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If n = 3^8 – 2^8 which of the following is NOT a factor of n [#permalink ]
20 May 2012, 05:58

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Question Stats:

58% (02:10) correct

42% (01:01) wrong

based on 162 sessions
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

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Re: If n = 3^8 – 2^8 which of the following is NOT a factor of n [#permalink ]
20 May 2012, 06:13
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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 ]
24 May 2012, 06:45
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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,

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Last edited by

cyberjadugar on 24 May 2012, 09:06, 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 ]
21 May 2012, 10:11
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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 ]
11 Aug 2013, 05:29
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Re: If n = 3^8 – 2^8 which of the following is NOT a factor of n [#permalink ]
24 May 2012, 07:50

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 ]
24 May 2012, 08:34

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 ]
24 May 2012, 09:07

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 ]
05 Apr 2013, 06:18

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 by3^1+2^1 = 53^2+2^2 = 133^4+2^4 = 973^8+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 ]
04 Aug 2013, 21:21

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