GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Dec 2018, 06:38

# R1 Decisions:

Michigan Ross Chat (US calls are expected today)  |  UCLA Anderson Chat  (Calls expected to start at 7am PST; Applicants from Asia will hear first)

### 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

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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### 10 Keys to nail DS and CR questions

December 17, 2018

December 17, 2018

06:00 PM PST

07:00 PM PST

Join our live webinar and learn how to approach Data Sufficiency and Critical Reasoning problems, how to identify the best way to solve each question and what most people do wrong.
• ### R1 Admission Decisions: Estimated Decision Timelines and Chat Links for Major BSchools

December 17, 2018

December 17, 2018

10:00 PM PST

11:00 PM PST

From Dec 5th onward, American programs will start releasing R1 decisions. Chat Rooms: We have also assigned chat rooms for every school so that applicants can stay in touch and exchange information/update during decision period.

# A and B can do a piece of work in 10 days, while B and C can do the sa

Author Message
TAGS:

### Hide Tags

Intern
Joined: 11 Sep 2013
Posts: 6
A and B can do a piece of work in 10 days, while B and C can do the sa  [#permalink]

### Show Tags

Updated on: 08 Nov 2016, 01:48
1
4
00:00

Difficulty:

95% (hard)

Question Stats:

58% (03:13) correct 42% (03:42) wrong based on 119 sessions

### HideShow timer Statistics

A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?

A. 16
B. 32
C. 64
D. 96
E. None of These

Originally posted by Emdadul28 on 08 Nov 2016, 01:45.
Last edited by Bunuel on 08 Nov 2016, 01:48, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 51261
Re: A and B can do a piece of work in 10 days, while B and C can do the sa  [#permalink]

### Show Tags

08 Nov 2016, 02:03
4
3
A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?

A. 16
B. 32
C. 64
D. 96
E. None of These

Let the rates of A, B and C be a, b, and c respectively.

A and B can do a piece of work in 10 days: a + b = 1/10;
B and C can do the same work in 15 days: b + c = 1/15;
C and A can do the same work in 25 days: c + a = 1/25.

Sum the above 3 equations: 2(a + b + c) = 31/150 --> a + b + c = 31/300
Subtract a + b = 1/10 from above to get c = 1/300.

For 4 days all 3 worked and completed 4*(a + b + a) = 124/300 of the work.
For the next 4 days B and C worked and they completed 4(b + c) = 4/15 = 80/300 of the work.

So, by the time C is left alone 1 - (124/300 + 80/300) = 96/300 of the work is left to be completed by C alone.
Time = Job/Rate = (96/300)/(1/300) = 96 days.

_________________
##### General Discussion
Intern
Joined: 11 Sep 2013
Posts: 6
Re: A and B can do a piece of work in 10 days, while B and C can do the sa  [#permalink]

### Show Tags

08 Nov 2016, 04:01
Bunuel wrote:
A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?

A. 16
B. 32
C. 64
D. 96
E. None of These

Let the rates of A, B and C be a, b, and c respectively.

A and B can do a piece of work in 10 days: a + b = 1/10;
B and C can do the same work in 15 days: b + c = 1/15;
C and A can do the same work in 25 days: c + a = 1/25.

Sum the above 3 equations: 2(a + b + c) = 31/150 --> a + b + c = 31/300
Subtract a + b = 1/10 from above to get c = 1/300.

For 4 days all 3 worked and completed 4*(a + b + a) = 124/300 of the work.
For the next 4 days B and C worked and they completed 4(b + c) = 4/15 = 80/300 of the work.

So, by the time C is left alone 1 - (124/300 + 80/300) = 96/300 of the work is left to be completed by C alone.
Time = Job/Rate = (96/300)/(1/300) = 96 days.

Quote:
Assume that total units of work =LCM (10,15,25) = 60 units

Since A and B finish the work in 10 days, work done by them in a day = 60/10 = 6 units/day

AND B and C finish the work in 15 days, work done by them in a day = 60/15 = 4 units/day

AND C and A finish the work in 20 days, work done by them in a day = 60/20 = 3 units/day

@@@ Thanks for this. Can I do this math like this way? If so then help me to complete this math.
Math Expert
Joined: 02 Sep 2009
Posts: 51261
Re: A and B can do a piece of work in 10 days, while B and C can do the sa  [#permalink]

### Show Tags

08 Nov 2016, 05:35
Bunuel wrote:
A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?

A. 16
B. 32
C. 64
D. 96
E. None of These

Let the rates of A, B and C be a, b, and c respectively.

A and B can do a piece of work in 10 days: a + b = 1/10;
B and C can do the same work in 15 days: b + c = 1/15;
C and A can do the same work in 25 days: c + a = 1/25.

Sum the above 3 equations: 2(a + b + c) = 31/150 --> a + b + c = 31/300
Subtract a + b = 1/10 from above to get c = 1/300.

For 4 days all 3 worked and completed 4*(a + b + a) = 124/300 of the work.
For the next 4 days B and C worked and they completed 4(b + c) = 4/15 = 80/300 of the work.

So, by the time C is left alone 1 - (124/300 + 80/300) = 96/300 of the work is left to be completed by C alone.
Time = Job/Rate = (96/300)/(1/300) = 96 days.

Quote:
Assume that total units of work =LCM (10,15,25) = 60 units

Since A and B finish the work in 10 days, work done by them in a day = 60/10 = 6 units/day

AND B and C finish the work in 15 days, work done by them in a day = 60/15 = 4 units/day

AND C and A finish the work in 20 days, work done by them in a day = 60/20 = 3 units/day

@@@ Thanks for this. Can I do this math like this way? If so then help me to complete this math.

You can continue basically exactly the same way with this approach.
_________________
Senior Manager
Joined: 06 Jun 2016
Posts: 258
Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
A and B can do a piece of work in 10 days, while B and C can do the sa  [#permalink]

### Show Tags

08 Nov 2016, 06:06
Bunuel wrote:
A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?

A. 16
B. 32
C. 64
D. 96
E. None of These

Let the rates of A, B and C be a, b, and c respectively.

A and B can do a piece of work in 10 days: a + b = 1/10;
B and C can do the same work in 15 days: b + c = 1/15;
C and A can do the same work in 25 days: c + a = 1/25.

Sum the above 3 equations: 2(a + b + c) = 31/150 --> a + b + c = 31/300
Subtract a + b = 1/10 from above to get c = 1/300.

For 4 days all 3 worked and completed 4*(a + b + a) = 124/300 of the work.
For the next 4 days B and C worked and they completed 4(b + c) = 4/15 = 80/300 of the work.

So, by the time C is left alone 1 - (124/300 + 80/300) = 96/300 of the work is left to be completed by C alone.
Time = Job/Rate = (96/300)/(1/300) = 96 days.

Quote:
Assume that total units of work =LCM (10,15,25) = 60 units LCM(10,15,25)=300

Since A and B finish the work in 10 days, work done by them in a day = 60/10 = 6 units/day 300/10= 30 units

AND B and C finish the work in 15 days, work done by them in a day = 60/15 = 4 units/day 300/15= 20 units

AND C and A finish the work in 20 days, work done by them in a day = 60/20 = 3 units/day
AND C and A finish the work in 25 days, work done by them in a day = 300/25 = 12 units/day

Certain data have been wrongly noted down

@@@ Thanks for this. Can I do this math like this way? If so then help me to complete this math.
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4277
Location: India
GPA: 3.5
Re: A and B can do a piece of work in 10 days, while B and C can do the sa  [#permalink]

### Show Tags

08 Nov 2016, 10:01
3
A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?

A. 16
B. 32
C. 64
D. 96
E. None of These

Let the total work be 150 units

Efficiency of A + B = 15 units/day
Efficiency of B + C = 10 units/day
Efficiency of A + C = 6 units/day

Efficiency of A + B + C = 15.5 units/day

So, Efficiency of A is = Efficiency of A + B + C - Efficiency of B + C

Or, Efficiency of A is = 15.5 - 10

Or, Efficiency of A is = 5.5

Similarly Efficiency of B is = 9.5 and, Efficiency of C is = 0.50

Quote:
they started working together, after 4 days A left.

Work done by A + B + C in 4 days is 15.5*4 = 62

Now, B + C works

Quote:
After another 4 days B left.

Work done by B + C in 4 days is 10*4 = 40 units

So, total work done is 102 units, and work left is 48 units..

Time taken by C to finish this work is $$\frac{48}{0.5}$$ = 96 days...

Hence, answer will be (D) 96 days..

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Non-Human User
Joined: 09 Sep 2013
Posts: 9197
Re: A and B can do a piece of work in 10 days, while B and C can do the sa  [#permalink]

### Show Tags

24 Feb 2018, 02:52
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: A and B can do a piece of work in 10 days, while B and C can do the sa &nbs [#permalink] 24 Feb 2018, 02:52
Display posts from previous: Sort by