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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]  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]  12 Dec 2012, 04:46
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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.

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Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink]  26 Nov 2014, 04:17
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keysx015 wrote:
Bunuel, Do you have a list of problems like this. More specifically, problems that require me to break down exponents. I never see it until afterwards and then it makes perfect sense. I feel like need more practice.

Search the pages below.
DS Divisibility/Multiples/Factors questions to practice: search.php?search_id=tag&tag_id=354
PS Divisibility/Multiples/Factors questions to practice: search.php?search_id=tag&tag_id=185
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Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink]  30 Dec 2015, 20:22
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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

Just want to point out an observation here: If you are short on time, you can eliminate 3 options in seconds and your probability of getting the right answer goes to 50%. (B), (D) and (E) can certainly not be the answer.

Here's why: Say, 65 is the answer (it is not a factor of n). But then at least one of 13 and 5 is not a factor of n because 65 = 13*5. Then there would be at least two correct answers but that is not possible. This means 65 is a factor of n and hence 13 and 5 both need to be factors of n too.
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Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink]  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]  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

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Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink]  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]  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

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Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink]  11 Sep 2014, 11:21
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
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If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink]  25 Nov 2014, 17:17
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Bunuel, Do you have a list of problems like this. More specifically, problems that require me to break down exponents. I never see it until afterwards and then it makes perfect sense. I feel like need more practice.
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Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink]  28 Dec 2015, 21:42
Hello from the GMAT Club BumpBot!

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If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink]  30 Dec 2015, 03:23
Expert's post
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

Whenever you see anything of the form $$a^2 - b^2$$, write it as (a-b)*(a+b)

Coming to the question at hand,
n = $$3^8 - 2^8$$ =$$(3^4 - 2^4) * (3^4 + 2^4)$$

Again applying the same rule on $$(3^4 - 2^4)$$ ,
n = $$(3^2 - 2^2)*(3^2 + 2^2)*(3^4 + 2^4)$$ = $$(3 - 2)*(3+2)*(3^2 + 2^2)*(3^4 + 2^4)$$
n = 1*5*(9+4)*(81+16) = 1*5*13*97

On checking the options, we see that 35 cannot be formed by the factors of n, hence the correct answer

Option C
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If n = 3^8 - 2^8, which of the following is NOT a factor of   [#permalink] 30 Dec 2015, 03:23
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