Last visit was: 18 Nov 2025, 14:06

It is currently 18 Nov 2025, 14:06

Toolkit

Practice Tests

Quantitative Questions

Problem Solving (PS)

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

Request Expert Reply

Confirm Cancel

Nov 19
GMAT 705 in 30 days: Best Study Strategy for Working Professionals
12:30 PM EST
-
01:30 PM EST
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more
Nov 20
GMAT 675 with 96th percentile in DI- Kamakshi’s Winning Strategy
01:30 PM EST
-
02:30 PM IST
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Nov 22
GMAT RC Masterclass
11:00 AM IST
-
01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment
Nov 23
Conquer Algebra on the GMAT Focus Edition
11:00 AM IST
-
01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease.
Nov 24
FREE Focus Edition Mock!
07:00 PM PST
-
08:00 PM PST
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Nov 25
Try OnDemand GMAT Masterclass
10:00 AM EST
-
11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.

Back to Forum

Create Topic

GMAT Club World Cup 2022 (DAY 8): If the least common multiple of

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 18 Nov 2025

Posts: 105,355

Own Kudos:

778,062

[44]

Given Kudos: 99,964

Products:

Expert

Expert reply

Posts: 105,355

Kudos: 778,062

[44]

20 Jul 2022, 08:00

Kudos

Bookmarks

00:00

Start Timer

Pause Timer

Resume Timer

Show Answer

Hide

Show

History

Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

29% (02:18) correct

71% (02:20) wrong

based on 244 sessions

History

Date

Time

Result

Not Attempted Yet

If the least common multiple of positive integers, x, y and z is 30, then how many different values can \(|x - y| + |x - z| + |y - z|\) take ?

A. 17
B. 18
C. 19
D. 20
E. 21

This question was provided by GMAT Club
for the GMAT Club World Cup Competition

Compete, Get Better, Win prizes and more

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 Answer

Official Answer

Most Helpful Reply

chetan2u

GMAT Expert

Joined: 02 Aug 2009

Last visit: 15 Nov 2025

Posts: 11,238

Own Kudos:

43,696

[7]

Given Kudos: 335

Status:Math and DI Expert

Location: India

Concentration: Human Resources, General Management

GMAT Focus 1: 735 Q90 V89 DI81 Verified score

Products:

Expert

Expert reply

GMAT Focus 1: 735 Q90 V89 DI81 Verified score

Posts: 11,238

Kudos: 43,696

[7]

21 Jul 2022, 20:08

Kudos

Bookmarks

Bunuel

If the least common multiple of positive integers, x, y and z is 30, then how many different values can \(|x - y| + |x - z| + |y - z|\) take ?

A. 17
B. 18
C. 19
D. 20
E. 21

This question was provided by GMAT Club
for the GMAT Club World Cup Competition

Compete, Get Better, Win prizes and more

gmatophobia, the question is about realising the way the MOD will behave in different scenarios. I have not gone through the replies above so if it is a repeat, pardon me.

|x-y|+|x-z|+|y-z|
There are various ways x, y and z can be placed.
1) x>y>z: This will make x-y, x-z and y-z positive. So, |x-y|+|x-z|+|y-z|=x-y+x-z+y-z=2(x-z)
2) z>x>y: This will make x-y positive and, x-z and y-z negative. So, |x-y|+|x-z|+|y-z|=x-y+z-x+z-y=2(z-y)
We can check others too, but in each case we get the expression equal to TWICE of the RANGE, that is Max-Min.

Knowing this, let us find the different values of the ranges.

For this, we require to know different values that these integers can take.
Factors of 30: 30,15,10,6,5,3,2,1

Differences:
Largest is 30: 29,28,27,25,24,20,15,0
Largest is 15: 14,13,12,10,9,5,0
Largest is 10: 9,8,7,5,4,0
Largest is 6: 5,4,3,1,0
Largest is 5: 4,3,2,0
Largest is 3: 2,1,0
Largest is 2: 1,0

Different values: 29,28,27,25,24,20,15,14,13,12,10,9,8,7,5,4,3,2,1

19 values

C

General Discussion

Fido10

Joined: 12 Aug 2020

Last visit: 27 Aug 2024

Posts: 103

Own Kudos:

165

[4]

Given Kudos: 298

Location: Morocco

Products:

Posts: 103

Kudos: 165

[4]

20 Jul 2022, 08:41

Kudos

Bookmarks

The unique decomposition of prime numbers of 30 gives : 30=2 x 3 x 5

the x, y and z belong to the set ( 2, 3, 5)

x y z
2 3 5
2 5 3
5 3 2
5 2 3
3 5 2
3 2 5
(x-y) have 6 possibilities
(x-z) have 6 possibilities
(y-z) have 6 possibilities

total number of possibilities is then 18,
Answer is B

ThatDudeKnows

Tutor

Joined: 11 May 2022

Last visit: 27 Jun 2024

Posts: 1,070

Own Kudos:

977

[3]

Given Kudos: 79

Expert

Expert reply

Posts: 1,070

Kudos: 977

[3]

20 Jul 2022, 08:42

Kudos

Bookmarks

Bunuel

If the least common multiple of positive integers, x, y and z is 30, then how many different values can \(|x - y| + |x - z| + |y - z|\) take ?

A. 17
B. 18
C. 19
D. 20
E. 21

This question was provided by GMAT Club
for the GMAT Club World Cup Competition

Compete, Get Better, Win prizes and more

The possible values for x, y, and z are 30, 15, 10, 6, 5, 3, 2, 1.

The only way to have x=y=z is if they are all 30. In that case, our sum will be 0+0+0 = 0.

If we have at least two distinct values and the largest is 30, the other two could be anything in the list.
Let's look at 30,1,1 and 30,2,1 to see if we can learn anything.
30,1,1: 29+29+0 = 58
30,2,1: 28+29+1 = 58
Aha! When we have at least two distinct values, (the distance between the largest and the median)+(the distance between the median and the smallest)=(the distance between the largest and the smallest), so our sum will be 2x(the distance between the largest and the smallest). We are therefore looking for the number of distinct min/max ranges among triples.

Since we are taking all three distances between any two elements, A,B,C = B,A,C = C,B,A etc.

Here are the possible triples. We know we can eliminate any that have a min-max range that we've already listed because they will have a sum for which we've already accounted.

30,30,30 - 0
30,30,15 - 15
30,30,10 - 20
30,30,6 - 24
30,30,5 - 25
30,30,3 - 27
30,30,2 - 28
30,30,1 - 29
30,15,15 - 15 Eliminate
30,15,10 - 20 Eliminate
30,15,6 - 24 Eliminate
30,15,5 - 25 Eliminate
30,15,3 - 27 Eliminate
30,15,2 - 28 Eliminate
30,15,1 - 29 Eliminate
15,10,10 - 5
15,10,6 - 9
15,10,5 - 10
15,10,3 - 12
15,10,2 - 13
15,10,1 - 14
10,6,6 - 4
10,6,5 - 5 Eliminate
10,6,3 - 7
10,6,2 - 8
10,6,1 - 9 Eliminate
10,3,3 - 7 Eliminate
10,3,2 - 8 Eliminate
10,3,1 - 9 Eliminate
6,5,5 - 1
6,5,3 - 3
6,5,2 - 4 Eliminate
6,5,1 - 5 Eliminate

Count up the non-eliminated ones. 19.

Answer choice C.

Kinshook

Major Poster

Joined: 03 Jun 2019

Last visit: 18 Nov 2025

Posts: 5,793

Own Kudos:

5,508

Given Kudos: 161

Location: India

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

WE:Engineering (Transportation)

Products:

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

Posts: 5,793

Kudos: 5,508

22 Jul 2022, 09:47

Kudos

Bookmarks

Bunuel please check my solution
OA is D 20 and NOT C 19.
Please count the solutions.

Bunuel

If the least common multiple of positive integers, x, y and z is 30, then how many different values can \(|x - y| + |x - z| + |y - z|\) take ?

A. 17
B. 18
C. 19
D. 20
E. 21

This question was provided by GMAT Club
for the GMAT Club World Cup Competition

Compete, Get Better, Win prizes and more

Kinshook

Major Poster

Joined: 03 Jun 2019

Last visit: 18 Nov 2025

Posts: 5,793

Own Kudos:

5,508

Given Kudos: 161

Location: India

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

WE:Engineering (Transportation)

Products:

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

Posts: 5,793

Kudos: 5,508

22 Jul 2022, 09:49

Kudos

Bookmarks

Bunuel please check the solution
and correct OA as D 20

Kinshook

Asked: If the least common multiple of positive integers, x, y and z is 30, then how many different values can \(|x - y| + |x - z| + |y - z|\) take ?

30 = 2*3*5
Number of factors of 30 = {1,2,3,5,6,10,15,30} = (1+2)(1+3)(1+5) : 8 factors
LCM(x,y,z) = 30

Without loss of generality, let us assume that x>=y>=z

|x - y| + |x - z| + |y - z| = (x-y) + (x-z) + (y-z) = 2x -2z = 2(x-z)
x-z = {29,28,27,25,24,20,15,14,13,12,10,9,8,7,5,4,3,2,1,0} : 20 different values
|x - y| + |x - z| + |y - z| = 2(x-z) = {58,56,54,50,48,40,30,28,26,24,20,18,16,14,10,8,6,4,2,0} : 20 different values

For illustration: -
If x=30; y=30, z=30; |x - y| + |x - z| + |y - z| = 0
If x=30; y=30, z=15; |x - y| + |x - z| + |y - z| = 30
If x=30; y=30, z=10; |x - y| + |x - z| + |y - z| = 40
If x=30; y=30, z=6; |x - y| + |x - z| + |y - z| = 48
If x=30; y=30, z=5; |x - y| + |x - z| + |y - z| = 50
If x=30; y=30, z=3; |x - y| + |x - z| + |y - z| = 54
If x=30; y=30, z=2; |x - y| + |x - z| + |y - z| = 56
If x=30; y=30, z=1; |x - y| + |x - z| + |y - z| = 58

If x=15; y=15, z=10; |x - y| + |x - z| + |y - z| = 10
If x=15; y=15, z=6; |x - y| + |x - z| + |y - z| = 18
If x=15; y=15, z=5; |x - y| + |x - z| + |y - z| = 20
If x=15; y=15, z=3; |x - y| + |x - z| + |y - z| = 24
If x=15; y=15, z=2; |x - y| + |x - z| + |y - z| = 26
If x=15; y=15, z=1; |x - y| + |x - z| + |y - z| = 28

If x=10; y=10, z=6; |x - y| + |x - z| + |y - z| = 8
If x=10; y=10, z=5; |x - y| + |x - z| + |y - z| = 10
If x=10; y=10, z=3; |x - y| + |x - z| + |y - z| = 14
If x=10; y=10, z=2; |x - y| + |x - z| + |y - z| = 16
If x=10; y=10, z=1; |x - y| + |x - z| + |y - z| = 18

If x=6; y=6, z=5; |x - y| + |x - z| + |y - z| = 2
If x=6; y=6, z=3; |x - y| + |x - z| + |y - z| = 6
If x=6; y=6, z=2; |x - y| + |x - z| + |y - z| = 8
If x=6; y=6, z=1; |x - y| + |x - z| + |y - z| = 10

If x=5; y=5, z=3; |x - y| + |x - z| + |y - z| = 4
If x=5; y=5, z=2; |x - y| + |x - z| + |y - z| = 6
If x=5; y=5, z=1; |x - y| + |x - z| + |y - z| = 8

If x=3; y=3, z=2; |x - y| + |x - z| + |y - z| = 2
If x=3; y=3, z=1; |x - y| + |x - z| + |y - z| = 4

If x=2; y=2, z=1; |x - y| + |x - z| + |y - z| = 2

|x - y| + |x - z| + |y - z| + {0,2,4,6,8,10,14,16,18,20,24,26,28,30,40,48,50,54,56,58} : 20 different values.

IMO D

ThatDudeKnows

Tutor

Joined: 11 May 2022

Last visit: 27 Jun 2024

Posts: 1,070

Own Kudos:

977

Given Kudos: 79

Expert

Expert reply

Posts: 1,070

Kudos: 977

22 Jul 2022, 10:14

Kudos

Bookmarks

Kinshook

Bunuel please check the solution
and correct OA as D 20

Kinshook

Kinshook

If x=15; y=15, z=5, the LCM is 15, not 30.
15, 15, 3 --> LCM 15, not 30
10, 10, 5 --> LCM 10, not 30
10, 10, 2 --> LCM 10, not 30
10, 10, 1 --> LCM 10, not 30
6, 6, 3 --> LCM 6, not 30
6, 6, 2 --> LCM 6, not 30
6, 6, 1 --> LCM 6, not 30
5, 5, 3 --> LCM 15, not 30
5, 5, 1 --> LCM 5, not 30
3, 3, 1 --> LCM 3, not 30
2, 2, 1 --> LCM 2, not 30

Your list also omits all the options where the two larger values are not equal:
30,15,15
30,15,10
30,15,6
30,15,5
30,15,3
30,15,2
30,15,1
15,10,10
15,10,6
15,10,5
15,10,3
15,10,2
15,10,1
10,6,6
10,6,5
10,6,3
10,6,2
10,6,1
10,3,3
10,3,2
10,3,1
6,5,5
6,5,3
6,5,2
6,5,1

Kinshook

Major Poster

Joined: 03 Jun 2019

Last visit: 18 Nov 2025

Posts: 5,793

Own Kudos:

5,508

Given Kudos: 161

Location: India

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

WE:Engineering (Transportation)

Products:

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

Posts: 5,793

Kudos: 5,508

22 Jul 2022, 22:28

Kudos

Bookmarks

ThatDudeKnows
OK. Thanks

ThatDudeKnows

Kinshook

Bunuel please check the solution
and correct OA as D 20

Kinshook

Adarsh_24

Joined: 06 Jan 2024

Last visit: 03 Apr 2025

Posts: 251

Own Kudos:

Given Kudos: 2,016

Posts: 251

Kudos: 57

08 Aug 2024, 05:40

Kudos

Bookmarks

chetan2u

Bunuel

If the least common multiple of positive integers, x, y and z is 30, then how many different values can \(|x - y| + |x - z| + |y - z|\) take ?

A. 17
B. 18
C. 19
D. 20
E. 21

This question was provided by GMAT Club
for the GMAT Club World Cup Competition

Compete, Get Better, Win prizes and more

Bunuel chetan2u Why are we not considering difference 0? Is it implied that x, y and z cant repeat?
If so, how can 1 be considered without repeating once?

CityOfStar

Joined: 29 Dec 2023

Last visit: 05 Jun 2025

Posts: 8

Own Kudos:

Given Kudos: 63

GMAT Focus 1: 645 Q86 V81 DI78 Verified score

Posts: 8

Kudos: 30

22 Aug 2024, 15:38

Kudos

Bookmarks

chetan2u

Bunuel

If the least common multiple of positive integers, x, y and z is 30, then how many different values can \(|x - y| + |x - z| + |y - z|\) take ?

A. 17
B. 18
C. 19
D. 20
E. 21

This question was provided by GMAT Club
for the GMAT Club World Cup Competition

Compete, Get Better, Win prizes and more

Largesr one can only till 5, and in this case only 5,3,2 will work, so Max-Min is only 3, not 2. Your answer is lacking of 0 but adding 2.

Different values: 29,28,27,25,24,20,15,14,13,12,10,9,8,7,5,4,3,0,1

Moderators:

Bunuel

Math Expert

105355 posts

Krunaal

Tuck School Moderator

805 posts

Prep Toolkit

Announcements

Master in Management, Finance, Business Analytics and more Master’s Programs!

Solving 705+ Level MSR Questions with Data Synthesis Skils

Tuesday, Nov 18, 2025
10:30am NY / 3:30pm London / 9pm Mumbai

Live Profile Evaluation Chat Session with ARINGO

Wednesday, November 19, 2025
09:00 am PDT | 10:30 pm IST
Location: GMAT Club Chat

Top GMAT Focus Debriefs

GMAT Club World Cup 2022 (DAY 8): If the least common multiple of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

GMAT Club World Cup 2022 (DAY 8): If the least common multiple of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards