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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]

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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
[Reveal] Spoiler: OA
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Joined: 02 Sep 2009
Posts: 43853
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink]

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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]

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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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Posts: 419
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink]

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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]

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20 Apr 2014, 19:11
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$$3^8 - 2^8$$

$$= 81^2 - 16^2$$

= 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]

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11 Sep 2014, 11:21
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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

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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Joined: 17 Aug 2014
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If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink]

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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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Posts: 43853
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink]

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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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GMAT 1: 760 Q50 V44
If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink]

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30 Dec 2015, 03:23
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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

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

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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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 2192 Location: United States (CA) Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink] ### Show Tags 10 Jun 2016, 10:52 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED 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 We would never be asked to calculate 3^8 or 2^8, so we must approach this problem not as an arithmetic question but as an algebraic one. The first thing we must recognize is that we are being tested on the algebraic factoring technique called the "difference of squares." Recall that the general form of the difference of squares is: x^2 – y^2 = (x + y)(x – y) Similarly, we can treat 3^8 – 2^8 as a difference of squares, which can be expressed as: n = (3^4 + 2^4)(3^4 – 2^4) We can further factor 3^4 – 2^4 as an additional difference of squares, which can be expressed as: (3^2 + 2^2)(3^2 - 2^2) This finally gives us: n = 3^8 - 2^8 = (3^4 + 2^4)(3^2 + 2^2)(3^2 - 2^2) The numbers are now easy to calculate: n = (81 + 16)(9 + 4)(9 – 4) n = (97)(13)(5) We are being asked which of the answer choices is NOT a factor of n, which we have determined to be equal to the product (97)(13)(5). So we must find the answer choice that does not evenly divide into (97)(13)(5). Right away we see that 97, 13 and 5 are all factors of (97)(13)(5). This leaves us with 65 and 35. We should notice that (97)(13)(5) = (97)(65). Thus, 65 also is a factor of n. Only 35 is not. Answer is C. _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Manager Joined: 03 Jan 2017 Posts: 193 Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink] ### Show Tags 25 Mar 2017, 09:24 n=3^8-2^8 let's split it (3^4-2^4)*(3^4+2^4)=65*97 Then let's test the answers C is fine Senior Manager Joined: 06 Dec 2016 Posts: 253 Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink] ### Show Tags 25 Mar 2017, 18:25 My approach 3^8 - 2^8 (3^4)^2 - (2^4)^2 (81)^2 - (16)^2 6561 - 256 6305 Then I would process elimination (A) 97 - 6305/97 is an integer. Not the answer (B) 65 - 6305/65 is an integer. Not the answer (C) 35 - 6305/35 is not an integer. The answer (D) 13 - 6305/13 is an integer. Not the answer (E) 5 - 6305/5 is an integer. Not the answer. Director Joined: 02 Sep 2016 Posts: 786 Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink] ### Show Tags 01 Apr 2017, 03:41 1 This post received KUDOS n=3^8-2^8 Its a real time saver to learn algebraic identities. We know that: a^2-b^2= (a+b)(a-b) Let's use it in the above expression. Why did I get this idea? Because 8= 2*4 n= [(3^4)^2- (2^4)^2] n= (3^4+2^4)(3^4-2^4) n=(81+16)(81-16) n= (97)(65) n=97*13*5 97,13, 5, and 65 are factors of n. The answer is C. _________________ Help me make my explanation better by providing a logical feedback. If you liked the post, HIT KUDOS !! Don't quit.............Do it. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7947 Location: Pune, India Re: If n = 3^8 - 2^8, which of the following is NOT a factor of [#permalink] ### Show Tags 18 Jan 2018, 07:32 1 This post received KUDOS Expert's post VeritasPrepKarishma wrote: 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 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. Responding to a pm: Check here for the answer: https://gmatclub.com/forum/if-n-3-8-2-8 ... l#p1154050 What I have given above is the way to eliminate 3 options. That gives you a 50-50 probability of getting the answer (up from 20%). To get to the answer, we need to evaluate n (as done by Bunuel above). _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: If n = 3^8 - 2^8, which of the following is NOT a factor of   [#permalink] 18 Jan 2018, 07:32
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