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

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If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink] New post 12 Dec 2012, 04:42
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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
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Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink] New post 12 Dec 2012, 04:46
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Walkabout wrote:
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.
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Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink] New post 14 Dec 2012, 02:19
Ans:

we will apply the formula a^2-b^2 here and expand the equation . in the end we get (3-2)(3+2)(3^2+2^2)(3^4+2^4)= 1x5x13x97 , therefore the answer is (C).
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Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink] New post 06 Apr 2013, 05:28
3^8 - 2^8
=(3^4 + 2^4)(3^4 - 2^4)
=(3^4 + 2^4)(3^2 + 2^2)(3^2 - 2^2)
=(3^4 + 2^4)(3^2 + 2^2)(3 + 2)(3 - 2)
=(81 + 16)(9 + 4)(3 + 2)(3 - 2)
=97*13*5*1

A. 97 -- Factor of the expression
B. 65 -- Factor of the expression
C. 35
D. 13 -- Factor of the expression
E. 5 -- Factor of the expression

Correct answer is C.
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Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink] New post 20 Apr 2014, 16:57
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Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink] New post 20 Apr 2014, 19:11
3^8 - 2^8

= 81^2 - 16^2

= 97 * 65

35 is not a factor; all other options stand fit

Answer = C
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Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink] New post 11 Sep 2014, 11:21
Walkabout wrote:
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




3^8=81^2
2^8 = 16^2

now 81^2-16^2 in the format a^2-b^2 = (a+b)(a-b)

so 97*65

from the options only 35 is not a factor of above value
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of   [#permalink] 11 Sep 2014, 11:21
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