Jan 2013, 11:56
Hi Bunuel,

Can u plz xplain this step:

(4b+1)(4b)(4b+6)= (4b+1)(8b)(2b+3).Sufficient.

Thanks,
Shreeraj
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Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by [#permalink] New post 15 Jan 2013, 12:08
shreerajp99 wrote:
Hi Bunuel,

Can u plz xplain this step:

(4b+1)(4b)(4b+6)= (4b+1)(8b)(2b+3).Sufficient.

Thanks,
Shreeraj


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.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!

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Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by   [#permalink] 15 Jan 2013, 12:08
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