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If n = 3^8 – 2^8 which of the following is NOT a factor of n

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If n = 3^8 – 2^8 which of the following is NOT a factor of n [#permalink]

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New post 20 May 2012, 06:58
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If n = 3^8 – 2^8 which of the following is NOT a factor of n?

A. 97
B. 65
C. 35
D. 13
E. 5

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-3-8-2-8-which-of-the-following-is-not-a-factor-of-143986.html
[Reveal] Spoiler: OA
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Re: If n = 3^8 – 2^8 which of the following is NOT a factor of n [#permalink]

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New post 20 May 2012, 07:13
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3^8 - 2^8
= (3^4)^2 - (2^4)^2
=(3^4 + 2^4)(3^4 - 2^4)
=(81+16)(81-16)
=97*65
=97*13*5
Therefore, 35 is Not a factor of n.
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Re: If n = 3^8 – 2^8 which of the following is NOT a factor of n [#permalink]

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If n = 3^8 – 2^8 which of the following is NOT a factor of n?

A. 97
B. 65
C. 35
D. 13
E. 5

Apply \(a^2-b^2=(a-b)(a+b)\):

\(n = 3^8 - 2^8=(3^4-2^4)(3^4+2^4)=65*97=5*13*97\) --> 7 is not a factor of n, therefore 35=5*7 also is not a factor of n.

Answer: C.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-3-8-2-8-which-of-the-following-is-not-a-factor-of-143986.html
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Re: If n = 3^8 – 2^8 which of the following is NOT a factor of n [#permalink]

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New post 24 May 2012, 07:45
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Hi,

Another approach:
\((a^n - b^n)\) is divisible by a + b only when n is even.

Thus, \((3^8-2^8)\) will be divisible by
\(3^1+2^1\) = 5
\(3^2+2^2\) = 13
\(3^4+2^4\) = 97
\(3^8+2^8\) = ...

Since it is divisible by 5 & 13, it will be divisible by 65.

So, the answer is (C).

Regards,

Last edited by cyberjadugar on 24 May 2012, 10:06, edited 1 time in total.
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Re: If n = 3^8 – 2^8 which of the following is NOT a factor of n [#permalink]

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It will be important to remember the following for the test. It will help you simplify these type of questions:

1. (x+y)(x-y) = x^2-y^2
2. (x+y)(x+y) = x^2+2xy+y^2
3. (x-y)(x-y) = x^2-2xy+y^2

In this case, x = 3^4 and y = 2^4 and you will simplify with #1.
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Re: If n = 3^8 – 2^8 which of the following is NOT a factor of n [#permalink]

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New post 24 May 2012, 08:50
hmm interesting question! though i solved by cyberjadugar's method, i think the quadratic approach seems easier for this particular sum.
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Re: If n = 3^8 – 2^8 which of the following is NOT a factor of n [#permalink]

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cyberjadugar wrote:
Hi,

Another approach:
\((a^n - b^n)\) is divisible by a - b only when n is even.

Regards,


(a^n - b^n) is Always divisible by (a - b).
(a^n - b^n) is divisible by (a + b) Only if n is even.
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Re: If n = 3^8 – 2^8 which of the following is NOT a factor of n [#permalink]

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New post 24 May 2012, 10:07
BDSunDevil wrote:
cyberjadugar wrote:
Hi,

Another approach:
\((a^n - b^n)\) is divisible by a - b only when n is even.

Regards,


(a^n - b^n) is Always divisible by (a - b).
(a^n - b^n) is divisible by (a + b) Only if n is even.


Thanks for pointing this out..
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Re: If n = 3^8 – 2^8 which of the following is NOT a factor of n [#permalink]

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New post 05 Apr 2013, 07:18
cyberjadugar wrote:
Hi,

Another approach:
\((a^n - b^n)\) is divisible by a + b only when n is even.

Thus, \((3^8-2^8)\) will be divisible by
\(3^1+2^1\) = 5
\(3^2+2^2\) = 13
\(3^4+2^4\) = 97
\(3^8+2^8\) = ...

Since it is divisible by 5 & 13, it will be divisible by 65.

So, the answer is (C).

Regards,


It is not divisible by 3^8+2^8, only ^1,^2 and ^4
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Re: If n = 3^8 – 2^8 which of the following is NOT a factor of n [#permalink]

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New post 04 Aug 2013, 22:21
(3^8-2^8)
=(3-2)(3+2)(3^2+2^2)(3^4+2^4)
=1*5*13*97
35 is not a factor....so C
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Kaustubh

Re: If n = 3^8 – 2^8 which of the following is NOT a factor of n   [#permalink] 04 Aug 2013, 22:21
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