Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 29 Aug 2016, 21:22

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178
Followers: 4

Kudos [?]: 1893 [0], given: 0

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

### Show Tags

12 Dec 2012, 05:42
29
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

60% (02:33) correct 40% (01:51) wrong based on 894 sessions

### HideShow timer Statistics

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
Math Expert
Joined: 02 Sep 2009
Posts: 34496
Followers: 6297

Kudos [?]: 79888 [7] , given: 10022

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

### Show Tags

12 Dec 2012, 05:46
7
KUDOS
Expert's post
9
This post was
BOOKMARKED
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.

_________________
Intern
Joined: 24 Apr 2012
Posts: 48
Followers: 0

Kudos [?]: 21 [0], given: 1

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

### Show Tags

14 Dec 2012, 03:19
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).
_________________

www.mnemoniceducation.com

Senior Manager
Joined: 16 Dec 2011
Posts: 452
Followers: 11

Kudos [?]: 184 [0], given: 70

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

### Show Tags

06 Apr 2013, 06:28
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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11133
Followers: 511

Kudos [?]: 134 [0], given: 0

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

### Show Tags

20 Apr 2014, 17:57
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 38

Kudos [?]: 1664 [0], given: 193

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

### Show Tags

20 Apr 2014, 20:11
1
This post was
BOOKMARKED
$$3^8 - 2^8$$

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

= 97 * 65

35 is not a factor; all other options stand fit

_________________

Kindly press "+1 Kudos" to appreciate

Manager
Joined: 07 Apr 2014
Posts: 147
Followers: 1

Kudos [?]: 19 [0], given: 81

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

### Show Tags

11 Sep 2014, 12:21
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
Intern
Joined: 17 Aug 2014
Posts: 2
Followers: 0

Kudos [?]: 1 [0], given: 1

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

### Show Tags

25 Nov 2014, 18:17
1
This post was
BOOKMARKED
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.
Math Expert
Joined: 02 Sep 2009
Posts: 34496
Followers: 6297

Kudos [?]: 79888 [1] , given: 10022

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

### Show Tags

26 Nov 2014, 05:17
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
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
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11133
Followers: 511

Kudos [?]: 134 [0], given: 0

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

### Show Tags

28 Dec 2015, 22:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Senior Manager
Joined: 20 Aug 2015
Posts: 398
Location: India
GMAT 1: 760 Q50 V44
Followers: 20

Kudos [?]: 166 [0], given: 10

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

### Show Tags

30 Dec 2015, 04:23
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
_________________

Reach out to us at bondwithus@gmatify.com

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6838
Location: Pune, India
Followers: 1929

Kudos [?]: 11980 [1] , given: 221

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

### Show Tags

30 Dec 2015, 21:22
1
KUDOS
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

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.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Manager
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 242
Location: United States (CA)
Followers: 5

Kudos [?]: 37 [0], given: 0

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

### Show Tags

10 Jun 2016, 11:52
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.

_________________

Jeffrey Miller
Scott Woodbury-Stewart
Founder and CEO

Re: If n = 3^8 - 2^8, which of the following is NOT a factor of   [#permalink] 10 Jun 2016, 11:52
Similar topics Replies Last post
Similar
Topics:
1 If integers a and b are distinct factors of 30, which of the following 2 13 Dec 2015, 04:43
4 Which of the following is NOT a factor of the product of the 3 14 Aug 2013, 21:06
14 For which of the following values of n is (100+n)/n NOT an 12 23 Jul 2012, 04:19
26 If n = 3^8 – 2^8 which of the following is NOT a factor of n 9 20 May 2012, 06:58
14 If n is an integer, which of the following CANNOT be a factor of 3n+4? 5 19 May 2008, 16:26
Display posts from previous: Sort by