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

It is currently 23 Jan 2019, 08:12

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • Key Strategies to Master GMAT SC

     January 26, 2019

     January 26, 2019

     07:00 AM PST

     09:00 AM PST

    Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
  • Free GMAT Number Properties Webinar

     January 27, 2019

     January 27, 2019

     07:00 AM PST

     09:00 AM PST

    Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.

Which of the following is a prime factor of 5^8 - 2^8 ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52431
Which of the following is a prime factor of 5^8 - 2^8 ?  [#permalink]

Show Tags

New post 28 Mar 2018, 23:44
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

68% (01:30) correct 32% (01:28) wrong based on 75 sessions

HideShow timer Statistics

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
Premium Member CAT Tests
Which of the following is a prime factor of 5^8 - 2^8 ?  [#permalink]

Show Tags

New post 29 Mar 2018, 00:11
Bunuel wrote:
Which of the following is a prime factor of 5^8 - 2^8 ?

I. 2
II. 3
III. 7

(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III


Rule: \(a^2 - b^2 = (a+b)(a-b)\)

\(5^8 - 2^8\) can be re-written as \((5^4)^2 - (2^4)^2\)

Further simplifying the expression, we get
\((5^4)^2 - (2^4)^2 = (5^4 + 2^4)(5^4 - 2^4) = (625+16)(5^2 + 2^2)(5^2 - 2^2) = (641)(29)(21)\)

\(5^8 - 2^8\) is divisible by prime number(s) 3 and 7(but not 2) and Option D(II and III) is our answer!
_________________

You've got what it takes, but it will take everything you've got

Senior PS Moderator
User avatar
P
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 675
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: Which of the following is a prime factor of 5^8 - 2^8 ?  [#permalink]

Show Tags

New post 29 Mar 2018, 00:12
Bunuel wrote:
Which of the following is a prime factor of 5^8 - 2^8 ?

I. 2
II. 3
III. 7

(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III


\(5^8 - 2^8 = (5^4 + 2^4)(5^4 - 2^4)\) .... \(a^2 - b^2 = (a + b)(a - b)\)

\(= (5^4 + 2^4)*(5^2 + 2^2)*(5^2 - 2^2)\)

\(= (5^4 + 2^4)*(5^2 + 2^2) * (5 + 2) ( 5 - 2)\)

hence 7 and 3 are prime factors of the given number.

Also note that for all other factors... we are adding an odd number ( power of 5) to an even number ( power of 2) ... hence it is always odd.

Hence 2 is not a prime factor of given number.

Hence Option (D) is correct.

Best,
Gladi
_________________

Regards,
Gladi



“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)

Manager
Manager
User avatar
G
Joined: 15 Nov 2017
Posts: 115
Location: India
Concentration: Operations, Marketing
GPA: 4
WE: Operations (Retail)
Re: Which of the following is a prime factor of 5^8 - 2^8 ?  [#permalink]

Show Tags

New post 29 Mar 2018, 05:25
1
Bunuel wrote:
Which of the following is a prime factor of 5^8 - 2^8 ?

I. 2
II. 3
III. 7

(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III


5^8 - 2^8 is similar to a^n - b^n
Pls note that (a^n - b^n) is always divisible by (a-b); if n is even (a^n - b^n) is always divisible by (a+b)

Here: a+b= 7 and a-b= 3 are the factors(both prime) of 5^8 - 2^8.
Also note that, 5^8 is an odd no. and 2^8 is an even no. and therefore their subtraction will be an odd no. hence 2 cant be the factor

Ans. D
_________________

All egmat SC Resource for FREE

Like = +Kudos

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4612
Location: United States (CA)
Re: Which of the following is a prime factor of 5^8 - 2^8 ?  [#permalink]

Show Tags

New post 30 Mar 2018, 09:54
Bunuel wrote:
Which of the following is a prime factor of 5^8 - 2^8 ?

I. 2
II. 3
III. 7

(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III


Using the difference of squares, we have:

(5^4 - 2^4)(5^4 + 2^4) = (5^2 - 2^2)(5^2 + 2^2)(5^4 + 2^4) = 21 x 29 x 641

We can quickly see that 21 x 29 x 641 does not contain a prime factor of 2.

We can also see that 21 is divisible by both 3 and 7, so 3 and 7 are both prime factors of 5^8 - 2^8. 7.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMAT Club Bot
Re: Which of the following is a prime factor of 5^8 - 2^8 ? &nbs [#permalink] 30 Mar 2018, 09:54
Display posts from previous: Sort by

Which of the following is a prime factor of 5^8 - 2^8 ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.