Events & Promotions
| Last visit was: 27 Sep 2026, 00:46 |
It is currently 27 Sep 2026, 00:46 |
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 2701:30 AM EDT
-02:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Sep 2807:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 28, 2026 - Oct. 16, 2027, 7:00pm-10:00pm EST
Sep 2911:00 AM EDT
-01:00 PM EDT
" Description: Top scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thur Sept. 29, 2026 - Dec. 3, 2026, 11:00am-1:00pm EST
Oct 0102:00 AM EDT
-03:00 AM EDT
Tejas studied hard but kept repeating the same mistakes. After 3 attempts at 645, a focused 4-week strategy helped him identify and fix what was holding him back—leading to a 695 with just 12–15 hours of study per week.
Oct 0107:00 AM BST
-08:00 AM GMT
Welcome to the GMAT Club's Free Interview Prep Event for Top MBA Programs! Buy tickets - Virtual series that’s all set to equip you to -excel in your MBA interviews.
Oct 0301:00 PM EDT
-04:00 PM EDT
Top scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Saturdays Oct. 3, 2026 - Dec. 26, 2026, 1:00pm-4:00pm EST
![If 0 < x < 1000, and [x/2] + [x/3] + [x/5] = 31x/30 where [x] denotes](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If 0 < x < 1000, and [x/2] + [x/3] + [x/5] = 31x/30 where [x] denotes"){kind=icon}
11 Mar 2020, 02:33
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:18) correct
39%
(02:13)
wrong
based on 358
sessions
History
Date
Time
Result
Not Attempted Yet
If \(0 < x < 1000\), and \([\frac{x}{2}] + [\frac{x}{3}] + [\frac{x}{5}] = \frac{31x}{30}\) where [x] denotes the greatest integer less than or equal to x, then the number of possible values of x will be
A. 30
B. 33
C. 43
D. 44
E. 45
Are You Up For the Challenge: 700 Level Questions
A. 30
B. 33
C. 43
D. 44
E. 45
Are You Up For the Challenge: 700 Level Questions
11 Mar 2020, 02:48
Kudos
Bookmarks
If \(0<x<1000\), and \([\frac{x}{2}]+[\frac{x}{3}]+[\frac{x}{5}]=\frac{31x}{30}\) where [x] denotes the greatest integer less than or equal to x, then the number of possible values of x will be
The value of \([\frac{x}{2}]+[\frac{x}{3}]+[\frac{x}{5}]\) will be always INTEGER.
--> The value of \(\frac{31x}{30}\) must be integer too.
In order the value of \(\frac{31x}{30}\) to be integer, \(x\) must be \(30\), \(60\), \(90\)..... \(990\)
\(x_1= 30\)
\(x_n = 990\)
--> \(n = \frac{(990-30)}{30} +1 = 33\)
Answer (B)
The value of \([\frac{x}{2}]+[\frac{x}{3}]+[\frac{x}{5}]\) will be always INTEGER.
--> The value of \(\frac{31x}{30}\) must be integer too.
In order the value of \(\frac{31x}{30}\) to be integer, \(x\) must be \(30\), \(60\), \(90\)..... \(990\)
\(x_1= 30\)
\(x_n = 990\)
--> \(n = \frac{(990-30)}{30} +1 = 33\)
Answer (B)
General Discussion
Updated on: 11 Mar 2020, 02:52
Originally posted by GMATinsight on 11 Mar 2020, 02:45.
Last edited by GMATinsight on 11 Mar 2020, 02:52, edited 1 time in total.
Last edited by GMATinsight on 11 Mar 2020, 02:52, edited 1 time in total.
Kudos
Bookmarks
Bunuel
\([\frac{x}{2}] + [\frac{x}{3}] + [\frac{x}{5}] = \frac{31x}{30}\) = Integer
I.e. x Must be a multiple of 30 for 31x/30 to be an Integer
at x = 30, \([\frac{30}{2}] + [\frac{30}{3}] + [\frac{30}{5}] = 15+10+6 = 31 =\frac{31x}{30}\)
Since all options suggest that total possible values of x must be 30 or more
where total values of x as per range 0 < x < 1000 = 1000/30 = 33
Let's try with biggest value of x
at x = 990, \([\frac{990}{2}] + [\frac{990}{3}] + [\frac{990}{5}] = 495+330+198 = 1023 = \frac{31x}{30}\)
I.e. Total possible values of x must be 33 hence
ANswer: Option B
All values of x from 30 to 990 satisfy the given relation
11 Mar 2020, 02:57
Kudos
Bookmarks
Any number can be written as sum of integral part and fraction part.
A=[A]+{A}
represents integral part
{} represents fraction part
[A]=A-{A}
[x/2] + [x/3] + [x/5]= x/2-{x/2}+x/3-{x/3}+x/5-{x/5}
31x/30 - {x/2}-{x/3}-{x/5}= 31x/30
{x/2}+{x/3}+{x/5}=0
sum of 3 non-negative numbers is zero, if each of them is zero
or x is a multiple of 2,3 and 5
x= LCM(2,3,5)k= 30k, where k is an integer
0<30k<1000
0<k<33.xyz
k can take 33 values
A=[A]+{A}
represents integral part
{} represents fraction part
[A]=A-{A}
[x/2] + [x/3] + [x/5]= x/2-{x/2}+x/3-{x/3}+x/5-{x/5}
31x/30 - {x/2}-{x/3}-{x/5}= 31x/30
{x/2}+{x/3}+{x/5}=0
sum of 3 non-negative numbers is zero, if each of them is zero
or x is a multiple of 2,3 and 5
x= LCM(2,3,5)k= 30k, where k is an integer
0<30k<1000
0<k<33.xyz
k can take 33 values
Bunuel
