Last visit was: 28 Apr 2026, 14:16 It is currently 28 Apr 2026, 14:16
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: 28 Apr 2026
Posts: 109,950
Own Kudos:
811,779
 [18]
Given Kudos: 105,927
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: 109,950
Kudos: 811,779
 [18]
How many five-digit positive integers can be formed using each of the 08 May 2020, 09:30
Kudos
Add Kudos
18
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

54% (02:12) correct 46% (02:37) wrong based on 254 sessions

History

Date
Time
Result
Not Attempted Yet
How many five-digit positive integers can be formed using each of the digits from {1, 2, 3, 5} at least once such that they are a multiple of 15?

A. 36
B. 24
C. 18
D. 15
E. 12


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
E
User avatar
sujoykrdatta
User avatar
Joined: 26 Jun 2014
Last visit: 26 Apr 2026
Posts: 587
Own Kudos:
1,191
 [3]
Given Kudos: 14
Status:Mentor & Coach | GMAT Q51 | CAT 99.98
GMAT 1: 740 Q51 V39
Expert
Expert reply
GMAT 1: 740 Q51 V39
Posts: 587
Kudos: 1,191
 [3]
How many five-digit positive integers can be formed using each of the Updated on: 08 May 2020, 17:46
Originally posted by sujoykrdatta on 08 May 2020, 16:58.
Last edited by sujoykrdatta on 08 May 2020, 17:46, edited 1 time in total.
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
How many five-digit positive integers can be formed using each of the digits from {1, 2, 3, 5} at least once such that they are a multiple of 15?

A. 36
B. 24
C. 18
D. 15
E. 12
Are You Up For the Challenge: 700 Level Questions
Show more



Note: The question says that you should use 1, 2, 3, 5 at least once; it does not say that you should use only those digits


To make a number a multiple of 15, the number must be a multiple of 5, which, in this case, only possible if the units digit is 5 or 0
Also, the number must be a multiple of 3 => Sum of the digits is a multiple of 3

Since we need to use all the digits at least once, we already have a 4-digit number with sum of digits 1+2+3+5 = 11

If we wish to use the digit 0 at the end (units digit), the digits would be 1, 2, 3, 5, 0 => sum of the digits is 11, not divisible by 3. Hence, 0 cannot be used.

Thus, the possibilities are (keeping 5 fixed at the end):

# 1, 2, 3, 1, 5 => sum = 12 => Number of ways = 4!/2! = 12
# 1, 2, 3, 4, 5 => sum = 15 => Number of ways = 4! = 24
# 1, 2, 3, 7, 5 => sum = 18 => Number of ways = 4! = 24

Thus, we can form 12 + 24 + 24 = 60 such numbers


Now: This does not match any of the answer options.
So I am thinking that the question actually wanted to say that you can use ONLY the digits 1,2,3,5 at least once.
In that case, the answer is 12 (option E)
User avatar
firas92
User avatar
Current Student
Joined: 16 Jan 2019
Last visit: 02 Dec 2024
Posts: 616
Own Kudos:
1,766
Given Kudos: 142
Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
WE:Sales (Other)
Products:
My Reviews
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
Posts: 616
Kudos: 1,766
How many five-digit positive integers can be formed using each of the 08 May 2020, 17:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sujoykrdatta
Bunuel
How many five-digit positive integers can be formed using each of the digits from {1, 2, 3, 5} at least once such that they are a multiple of 15?

A. 36
B. 24
C. 18
D. 15
E. 12
Are You Up For the Challenge: 700 Level Questions



Note: The question says that you should use 1, 2, 3, 5 at least once; it does not say that you should use only those digits


To make a number a multiple of 15, the number must be a multiple of 5, which, in this case, only possible if the units digit is 5 or 0
Also, the number must be a multiple of 3 => Sum of the digits is a multiple of 3

Since we need to use all the digits at least once, we already have a 4-digit number with sum of digits 1+2+3+5 = 11

If we wish to use the digit 0 at the end (units digit), the digits would be 1, 2, 3, 5, 0 => sum of the digits is 11, not divisible by 3. Hence, 0 cannot be used.

Thus, the possibilities are:

# 1, 2, 3, 5, 1 => sum = 12
# 1, 2, 3, 5, 4 => sum = 15
# 1, 2, 3, 5, 7 => sum = 18


In each case, since the units digit is 5, we can arrange the other 4 digits (with one digit repeating) in 4!/2! = 6 ways
Thus, total cases = 6 x 3 = 18


Thus, we can form 18 such numbers
Answer C
Show more

Hi sujoykrdatta

In the highlighted cases, there is no repetition of digits so the four digits excluding 5 can be arranged in 4! ways right?

Btw, 4!/2!=12 and not 6

Posted from my mobile device
User avatar
sujoykrdatta
User avatar
Joined: 26 Jun 2014
Last visit: 26 Apr 2026
Posts: 587
Own Kudos:
1,191
Given Kudos: 14
Status:Mentor & Coach | GMAT Q51 | CAT 99.98
GMAT 1: 740 Q51 V39
Expert
Expert reply
GMAT 1: 740 Q51 V39
Posts: 587
Kudos: 1,191
How many five-digit positive integers can be formed using each of the 08 May 2020, 17:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
firas92
sujoykrdatta
Bunuel
How many five-digit positive integers can be formed using each of the digits from {1, 2, 3, 5} at least once such that they are a multiple of 15?

A. 36
B. 24
C. 18
D. 15
E. 12
Are You Up For the Challenge: 700 Level Questions



Note: The question says that you should use 1, 2, 3, 5 at least once; it does not say that you should use only those digits


To make a number a multiple of 15, the number must be a multiple of 5, which, in this case, only possible if the units digit is 5 or 0
Also, the number must be a multiple of 3 => Sum of the digits is a multiple of 3

Since we need to use all the digits at least once, we already have a 4-digit number with sum of digits 1+2+3+5 = 11

If we wish to use the digit 0 at the end (units digit), the digits would be 1, 2, 3, 5, 0 => sum of the digits is 11, not divisible by 3. Hence, 0 cannot be used.

Thus, the possibilities are:

# 1, 2, 3, 5, 1 => sum = 12
# 1, 2, 3, 5, 4 => sum = 15
# 1, 2, 3, 5, 7 => sum = 18


In each case, since the units digit is 5, we can arrange the other 4 digits (with one digit repeating) in 4!/2! = 6 ways
Thus, total cases = 6 x 3 = 18


Thus, we can form 18 such numbers
Answer C

Hi sujoykrdatta

In the highlighted cases, there is no repetition of digits so the four digits excluding 5 can be arranged in 4! ways right?

Btw, 4!/2!=12 and not 6

Posted from my mobile device
Show more


Oops - Yes :|

I guess I am making school-level errors now :|

Corrected - thank you
User avatar
lacktutor
User avatar
Joined: 25 Jul 2018
Last visit: 23 Oct 2023
Posts: 658
Own Kudos:
1,448
 [3]
Given Kudos: 69
Posts: 658
Kudos: 1,448
 [3]
How many five-digit positive integers can be formed using each of the 31 May 2020, 02:35
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
How many five-digit positive integers can be formed using each of the digits from {1, 2, 3, 5} at least once such that they are a multiple of 15?

Any five-digit positive integer, which is a multiple of 15 and formed using the digits from {1, 2, 3, 5} should end ....5.
Well, we could form 5-digit numbers:
---> 1123|5: ---> \(\frac{4!}{2!}= 12\)
---> 1223|5: ---> \(\frac{4!}{2!}= 12\)
---> 1323|5: ---> \(\frac{4!}{2!}= 12\)
---> 1523|5: ---> \(\frac{4!}{2!}= 12\)

So, we need to check those numbers whether they are divisible by 3 or not:
---> 1+1+2+3+5= 12 (divisible by 3)
---> 1+2+2+3+5=13 (not divisible by 3)
---> 1+3+2+3+5= 14 (not divisible by 3)
---> 1+5+2+3+5= 16 (not divisible by 3)

In total, there are 12 numbers, which are multiple of 15.
Answer (E).
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 28 Apr 2026
Posts: 5,989
Own Kudos:
5,862
 [1]
Given Kudos: 163
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,989
Kudos: 5,862
 [1]
How many five-digit positive integers can be formed using each of the 10 Jul 2021, 21:40
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Asked: How many five-digit positive integers can be formed using each of the digits from {1, 2, 3, 5} at least once such that they are a multiple of 15?

15 = 3*5
The 5-digit number formed using each of the digits from {1, 2, 3, 5} at least once such that they are a multiple of 15 should be multiple of 3 & 5 both.

For the number to be multiple of 5, last digit should be 5 only since 0 is not available.
For the number to be multiple of 3, sum of digits should be multiple of 3.

The 5-digit number be abcd5.
a + b + c + d + 5 = 3k
a + b + c + d = 3k - 5 = 3(k-2) + 1 = 3m + 1

Since each of the digits from {1, 2, 3, 5} is used at least once.
1 + 3 + 2 + 5 = 11
11 + 1 = 12

Therefore, 1 will be used twice while other digits from {2,3} is will be used once and 5 will be the last digit.

Number of such cases = 4!/2! = 12

IMO E
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 28 Apr 2026
Posts: 5,989
Own Kudos:
5,862
Given Kudos: 163
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,989
Kudos: 5,862
How many five-digit positive integers can be formed using each of the 10 Jul 2021, 21:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi sujoykrdatta

You can not use numbers 4 & 7 since the five-digit positive integers can be formed using each of the digits from {1, 2, 3, 5} at least once.

sujoykrdatta
Bunuel
How many five-digit positive integers can be formed using each of the digits from {1, 2, 3, 5} at least once such that they are a multiple of 15?

A. 36
B. 24
C. 18
D. 15
E. 12
Are You Up For the Challenge: 700 Level Questions



Note: The question says that you should use 1, 2, 3, 5 at least once; it does not say that you should use only those digits


To make a number a multiple of 15, the number must be a multiple of 5, which, in this case, only possible if the units digit is 5 or 0
Also, the number must be a multiple of 3 => Sum of the digits is a multiple of 3

Since we need to use all the digits at least once, we already have a 4-digit number with sum of digits 1+2+3+5 = 11

If we wish to use the digit 0 at the end (units digit), the digits would be 1, 2, 3, 5, 0 => sum of the digits is 11, not divisible by 3. Hence, 0 cannot be used.

Thus, the possibilities are (keeping 5 fixed at the end):

# 1, 2, 3, 1, 5 => sum = 12 => Number of ways = 4!/2! = 12
# 1, 2, 3, 4, 5 => sum = 15 => Number of ways = 4! = 24
# 1, 2, 3, 7, 5 => sum = 18 => Number of ways = 4! = 24

Thus, we can form 12 + 24 + 24 = 60 such numbers


Now: This does not match any of the answer options.
So I am thinking that the question actually wanted to say that you can use ONLY the digits 1,2,3,5 at least once.
In that case, the answer is 12 (option E)
Show more
User avatar
samarpan.g28
User avatar
Joined: 08 Dec 2023
Last visit: 18 Feb 2026
Posts: 315
Own Kudos:
136
Given Kudos: 1,236
Location: India
Concentration: General Management, Human Resources
Schools: IIMA '26 Schulich Sept '26 Montreal '26 HEC Sept '26
GPA: 8.88
WE:Engineering (Technology)
Schools: IIMA '26 Schulich Sept '26 Montreal '26 HEC Sept '26
Posts: 315
Kudos: 136
How many five-digit positive integers can be formed using each of the 16 Jan 2024, 08:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
How many five-digit positive integers can be formed using each of the digits from {1, 2, 3, 5} at least once such that they are a multiple of 15?

A. 36
B. 24
C. 18
D. 15
E. 12


Are You Up For the Challenge: 700 Level Questions
Show more

Multiple of 15 means the number is multiple of 3 and 5 too. If the number is multiple of 3, then the sum of digits is a multiple of 3. If the number is multiple of 5, then the number is divisible by 5 which means last digit shall always be 5. Now, 1+2+3+5=11. If we add 1 to it, then the sum becomes 12 and it becomes a 5-digit number too. Arrange the 5 digits keeping 5 at the end - 4!/2!=12(E).
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,987
Own Kudos:
1,119
Posts: 38,987
Kudos: 1,119
How many five-digit positive integers can be formed using each of the 16 Apr 2025, 08:19
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
109950 posts
Krunaal
Tuck School Moderator
852 posts