Last visit was: 26 Apr 2026, 00:30 It is currently 26 Apr 2026, 00:30
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: 26 Apr 2026
Posts: 109,831
Own Kudos:
811,317
 [13]
Given Kudos: 105,889
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,831
Kudos: 811,317
 [13]
Which of the following must be an integer if x is a positive integer 12 Mar 2018, 22:14
Kudos
Add Kudos
13
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:

35% (medium)

Question Stats:

68% (01:28) correct 32% (01:31) wrong based on 629 sessions

History

Date
Time
Result
Not Attempted Yet
Which of the following must be an integer if x is a positive integer and \(\frac{4}{x} + \frac{5}{x} + \frac{6}{x}\) is an integer ?

A. x/5
B. 5/x
C. x/30
D. 30/x
E. x/120
ShowHide Answer
Official Answer
D
User avatar
arvind910619
User avatar
Joined: 20 Dec 2015
Last visit: 18 Oct 2024
Posts: 814
Own Kudos:
615
 [3]
Given Kudos: 755
Status:Learning
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE:Engineering (Manufacturing)
Products:
My Reviews
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
Posts: 814
Kudos: 615
 [3]
Which of the following must be an integer if x is a positive integer 12 Mar 2018, 23:42
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
X can be 15,5 or 3 if take x=3 then only D follows .
if we take x=5 both A ,B and D follows
If x=15 then A and D follows so we can see that only D is correct
avatar
Jahfors
avatar
Joined: 26 Sep 2016
Last visit: 22 Aug 2022
Posts: 6
Given Kudos: 14
Posts: 6
Kudos: 0
Which of the following must be an integer if x is a positive integer 13 Mar 2018, 00:02
Kudos
Add Kudos
Bookmarks
Bookmark this Post
arvind910619
X can be 15,5 or 3 if take x=3 then only D follows .
if we take x=5 both A ,B and D follows
If x=15 then A and D follows so we can see that only D is correct
Show more
How did u count that 15,5 and 3?
User avatar
arvind910619
User avatar
Joined: 20 Dec 2015
Last visit: 18 Oct 2024
Posts: 814
Own Kudos:
615
 [3]
Given Kudos: 755
Status:Learning
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE:Engineering (Manufacturing)
Products:
My Reviews
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
Posts: 814
Kudos: 615
 [3]
Which of the following must be an integer if x is a positive integer 13 Mar 2018, 01:14
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Jahfors
arvind910619
X can be 15,5 or 3 if take x=3 then only D follows .
if we take x=5 both A ,B and D follows
If x=15 then A and D follows so we can see that only D is correct
How did u count that 15,5 and 3?
Show more

HI 4/x+5/x+6/x is an integer 15/x = integer
So x can take values 15 ,3 , 5 and 1
User avatar
jfranciscocuencag
User avatar
Joined: 12 Sep 2017
Last visit: 17 Aug 2024
Posts: 227
Own Kudos:
144
 [1]
Given Kudos: 132
Posts: 227
Kudos: 144
 [1]
Which of the following must be an integer if x is a positive integer 19 Feb 2019, 10:41
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
LCM of 2,3, and 5 is 30.

We can discard fastly A, C, and E because x can be 1.

A. x/5 - discard
B. 5/x
C. x/30 - discard
D. 30/x - (LCM of 2,3, and 5)
E. x/120 - discard

Hence, 30/x must be an integer.
User avatar
IanStewart
User avatar
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 24 Apr 2026
Posts: 4,143
Own Kudos:
11,279
 [1]
Given Kudos: 99
Expert
Expert reply
Posts: 4,143
Kudos: 11,279
 [1]
Which of the following must be an integer if x is a positive integer 19 Feb 2019, 16:50
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
4/x + 5/x + 6/x is just equal to 15/x. If that's an integer, 30/x is clearly also an integer, since it's twice as big.
avatar
jjmcnamara9
avatar
Joined: 15 Oct 2018
Last visit: 31 Jul 2019
Posts: 1
Posts: 1
Kudos: 0
Which of the following must be an integer if x is a positive integer 20 Feb 2019, 20:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
3 consecutive integers will always be divisible by 3. So if 4, 5, and 6 over x are all integers, then x must be divisible by 3. 30 is divisible by 3, therefore option D.
avatar
Talha95
avatar
Joined: 07 Feb 2019
Last visit: 04 Jan 2021
Posts: 15
Own Kudos:
4
Given Kudos: 31
Posts: 15
Kudos: 4
Which of the following must be an integer if x is a positive integer 21 Feb 2019, 09:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
After solving the equation, we get 15/X.As 15 is divided by X, so 30/X also divided by X.

Posted from my mobile device
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 25 Apr 2026
Posts: 22,286
Own Kudos:
26,537
 [2]
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: 22,286
Kudos: 26,537
 [2]
Which of the following must be an integer if x is a positive integer 21 Feb 2019, 18:01
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
Which of the following must be an integer if x is a positive integer and \(\frac{4}{x} + \frac{5}{x} + \frac{6}{x}\) is an integer ?

A. x/5
B. 5/x
C. x/30
D. 30/x
E. x/120
Show more

Adding the fractions together, we have:

15/x = integer.

Thus, x must be a factor of 15. In that case, x must also be a factor of any multiple of 15, and thus 30/x will always be an integer.

Answer: D
avatar
Mikimix
avatar
Joined: 12 Feb 2018
Last visit: 03 Jun 2019
Posts: 6
Own Kudos:
3
Given Kudos: 58
Posts: 6
Kudos: 3
Which of the following must be an integer if x is a positive integer 24 Feb 2019, 04:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Adding up all the fractions we can clearly see that x must be a multiple of 3 or 5 or both. Considering all the possible cases:

A- if X were 3 this answer would not be an integer
B - same
C- x could not be bigger than 15 so this terms is not an integer
D- right answer
E - x cannot be bigger than 15, otherwise 15/x would not be an integer.

Kudus if you appreciated!
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,987
Own Kudos:
1,118
Posts: 38,987
Kudos: 1,118
Which of the following must be an integer if x is a positive integer 29 Oct 2024, 19:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109831 posts
Krunaal
Tuck School Moderator
852 posts