GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 May 2019, 06:20

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

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: 174
If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

Show Tags

12 Dec 2012, 05:42
11
101
00:00

Difficulty:

65% (hard)

Question Stats:

61% (01:59) correct 39% (02:12) wrong based on 1909 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
Math Expert
Joined: 02 Sep 2009
Posts: 55266
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

Show Tags

12 Dec 2012, 05:46
23
38
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.

_________________
General Discussion
Intern
Joined: 24 Apr 2012
Posts: 47
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

Show Tags

14 Dec 2012, 03:19
1
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: 296
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

Manager
Joined: 11 Jul 2009
Posts: 105
WE: Design (Computer Software)
Re: If n = 3^8 – 2^8 which of the following is NOT a factor of n  [#permalink]

Show Tags

04 Aug 2013, 22:21
1
(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
_________________
Kaustubh
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1812
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
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
2
$$3^8 - 2^8$$

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

= 97 * 65

35 is not a factor; all other options stand fit

_________________
Kindly press "+1 Kudos" to appreciate
Manager
Joined: 07 Apr 2014
Posts: 105
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

Show Tags

11 Sep 2014, 12:21
2
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
If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

Show Tags

25 Nov 2014, 18:17
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: 55266
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
2
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
_________________
Senior Manager
Joined: 20 Aug 2015
Posts: 388
Location: India
GMAT 1: 760 Q50 V44
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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9232
Location: Pune, India
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

Show Tags

30 Dec 2015, 21:22
6
2
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

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6206
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, 11:52
1
2
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.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Joined: 03 Jan 2017
Posts: 144
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

Show Tags

25 Mar 2017, 10:24
n=3^8-2^8
let's split it
(3^4-2^4)*(3^4+2^4)=65*97
C is fine
Manager
Joined: 06 Dec 2016
Posts: 245
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

Show Tags

25 Mar 2017, 19:25
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: 659
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

Show Tags

01 Apr 2017, 04:41
1
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.
_________________
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: 9232
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, 08:32
1
VeritasPrepKarishma 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

VP
Joined: 09 Mar 2016
Posts: 1284
If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

Show Tags

06 May 2018, 05:26
Bunuel 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.

niks18 hello, can you please give me a prompt how to solve this question i got stuck ...

$$n = 3^8 - 2^8=(3^4-2^4)(3^4+2^4)$$ from here i get this $$9^8+6^8-6^8-4^8$$ now what next ?

by the way, my first thought looking at this $$n = 3^8 - 2^8$$, was that I simply need to subtract so I got simply 1 and got confused... why wouldn't this approch work here ... then I saw Bunuel s mind blowing approach so started solving and got stuck half way or may be on 1/3 of the way

by the way this formula $$a^2-b^2=(a-b)(a+b)$$ features exponent 2 where as in the question it is 8, so no materr what is exponent this formula would worki right ?
Retired Moderator
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

Show Tags

06 May 2018, 09:57
1
dave13 wrote:
Bunuel 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.

niks18 hello, can you please give me a prompt how to solve this question i got stuck ...

$$n = 3^8 - 2^8=(3^4-2^4)(3^4+2^4)$$ from here i get this $$9^8+6^8-6^8-4^8$$ now what next ?

by the way, my first thought looking at this $$n = 3^8 - 2^8$$, was that I simply need to subtract so I got simply 1 and got confused... why wouldn't this approch work here ... then I saw Bunuel s mind blowing approach so started solving and got stuck half way or may be on 1/3 of the way

by the way this formula $$a^2-b^2=(a-b)(a+b)$$ features exponent 2 where as in the question it is 8, so no materr what is exponent this formula would worki right ?

Hi dave13

The highlighted part is incorrect. Go through multiplication of exponents once to understand your mistake there.

Secondly $$a^2-b^2=(a-b)(a+b)$$. now we are given $$3^8 - 2^8$$ whose exponents are 8, so to use the formula you can manupulate the exponents as

$$(3^4)^2 - (2^4)^2$$ and thus you can use the formula.
Intern
Joined: 15 Sep 2018
Posts: 30
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

Show Tags

25 Sep 2018, 06:13
1
$$3^8$$ can be rewritten as $$3^{(4(2))}$$ or $$(3^4 )^2$$. Similarly, $$2^8$$ can be rewritten as $$2^{4(2)}$$ or $$(2^4 )^2$$.

Since both are perfect squares, we can apply the property when working with the difference of two squares:

$$a^2-b^2=(a+b)(a-b)$$

Hence,

$$3^8-2^8=(3^4 )^2-(2^4 )^2$$
$$=(3^4+2^4 )(3^4-2^4 )$$
$$=(81+16)(81-16)$$

We have $$3^8-2^8=97 \times 65= 97 \times 5 \times 13$$. This shows that $$5$$, $$13$$, and $$97$$ are factors of the total.

In addition, since $$7$$ is not a factor of $$3^8-2^8$$, $$35$$ (which is equal to $$5 \times 7$$) can’t be a factor as well.

CEO
Joined: 12 Sep 2015
Posts: 3724
If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

Show Tags

06 Mar 2019, 11:06
Top Contributor
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

A quick way to solve this it to first recognize that $$3^8 - 2^8$$is a difference of squares, which can be factored.

So, $$n = 3^8 - 2^8$$

$$= (3^4 + 2^4)(3^4 - 2^4)$$

$$= (3^4 + 2^4)(3^2 + 2^2)(3^2 - 2^2)$$

$$= (3^4 + 2^4)(3^2 + 2^2)(3 + 2)(3 - 2)$$

$$= (97)(13)(5)(1)$$

At this point, we can see that 97, 65 (aka 13 x 5), 13 and 5 are all factors of n

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
If n = 3^8 - 2^8, which of the following is NOT a factor of   [#permalink] 06 Mar 2019, 11:06
Display posts from previous: Sort by