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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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20 May 2012, 06:58
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Difficulty:

45% (medium)

Question Stats:

57% (02:14) correct 43% (01:05) wrong based on 383 sessions

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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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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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21 May 2012, 11:11
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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]

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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.

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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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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24 May 2012, 09:34
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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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24 May 2012, 10:07
BDSunDevil 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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05 Apr 2013, 07:18
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.

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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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

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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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11 Aug 2013, 06:29
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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.

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] 11 Aug 2013, 06:29
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