Last visit was: 24 Apr 2026, 04:13 It is currently 24 Apr 2026, 04:13
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
iamasif
User avatar
Joined: 14 Jul 2019
Last visit: 05 Dec 2021
Posts: 3
Own Kudos:
29
 [25]
Given Kudos: 722
Location: Bangladesh
GPA: 3.48
Posts: 3
Kudos: 29
 [25]
Three workers A, B, C working individually can complete a task 24 Nov 2020, 08:59
6
Kudos
Add Kudos
19
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:

95% (hard)

Question Stats:

35% (02:27) correct 65% (02:12) wrong based on 198 sessions

History

Date
Time
Result
Not Attempted Yet
Three workers A, B, C working individually can complete a task in 30 days, 15 days, and 10 days respectively. If A starts the task alone, and B and C helps A on every second and third day respectively, on which day will the task be completed?

A. 10
B. 12
C. 14
D. 15
E. None of these
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
globaldesi
User avatar
Joined: 28 Jul 2016
Last visit: 23 Feb 2026
Posts: 1,141
Own Kudos:
1,999
 [6]
Given Kudos: 67
Location: India
Concentration: Finance, Human Resources
Schools: ISB '18 (D)
GPA: 3.97
WE:Project Management (Finance: Investment Banking)
Products:
My Reviews
Schools: ISB '18 (D)
Posts: 1,141
Kudos: 1,999
 [6]
Three workers A, B, C working individually can complete a task 24 Nov 2020, 09:55
5
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
iamasif
Please correct me if I've done anything wrong. If anyone could find a simpler approach then please do share that approach.

A does in 1 day = \(\frac{1}{30}\)
B does in 1 day = \(\frac{1}{15}\)
C does in 1 day = \(\frac{1}{10}\)

Day 1 - Only A - \(\frac{1}{30}\)
Day 2 - A+B - \(\frac{1}{30}\) + \(\frac{1}{15}\) = \(\frac{1}{10}\)
Day 3 - A+C - \(\frac{1}{30}\) + \(\frac{1}{10}\) = \(\frac{2}{15}\)
Day 4 - A+B - \(\frac{1}{30}\) + \(\frac{1}{15}\) = \(\frac{1}{10}\)
Day 5 - Only A - \(\frac{1}{30}\)
Day 6 - A+B+C - \(\frac{1}{30}\) + \(\frac{1}{15}\) + \(\frac{1}{10}\) = \(\frac{1}{5}\)

This repeats from Day 7...



So, total work in 6 days = \(\frac{1}{30}\) + \(\frac{1}{10}\) + \(\frac{2}{15}\) + \(\frac{1}{10}\) + \(\frac{1}{30}\) + \(\frac{1}{5}\) = \(\frac{3}{5}\)

Remaining Task = \(\frac{2}{5}\), which takes 5 days more as,

Task completed in 5 days,
\(\frac{1}{30}\) + \(\frac{1}{10}\) + \(\frac{2}{15}\) + \(\frac{1}{10}\) + \(\frac{1}{30}\) = \(\frac{2}{5}\)

Therefore, 6+5 = 11 days needed.
Show more



then i think the question framing is wrong :
when the question says every second and third day:
It means second (alternate day)
and third means (every third day)
so basically on 6th day they three will be working

Apologies but the question language is little misleading
General Discussion
User avatar
ravigupta2912
User avatar
Current Student
Joined: 26 May 2019
Last visit: 16 Feb 2025
Posts: 717
Own Kudos:
299
 [3]
Given Kudos: 84
Location: India
Schools: Said '23 IESE '24 LBS '24 (D) ISB '23 (WA) INSEAD Aug 22 intake (D) Judge '23 (D)
GMAT 1: 650 Q46 V34
GMAT 2: 720 Q49 V40
GPA: 2.58
WE:Consulting (Consulting)
Products:
My Reviews
Schools: Said '23 IESE '24 LBS '24 (D) ISB '23 (WA) INSEAD Aug 22 intake (D) Judge '23 (D)
GMAT 2: 720 Q49 V40
Posts: 717
Kudos: 299
 [3]
Three workers A, B, C working individually can complete a task 24 Nov 2020, 09:08
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
I am not sure how OA is E. I arrived at A through this. If standard rate is 1/15 and 1/30, then if people work every second and third day, the rate would be 1/15*1/2 and 1/10*1/3 or 1/30 and 1/30

Accordingly combined rate would be 3/30 or 1/10. Hence time taken is 10 days.

What am I missing here?

Posted from my mobile device
User avatar
iamasif
User avatar
Joined: 14 Jul 2019
Last visit: 05 Dec 2021
Posts: 3
Own Kudos:
29
 [4]
Given Kudos: 722
Location: Bangladesh
GPA: 3.48
Posts: 3
Kudos: 29
 [4]
Three workers A, B, C working individually can complete a task 24 Nov 2020, 09:32
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Please correct me if I've done anything wrong. If anyone could find a simpler approach then please do share that approach.

A does in 1 day = \(\frac{1}{30}\)
B does in 1 day = \(\frac{1}{15}\)
C does in 1 day = \(\frac{1}{10}\)

Day 1 - Only A - \(\frac{1}{30}\)
Day 2 - A+B - \(\frac{1}{30}\) + \(\frac{1}{15}\) = \(\frac{1}{10}\)
Day 3 - A+C - \(\frac{1}{30}\) + \(\frac{1}{10}\) = \(\frac{2}{15}\)
Day 4 - A+B - \(\frac{1}{30}\) + \(\frac{1}{15}\) = \(\frac{1}{10}\)
Day 5 - Only A - \(\frac{1}{30}\)
Day 6 - A+B+C - \(\frac{1}{30}\) + \(\frac{1}{15}\) + \(\frac{1}{10}\) = \(\frac{1}{5}\)

This repeats from Day 7...

So, total work in 6 days = \(\frac{1}{30}\) + \(\frac{1}{10}\) + \(\frac{2}{15}\) + \(\frac{1}{10}\) + \(\frac{1}{30}\) + \(\frac{1}{5}\) = \(\frac{3}{5}\)

Remaining Task = \(\frac{2}{5}\), which takes 5 days more as,

Task completed in 5 days,
\(\frac{1}{30}\) + \(\frac{1}{10}\) + \(\frac{2}{15}\) + \(\frac{1}{10}\) + \(\frac{1}{30}\) = \(\frac{2}{5}\)

Therefore, 6+5 = 11 days needed.
User avatar
iamasif
User avatar
Joined: 14 Jul 2019
Last visit: 05 Dec 2021
Posts: 3
Own Kudos:
29
Given Kudos: 722
Location: Bangladesh
GPA: 3.48
Posts: 3
Kudos: 29
Three workers A, B, C working individually can complete a task 24 Nov 2020, 10:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
globaldesi
iamasif
Please correct me if I've done anything wrong. If anyone could find a simpler approach then please do share that approach.

A does in 1 day = \(\frac{1}{30}\)
B does in 1 day = \(\frac{1}{15}\)
C does in 1 day = \(\frac{1}{10}\)

Day 1 - Only A - \(\frac{1}{30}\)
Day 2 - A+B - \(\frac{1}{30}\) + \(\frac{1}{15}\) = \(\frac{1}{10}\)
Day 3 - A+C - \(\frac{1}{30}\) + \(\frac{1}{10}\) = \(\frac{2}{15}\)
Day 4 - A+B - \(\frac{1}{30}\) + \(\frac{1}{15}\) = \(\frac{1}{10}\)
Day 5 - Only A - \(\frac{1}{30}\)
Day 6 - A+B+C - \(\frac{1}{30}\) + \(\frac{1}{15}\) + \(\frac{1}{10}\) = \(\frac{1}{5}\)

This repeats from Day 7...



So, total work in 6 days = \(\frac{1}{30}\) + \(\frac{1}{10}\) + \(\frac{2}{15}\) + \(\frac{1}{10}\) + \(\frac{1}{30}\) + \(\frac{1}{5}\) = \(\frac{3}{5}\)

Remaining Task = \(\frac{2}{5}\), which takes 5 days more as,

Task completed in 5 days,
\(\frac{1}{30}\) + \(\frac{1}{10}\) + \(\frac{2}{15}\) + \(\frac{1}{10}\) + \(\frac{1}{30}\) = \(\frac{2}{5}\)

Therefore, 6+5 = 11 days needed.



then i think the question framing is wrong :
when the question says every second and third day:
It means second (alternate day)
and third means (every third day)
so basically on 6th day they three will be working

Apologies but the question language is little misleading
Show more

Yes, you're right. Look at the solution, on Day 6 they all work together (Day 6 - A+B+C - \(\frac{1}{30}\) + \(\frac{1}{15}\) + \(\frac{1}{10}\) = \(\frac{1}{5}\)
)
User avatar
TestPrepUnlimited
User avatar
Joined: 17 Sep 2014
Last visit: 30 Jun 2022
Posts: 1,223
Own Kudos:
1,138
 [1]
Given Kudos: 6
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Expert
Expert reply
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Posts: 1,223
Kudos: 1,138
 [1]
Three workers A, B, C working individually can complete a task Updated on: 24 Nov 2020, 21:43
Originally posted by TestPrepUnlimited on 24 Nov 2020, 21:36.
Last edited by TestPrepUnlimited on 24 Nov 2020, 21:43, edited 1 time in total.
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
iamasif
Three workers A, B, C working individually can complete a task in 30 days, 15 days, and 10 days respectively. If A starts the task alone, and B and C helps A on every second and third day respectively, on which day will the task be completed?

A. 10
B. 12
C. 14
D. 15
E. None of these
Show more

\(A\) works every day so let us start with a rate of 1/30. Next, B has a rate of 1/15 if he were to work every day. Instead, he works every two days. We may average out his work by saying he does 1/30 every day instead. Similarly, for C we average out his work so that he does 1/30 every day.

Thus the rate is 1/30*3 = 1/10. Let us use this rate for only 6 days however as we need to decide which exact day the task will be completed.

There is 40% of the task left, we may subtract from 60% instead to find how many days are required. The last day of each 6th day, all of ABC are working together. Their combined rate is 1/30 + 1/15 + 1/10 = 6/30 = 1/5 = 20% of the task. Thus if we take away the 6th day, they complete only 40% for the first 5 days of the 6. Then they need 6 + 5 = 11 days to complete 100%.

Ans: E
User avatar
TestPrepUnlimited
User avatar
Joined: 17 Sep 2014
Last visit: 30 Jun 2022
Posts: 1,223
Own Kudos:
1,138
 [1]
Given Kudos: 6
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Expert
Expert reply
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Posts: 1,223
Kudos: 1,138
 [1]
Three workers A, B, C working individually can complete a task 24 Nov 2020, 21:39
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ravigupta2912
I am not sure how OA is E. I arrived at A through this. If standard rate is 1/15 and 1/30, then if people work every second and third day, the rate would be 1/15*1/2 and 1/10*1/3 or 1/30 and 1/30

Accordingly combined rate would be 3/30 or 1/10. Hence time taken is 10 days.

What am I missing here?

Posted from my mobile device
Show more

Hi ravigupta2912 ,

You were assuming constant rates throughout the course of the job. That is ok every 6 days, but for the last part we need to add the rates (or subtract from 60%) one by one since they get the job done unevenly during the last 40% of the job (the 6th day as much more weight compared to the average daily rate).
User avatar
ravigupta2912
User avatar
Current Student
Joined: 26 May 2019
Last visit: 16 Feb 2025
Posts: 717
Own Kudos:
299
Given Kudos: 84
Location: India
Schools: Said '23 IESE '24 LBS '24 (D) ISB '23 (WA) INSEAD Aug 22 intake (D) Judge '23 (D)
GMAT 1: 650 Q46 V34
GMAT 2: 720 Q49 V40
GPA: 2.58
WE:Consulting (Consulting)
Products:
My Reviews
Schools: Said '23 IESE '24 LBS '24 (D) ISB '23 (WA) INSEAD Aug 22 intake (D) Judge '23 (D)
GMAT 2: 720 Q49 V40
Posts: 717
Kudos: 299
Three workers A, B, C working individually can complete a task 24 Nov 2020, 22:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks TestPrepUnlimited. Understood, I needed to multiply that rate with 6 days (since 1/10 is avg for 6 day period) to derive the work done (6/10) in 6 days and then compute time needed for the balance 4/10 or 40% of work.
User avatar
globaldesi
User avatar
Joined: 28 Jul 2016
Last visit: 23 Feb 2026
Posts: 1,141
Own Kudos:
1,999
Given Kudos: 67
Location: India
Concentration: Finance, Human Resources
Schools: ISB '18 (D)
GPA: 3.97
WE:Project Management (Finance: Investment Banking)
Products:
My Reviews
Schools: ISB '18 (D)
Posts: 1,141
Kudos: 1,999
Three workers A, B, C working individually can complete a task 25 Nov 2020, 03:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
iamasif
globaldesi
iamasif
Please correct me if I've done anything wrong. If anyone could find a simpler approach then please do share that approach.

A does in 1 day = \(\frac{1}{30}\)
B does in 1 day = \(\frac{1}{15}\)
C does in 1 day = \(\frac{1}{10}\)

Day 1 - Only A - \(\frac{1}{30}\)
Day 2 - A+B - \(\frac{1}{30}\) + \(\frac{1}{15}\) = \(\frac{1}{10}\)
Day 3 - A+C - \(\frac{1}{30}\) + \(\frac{1}{10}\) = \(\frac{2}{15}\)
Day 4 - A+B - \(\frac{1}{30}\) + \(\frac{1}{15}\) = \(\frac{1}{10}\)
Day 5 - Only A - \(\frac{1}{30}\)
Day 6 - A+B+C - \(\frac{1}{30}\) + \(\frac{1}{15}\) + \(\frac{1}{10}\) = \(\frac{1}{5}\)

This repeats from Day 7...



So, total work in 6 days = \(\frac{1}{30}\) + \(\frac{1}{10}\) + \(\frac{2}{15}\) + \(\frac{1}{10}\) + \(\frac{1}{30}\) + \(\frac{1}{5}\) = \(\frac{3}{5}\)

Remaining Task = \(\frac{2}{5}\), which takes 5 days more as,

Task completed in 5 days,
\(\frac{1}{30}\) + \(\frac{1}{10}\) + \(\frac{2}{15}\) + \(\frac{1}{10}\) + \(\frac{1}{30}\) = \(\frac{2}{5}\)

Therefore, 6+5 = 11 days needed.



then i think the question framing is wrong :
when the question says every second and third day:
It means second (alternate day)
and third means (every third day)
so basically on 6th day they three will be working

Apologies but the question language is little misleading

Yes, you're right. Look at the solution, on Day 6 they all work together (Day 6 - A+B+C - \(\frac{1}{30}\) + \(\frac{1}{15}\) + \(\frac{1}{10}\) = \(\frac{1}{5}\)
)
Show more

apologies, I forgot to check the solution.
Ye sit is then correct . we have to check till 6 days how much is completed and then the rest
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 24 Apr 2026
Posts: 4,846
Own Kudos:
9,182
 [4]
Given Kudos: 226
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,846
Kudos: 9,182
 [4]
Three workers A, B, C working individually can complete a task 25 Nov 2020, 04:02
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
CONCEPT: Time and Work/Rate of completing a work
Efficiency is inversely proportionate to time.

SOLUTION: Let the total work = LCM(30,15,10)=30 units
A's efficiency =30/30=1unit/day; B's efficiency=30/15=2unit/day 'C's efficiency=30/10=3units/day.
Work done in three consecutive days= [1+(1+2)+(1+3)]=8 units.
Hence, work completed in 9 days= 8*3=24 units.
Work completed by A on 10th day=1 unit.
Work completed by A & B on 11th day =3 units.
Total work completed as of now =24+1+3=28 units.
On 12th day, the remaining 2 units of work is completed by utilizing 2/4=1/2 of the day.
(As 4 units is the efficiency of every 3rd day by A and C)
Hence, total days needed to complete the task is 11 1/2 days. (E)

Hope this helps. :) Keep studying :thumbsup:
Devmitra Sen
User avatar
ThatDudeKnows
User avatar
Joined: 11 May 2022
Last visit: 27 Jun 2024
Posts: 1,070
Own Kudos:
1,030
 [2]
Given Kudos: 79
Expert
Expert reply
Posts: 1,070
Kudos: 1,030
 [2]
Three workers A, B, C working individually can complete a task 24 May 2022, 18:47
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
iamasif
Three workers A, B, C working individually can complete a task in 30 days, 15 days, and 10 days respectively. If A starts the task alone, and B and C helps A on every second and third day respectively, on which day will the task be completed?

A. 10
B. 12
C. 14
D. 15
E. None of these
Show more


On rates questions, rather than saying one of the workers completes 1/30 or 1/15 or 1/10 of the job, I strongly recommend just making up what the job is in such a way that you can avoid messing around with the fractions!!

Let's say the task is to solve 30 GMAT questions.
A can complete the task in 30 days, so A solves one GMAT question per day.
B can complete the task in 15 days, so B solves two GMAT questions per day.
C can complete the task in 10 days, so C solves three GMAT questions per day.

On day 1, only A works, so 1 question gets solved.
On day 2, A and B work, so 1+2=3 questions get solved. We have now completed 4 questions.
On day 3, A and C work, so 1+3=4 questions get solved. We have now completed 8 questions.
On day 4, A and B work, so 1+2=3 questions get solved. We have now completed 11 questions.
On day 5, only A works, so 1 question gets solved. We have now completed 12 questions.
On day 6, all three work, so 1+2+3=6 questions get solved. We have now completed 18 questions.
On day 7, only A works, so 1 question gets solved. We have now completed 19 questions.
On day 8, A and B work, so 1+2=3 questions get solved. We have now completed 22 questions.
On day 9, A and C work, so 1+3=4 questions get solved. We have now completed 26 questions.
On day 10, A and B work, so 1+2=3 questions get solved. We have now completed 29 questions.
On day 11, only A works, so 1 question gets solved. We have now completed all 30 questions.

11 days is not listed as an answer choice.

Answer choice E.


FWIW, I wrote all that to make it clear what I was doing, but this is what I wrote on scratch paper:
1 A 1 1
2 AB 3 4
3 AC 4 8
4 AB 3 11
...
...
11 A 1 30
avatar
shohan2722
avatar
Joined: 16 Jan 2022
Last visit: 01 Sep 2022
Posts: 9
Own Kudos:
6
Given Kudos: 25
Posts: 9
Kudos: 6
Three workers A, B, C working individually can complete a task 02 Jun 2022, 13:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ThatDudeKnows
iamasif
Three workers A, B, C working individually can complete a task in 30 days, 15 days, and 10 days respectively. If A starts the task alone, and B and C helps A on every second and third day respectively, on which day will the task be completed?

A. 10
B. 12
C. 14
D. 15
E. None of these


On rates questions, rather than saying one of the workers completes 1/30 or 1/15 or 1/10 of the job, I strongly recommend just making up what the job is in such a way that you can avoid messing around with the fractions!!

Let's say the task is to solve 30 GMAT questions.
A can complete the task in 30 days, so A solves one GMAT question per day.
B can complete the task in 15 days, so B solves two GMAT questions per day.
C can complete the task in 10 days, so C solves three GMAT questions per day.

On day 1, only A works, so 1 question gets solved.
On day 2, A and B work, so 1+2=3 questions get solved. We have now completed 4 questions.
On day 3, A and C work, so 1+3=4 questions get solved. We have now completed 8 questions.
On day 4, A and B work, so 1+2=3 questions get solved. We have now completed 11 questions.
On day 5, only A works, so 1 question gets solved. We have now completed 12 questions.
On day 6, all three work, so 1+2+3=6 questions get solved. We have now completed 18 questions.
On day 7, only A works, so 1 question gets solved. We have now completed 19 questions.
On day 8, A and B work, so 1+2=3 questions get solved. We have now completed 22 questions.
On day 9, A and C work, so 1+3=4 questions get solved. We have now completed 26 questions.
On day 10, A and B work, so 1+2=3 questions get solved. We have now completed 29 questions.
On day 11, only A works, so 1 question gets solved. We have now completed all 30 questions.

11 days is not listed as an answer choice.

Answer choice E.


FWIW, I wrote all that to make it clear what I was doing, but this is what I wrote on scratch paper:
1 A 1 1
2 AB 3 4
3 AC 4 8
4 AB 3 11
...
...
11 A 1 30
Show more
Shouldn't A be working alone on Day 4? Then joined by B on Day 5? Then again by C on day 6? Then alone again on day 7? Isn't that what the wording of the question said? I'm sorry but I'm having trouble understanding the way you drew the pattern. Excellent explanation though. Kudos awarded
User avatar
ThatDudeKnows
User avatar
Joined: 11 May 2022
Last visit: 27 Jun 2024
Posts: 1,070
Own Kudos:
1,030
 [1]
Given Kudos: 79
Expert
Expert reply
Posts: 1,070
Kudos: 1,030
 [1]
Three workers A, B, C working individually can complete a task 02 Jun 2022, 14:46
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
shohan2722
ThatDudeKnows
iamasif
Three workers A, B, C working individually can complete a task in 30 days, 15 days, and 10 days respectively. If A starts the task alone, and B and C helps A on every second and third day respectively, on which day will the task be completed?

A. 10
B. 12
C. 14
D. 15
E. None of these


On rates questions, rather than saying one of the workers completes 1/30 or 1/15 or 1/10 of the job, I strongly recommend just making up what the job is in such a way that you can avoid messing around with the fractions!!

Let's say the task is to solve 30 GMAT questions.
A can complete the task in 30 days, so A solves one GMAT question per day.
B can complete the task in 15 days, so B solves two GMAT questions per day.
C can complete the task in 10 days, so C solves three GMAT questions per day.

On day 1, only A works, so 1 question gets solved.
On day 2, A and B work, so 1+2=3 questions get solved. We have now completed 4 questions.
On day 3, A and C work, so 1+3=4 questions get solved. We have now completed 8 questions.
On day 4, A and B work, so 1+2=3 questions get solved. We have now completed 11 questions.
On day 5, only A works, so 1 question gets solved. We have now completed 12 questions.
On day 6, all three work, so 1+2+3=6 questions get solved. We have now completed 18 questions.
On day 7, only A works, so 1 question gets solved. We have now completed 19 questions.
On day 8, A and B work, so 1+2=3 questions get solved. We have now completed 22 questions.
On day 9, A and C work, so 1+3=4 questions get solved. We have now completed 26 questions.
On day 10, A and B work, so 1+2=3 questions get solved. We have now completed 29 questions.
On day 11, only A works, so 1 question gets solved. We have now completed all 30 questions.

11 days is not listed as an answer choice.

Answer choice E.


FWIW, I wrote all that to make it clear what I was doing, but this is what I wrote on scratch paper:
1 A 1 1
2 AB 3 4
3 AC 4 8
4 AB 3 11
...
...
11 A 1 30
Shouldn't A be working alone on Day 4? Then joined by B on Day 5? Then again by C on day 6? Then alone again on day 7? Isn't that what the wording of the question said? I'm sorry but I'm having trouble understanding the way you drew the pattern. Excellent explanation though. Kudos awarded
Show more

I think this might boil down to a misunderstand of how the word “respectively” in a situation like this? “B and C helps A on every second and third day respectively” means that B helps on every second day and C helps on every third day. So, B helps on days 2, 4, 6, 8,…and C helps on 3, 6, 9,… Does that help?

Posted from my mobile device
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,442
Own Kudos:
79,400
 [4]
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,442
Kudos: 79,400
 [4]
Three workers A, B, C working individually can complete a task 02 Jun 2022, 21:55
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
iamasif
Three workers A, B, C working individually can complete a task in 30 days, 15 days, and 10 days respectively. If A starts the task alone, and B and C helps A on every second and third day respectively, on which day will the task be completed?

A. 10
B. 12
C. 14
D. 15
E. None of these
Show more

A works everyday - 1, 2, 3, 4, 5, 6, 7, 8...
B works alternately - 2, 4, 6, 8, 10, 12 ...
C works on thirds - 3, 6, 9, 12...

We have a cycle of 6 days. (the LCM of 1, 2, 3).

In 6 days, A works every day and completes 6/30 = 1/5 of work.
B works on 3 days and completes 3/15 = 1/5 of work.
C works on 2 days and completes 2/10 = 1/5 of work.
So they all complete 3/5th work in first 6 days. So for 2/5th of work ( remaining work), they will take less than 6 days. Hence answer would be (A) or (E).
On the 6th day, they complete 1/30 + 1/15 + 1/10 = 6/30 = 1/5th of work. So in 5 days, they do 2/5th of the work (because they do 3/5th in 6 days).

Hence total number of days taken = 6 + 5 = 11

Answer (E)
User avatar
Regor60
User avatar
Joined: 21 Nov 2021
Last visit: 19 Apr 2026
Posts: 529
Own Kudos:
420
Given Kudos: 462
Posts: 529
Kudos: 420
Three workers A, B, C working individually can complete a task 03 Jun 2022, 05:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
A's daily rate is 1/30, so after 10 days 1/3 of the job is completed

Since B works every other day, he worked 10/2= 5 days multiplied by his 1/15 rate =
1/3 of the job

In 10 days C worked only the 3rd, 6th and 9th day = 3 days
multiplied by his rate of 1/10 = 3/10 of the job.

Total completed in 10 days:

1/3 + 1/3 + 3/10 = 29/30

So, 1/30th of the job remaining.

On the 11th day only A works and because his daily rate is 1/30, he works the whole day to complete the remaining 1/30 of the job

11 days

Posted from my mobile device
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,967
Own Kudos:
1,117
Posts: 38,967
Kudos: 1,117
Three workers A, B, C working individually can complete a task 11 Nov 2025, 02:13
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
109809 posts
Krunaal
Tuck School Moderator
853 posts