NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 09:26 It is currently 25 Apr 2024, 09:26
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

The greatest prime factor of 7^5+7^4+7^3 is:

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618961 [5]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
The greatest prime factor of 7^5+7^4+7^3 is: [#permalink] New post   01 Mar 2017, 05:35
5
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

64% (01:05) correct 36% (01:08) wrong based on 318 sessions
Hide Show timer Statistics
The greatest prime factor of 7^5+7^4+7^3 is:

A. Less than 4
B. Between 4 and 10
C. Between 10 and 20
D. Between 20 and 30
E. Greater than 30
ShowHide Answer
Official Answer
C
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6820
Own Kudos [?]: 29926 [4]
Given Kudos: 799
Location: Canada
Send PM
Re: The greatest prime factor of 7^5+7^4+7^3 is: [#permalink] New post   01 Mar 2017, 06:05
1
Kudos
3
Bookmarks
Expert Reply
Top Contributor
Bunuel wrote:
The greatest prime factor of 7^5 + 7^4 + 7^3 is:

A. Less than 4
B. Between 4 and 10
C. Between 10 and 20
D. Between 20 and 30
E. Greater than 30


\(7^5 + 7^4 + 7^3 = 7^3(7^2 + 7^1 + 1)\)
\(= 7^3(49 + 7 + 1)\)
\(= 7^3(57)\)
\(=7^3(3)(19)\)
\(= (7)(7)(7)(3)(19)\)

The greatest prime factor is 19

Answer: C
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6072
Own Kudos [?]: 4689 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Re: The greatest prime factor of 7^5+7^4+7^3 is: [#permalink] New post   01 Mar 2017, 11:40
Bunuel wrote:
The greatest prime factor of 7^5+7^4+7^3 is:

A. Less than 4
B. Between 4 and 10
C. Between 10 and 20
D. Between 20 and 30
E. Greater than 30


7^5+7^4+7^3

= 7^3 ( 7^2 + 7 +1 )

= 7^3*57

= 7^3*( 3 * 19 )

Thus, the greatest prime number is 19..

Hence, answer must be (C) Between 10 and 20
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6273 [0]
Given Kudos: 1646
Send PM
Re: The greatest prime factor of 7^5+7^4+7^3 is: [#permalink] New post   02 Mar 2017, 18:36
Expert Reply
Bunuel wrote:
The greatest prime factor of 7^5+7^4+7^3 is:

A. Less than 4
B. Between 4 and 10
C. Between 10 and 20
D. Between 20 and 30
E. Greater than 30


Let’s simplify the given expression:

7^5+7^4+7^3

7^3(7^2 + 7^1 + 1)

7^3(49 + 7 + 1)

7^3(57) = 7^3 x 19 x 3

Thus, the greatest prime factor of 7^5+7^4+7^3 is 19, which is between 10 and 20.

Answer: C
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6273 [1]
Given Kudos: 1646
Send PM
Re: The greatest prime factor of 7^5+7^4+7^3 is: [#permalink] New post   02 Mar 2017, 18:39
1
Kudos
Expert Reply
Bunuel wrote:
The greatest prime factor of 7^5+7^4+7^3 is:

A. Less than 4
B. Between 4 and 10
C. Between 10 and 20
D. Between 20 and 30
E. Greater than 30


Let’s simplify the given expression:

7^5+7^4+7^3

7^3(7^2 + 7^1 + 1)

7^3(49 + 7 + 1)

7^3(57) = 7^3 x 19 x 3

Thus, the greatest prime factor of 7^5+7^4+7^3 is 19, which is between 10 and 20.

Answer: C
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32675
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: The greatest prime factor of 7^5+7^4+7^3 is: [#permalink] New post   18 May 2022, 03:58
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.
GMAT Club Bot
gmatclubot
Re: The greatest prime factor of 7^5+7^4+7^3 is: [#permalink]
18 May 2022, 03:58
Moderators:
Bunuel
Math Expert
92914 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions