Last visit was: 25 Sep 2026, 17:37 It is currently 25 Sep 2026, 17:37
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Sep 2026
Posts: 113,936
Own Kudos:
843,623
 [74]
Given Kudos: 111,826
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,936
Kudos: 843,623
 [74]
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer 15 May 2015, 03:50
4
Kudos
Add Kudos
70
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

59% (02:11) correct 41% (02:24) wrong based on 1109 sessions

History

Date
Time
Result
Not Attempted Yet
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?

A. None
B. One
C. Two
D. Three
E. Four

Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Sep 2026
Posts: 113,936
Own Kudos:
843,623
 [15]
Given Kudos: 111,826
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,936
Kudos: 843,623
 [15]
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer 18 May 2015, 07:10
5
Kudos
Add Kudos
10
Bookmarks
Bookmark this Post
Bunuel
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?

A. None
B. One
C. Two
D. Three
E. Four

Kudos for a correct solution.
Show more

OFFICIAL SOLUTION:

First of all, notice that x is a positive integer such that it does NOT have a factor p such that 1 < p < x simply means that x is a prime number.

Next, \(a = 5^{15} - 625^3=5^{15} - 5^{12}=5^{12}(5^3-1)=5^{12}*124=2^2*5^{12}*31\).

Finally, for a/x to be an integer where x is a prime, x can take 3 values: 2, 5, or 31.

Answer: D.
General Discussion
avatar
sujay840
avatar
Joined: 20 Sep 2013
Last visit: 14 Jul 2022
Posts: 1
Own Kudos:
6
 [1]
Given Kudos: 49
Location: India
Concentration: Entrepreneurship, General Management
WE:General Management (Manufacturing)
Posts: 1
Kudos: 6
 [1]
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer 06 Apr 2017, 00:38
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Bunuel
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?

A. None
B. One
C. Two
D. Three
E. Four

Kudos for a correct solution.

OFFICIAL SOLUTION:

First of all, notice that x is a positive integer such that it does NOT have a factor p such that 1 < p < x simply means that x is a prime number.

Next, \(a = 5^{15} - 625^3=5^{15} - 5^{12}=5^{12}(5^3-1)=5^{12}*124=2^2*5^{12}*31\).

Finally, for a/x to be an integer where x is a prime, x can take 3 values: 2, 5, or 31.

Answer: D.
Show more


Hi Bunnel,

Can you please clarify if the value of x = 2, then according to 1 < p < x, what will be the value of p. I marked option C because x has to be a prime number and I assumed p = 2 as its given 1 < p < x and x has to be greater than p
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Sep 2026
Posts: 113,936
Own Kudos:
843,623
Given Kudos: 111,826
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,936
Kudos: 843,623
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer 06 Apr 2017, 00:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sujay840
Bunuel
Bunuel
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?

A. None
B. One
C. Two
D. Three
E. Four

Kudos for a correct solution.

OFFICIAL SOLUTION:

First of all, notice that x is a positive integer such that it does NOT have a factor p such that 1 < p < x simply means that x is a prime number.

Next, \(a = 5^{15} - 625^3=5^{15} - 5^{12}=5^{12}(5^3-1)=5^{12}*124=2^2*5^{12}*31\).

Finally, for a/x to be an integer where x is a prime, x can take 3 values: 2, 5, or 31.

Answer: D.


Hi Bunnel,

Can you please clarify if the value of x = 2, then according to 1 < p < x, what will be the value of p. I marked option C because x has to be a prime number and I assumed p = 2 as its given 1 < p < x and x has to be greater than p
Show more

We are told that x is a positive integer such that it does NOT have a factor p such that 1 < p < x.

2 does not have a factor p such that 1 < p < 2.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 25 Sep 2026
Posts: 22,752
Own Kudos:
27,033
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,752
Kudos: 27,033
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer 02 Mar 2018, 10:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?

A. None
B. One
C. Two
D. Three
E. Four
Show more

We can start by simplifying a:

5^15 - 625^3 = 5^15 - (5^4)^3 = 5^15 - 5^12 = 5^12(5^3 - 1) = 5^12(124) = 5^12(4)(31) = 5^12( 2^2)(31)

If a/x is an integer, then x is a factor of a. However, if x does not have a factor p such that 1 < p < x, then x must be prime number. For example, if x = 5, we see that x doesn’t have a factor between 1 and itself. Since a has three distinct prime factors, there are three distinct values for x: 2, 5 and 31.

Answer: D
User avatar
nikitathegreat
User avatar
Joined: 16 Dec 2021
Last visit: 24 Sep 2026
Posts: 174
Own Kudos:
24
Given Kudos: 123
Location: India
Schools: ISB '23 LBS '24 NTU NUS Said '23
GMAT 1: 630 Q45 V31
Products:
My Reviews
Schools: ISB '23 LBS '24 NTU NUS Said '23
GMAT 1: 630 Q45 V31
Posts: 174
Kudos: 24
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer 31 May 2024, 01:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can someone help explain how do we know that x is a prime no. ?

It says that x doesnt have a factor p. If I take x =6, then we can have 1<5<6. here 5 is not a factor of 6 and 6=x is not a prime no.? I am not able to interpret the statement that x is prime no.

Thanks
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Sep 2026
Posts: 113,936
Own Kudos:
843,623
 [1]
Given Kudos: 111,826
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,936
Kudos: 843,623
 [1]
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer 31 May 2024, 01:44
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
 
nikitathegreat
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?

A. None
B. One
C. Two
D. Three
E. Four

Can someone help explain how do we know that x is a prime no. ?

It says that x doesnt have a factor p. If I take x =6, then we can have 1<5<6. here 5 is not a factor of 6 and 6=x is not a prime no.? I am not able to interpret the statement that x is prime no.

Thanks
Show more

6 does have factors p such that 1 < p < 6. For example, both 2 and 3 are factors of 6, satisfying 1 < p < 6. Only prime numbers satisfy the statement because a prime number has exactly two factors: 1 and itself, and does not have any other factor p such that 1 < p < prime.
User avatar
ablatt4
User avatar
Joined: 18 Dec 2024
Last visit: 24 Sep 2025
Posts: 86
Own Kudos:
3
Given Kudos: 89
Location: United States (FL)
Concentration: Finance
Schools: Duke '26 Darden '26 Johnson '26 UNC '26
Schools: Duke '26 Darden '26 Johnson '26 UNC '26
Posts: 86
Kudos: 3
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer 03 Sep 2025, 08:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
a=5^15 - 5^12

a=5^12 (124)

a=5^12 (2^2 *31)

5,2,31
D
Bunuel
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?

A. None
B. One
C. Two
D. Three
E. Four

Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
Show more
User avatar
rajdeep212003
User avatar
Joined: 11 Dec 2024
Last visit: 25 Sep 2026
Posts: 160
Own Kudos:
82
 [1]
Given Kudos: 18
Location: India
Schools: ISB '27 Kellogg INSEAD MiM '26
Products:
Forum Quiz
Schools: ISB '27 Kellogg INSEAD MiM '26
Posts: 160
Kudos: 82
 [1]
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer 07 Sep 2025, 08:10
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hope my process is good if anyone have anything easy feel free to response
Attachments

IMG20250907203836.jpg
IMG20250907203836.jpg [ 3.18 MiB | Viewed 2789 times ]

User avatar
Adit_
User avatar
Joined: 04 Jun 2024
Last visit: 29 Jul 2026
Posts: 866
Own Kudos:
333
Given Kudos: 165
Posts: 866
Kudos: 333
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer 25 Apr 2026, 23:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Really silly, but I am not sure why many a times I consider 625 to be 5^3 instead of 5^4.
Apart from that:

5^15 - 5^12:
5^12[5^3 - 1]
= 5^12 * 124.
= 5^12 * 4 * 31.
Prime numbers: 2,5,31.

Answer: Option D
Bunuel
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?

A. None
B. One
C. Two
D. Three
E. Four

Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
Show more
Moderator:
Bunuel
Math Expert
113936 posts