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Math Expert V
Joined: 02 Sep 2009
Posts: 57155
A, B and C can complete a piece of work in 24 days, 40 days and 60 day  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 68% (01:14) correct 32% (01:20) wrong based on 236 sessions

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A, B and C can complete a piece of work in 24 days, 40 days and 60 days, respectively. In how many days was the piece of work completed?

(1) A, B and C started working together, and A continued to work till the end.
(2) A, B and C started working together, B and C left the work 2 days and 7 days, respectively, before the completion of the work.

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Current Student P
Joined: 18 Aug 2016
Posts: 614
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: A, B and C can complete a piece of work in 24 days, 40 days and 60 day  [#permalink]

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2
Bunuel wrote:
A, B and C can complete a piece of work in 24 days, 40 days and 60 days, respectively. In how many days was the piece of work completed?

(1) A, B and C started working together, and A continued to work till the end.
(2) A, B and C started working together, B and C left the work 2 days and 7 days, respectively, before the completion of the work.

A does 1/24 of work in 1 day
B does 1/40 of work in 1 day
C does 1/60 of work in 1 day

(1) gives us A+B+C started together and A continued till the end but we do not know for how many days B & C worked
Not sufficient

(2) A+B+C started together, B worked for 2 days and C worked for 7 Days

We can say that

For 2 days (A+B+C)
For 5 days (A+C)
For the rest of days A alone

Lets assume the work to be 240 units
A works for 10 units/day
B works for 6 units/day
C works for 4 units/day

A+B+C = 20 units/day
A+C = 14 units/day

But we don't know if A continued till the end (Cannot assume that A completed the work after 7 days) hence Not sufficient
On combining both we can form the equation

2*20 + 5*14 + x*10 = 240

We can find x and add 7 days to it to get the answer

Hence C
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Luckisnoexcuse
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Joined: 30 Jan 2016
Posts: 1141
Re: A, B and C can complete a piece of work in 24 days, 40 days and 60 day  [#permalink]

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2
Bunuel wrote:
A, B and C can complete a piece of work in 24 days, 40 days and 60 days, respectively. In how many days was the piece of work completed?

(1) A, B and C started working together, and A continued to work till the end.
(2) A, B and C started working together, B and C left the work 2 days and 7 days, respectively, before the completion of the work.

(1) B and C could work any number of days, so not sufficient
(2) A worked (t+9) days

(t+9)x(1/24)+2/40+7/60=1;
(t+9)/24=120/120-6/120-14/120;
(t+9)/24=100/120;
t+9= 5/6x24 = 20 => a piece of work was completed in 20 days.

B
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GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 A, B and C can complete a piece of work in 24 days, 40 days and 60 day  [#permalink]

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Akela wrote:
Bunuel wrote:
A, B and C can complete a piece of work in 24 days, 40 days and 60 days, respectively. In how many days was the piece of work completed?

(1) A, B and C started working together, and A continued to work till the end.
(2) A, B and C started working together, B and C left the work 2 days and 7 days, respectively, before the completion of the work.

(1) B and C could work any number of days, so not sufficient
(2) A worked (t+9) days

(t+9)x(1/24)+2/40+7/60=1;
(t+9)/24=120/120-6/120-14/120;
(t+9)/24=100/120;
t+9= 5/6x24 = 20 => a piece of work was completed in 20 days.

B

Akela Although t+9 or t+7 wont matter but i think it should be t+7 (if u are assuming t days when A worked alone). please correct me if i am wrong
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Joined: 30 Jan 2016
Posts: 1141
Re: A, B and C can complete a piece of work in 24 days, 40 days and 60 day  [#permalink]

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mynamegoeson wrote:
Akela wrote:
Bunuel wrote:
A, B and C can complete a piece of work in 24 days, 40 days and 60 days, respectively. In how many days was the piece of work completed?

(1) A, B and C started working together, and A continued to work till the end.
(2) A, B and C started working together, B and C left the work 2 days and 7 days, respectively, before the completion of the work.

(1) B and C could work any number of days, so not sufficient
(2) A worked (t+9) days

(t+9)x(1/24)+2/40+7/60=1;
(t+9)/24=120/120-6/120-14/120;
(t+9)/24=100/120;
t+9= 5/6x24 = 20 => a piece of work was completed in 20 days.

B

Akela Although t+9 or t+7 wont matter but i think it should be t+7 (if u are assuming t days when A worked alone). please correct me if i am wrong

You're right, I misread statement 2. A worked t days, b worked (t-2) days, and c worked (t-7) days: t/24+(t-2)/40+(t-7)/60=1
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Re: A, B and C can complete a piece of work in 24 days, 40 days and 60 day  [#permalink]

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1
Hi ,
This Ds question we do not need to solve completely. Let us start with info in hand. We know by given data that
A's one day work =1/24
B's one day work =1/40
C's one day work =1/60
Q: In how many days was the piece of work completed?

(1) A, B and C started working together, and A continued to work till the end.
As there is no info when B and C left the work so we can not say in how many days work was completed. Insufficient
(2) A, B and C started working together, B and C left the work 2 days and 7 days, respectively, before the completion of the work.
Start with info 2: here we know how many days B and c Worked and rest is done by A. Hence this is sufficient .

for those who want to solve: lets say in total t days work was completed.

A's t day work =t/24
B's 2 day work= 2/40
C's 7 day work =7/60

t/24 + 2/40 +7/60 =1 solve this equation to find value of t.

Thanks
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Re: A, B and C can complete a piece of work in 24 days, 40 days and 60 day  [#permalink]

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mbaaspirant80 wrote:
Hi ,
This Ds question we do not need to solve completely. Let us start with info in hand. We know by given data that
A's one day work =1/24
B's one day work =1/40
C's one day work =1/60
Q: In how many days was the piece of work completed?

(1) A, B and C started working together, and A continued to work till the end.
As there is no info when B and C left the work so we can not say in how many days work was completed. Insufficient
(2) A, B and C started working together, B and C left the work 2 days and 7 days, respectively, before the completion of the work.
Start with info 2: here we know how many days B and c Worked and rest is done by A. Hence this is sufficient .

for those who want to solve: lets say in total t days work was completed.

A's t day work =t/24
B's 2 day work= 2/40
C's 7 day work =7/60

t/24 + 2/40 +7/60 =1 solve this equation to find value of t.

Thanks

Can u please tell me if my approach is correct or not and if I am solving it right or not?

A's one day work =1/24
B's one day work =1/40
C's one day work =1/60

Working together for first 2 days = (1/24 + 1/40+ 1/60) *2
A and C Working together for next 5 days = (1/24 + 1/60) *5
A working alone for rest of the days = (1/24)*x

(1/24 + 1/40+ 1/60) *2 + (1/24 + 1/60) *5 + (1/24)*x = 1

AND WE CAN FIND x by this?

Please tell me if i solved it right or wrong:?
Manager  B
Joined: 11 Feb 2017
Posts: 183
Re: A, B and C can complete a piece of work in 24 days, 40 days and 60 day  [#permalink]

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Bunuel wrote:
A, B and C can complete a piece of work in 24 days, 40 days and 60 days, respectively. In how many days was the piece of work completed?

(1) A, B and C started working together, and A continued to work till the end.
(2) A, B and C started working together, B and C left the work 2 days and 7 days, respectively, before the completion of the work.

Can u please tell me if my approach is correct or not and if I am solving it right or not?

A's one day work =1/24
B's one day work =1/40
C's one day work =1/60

Working together for first 2 days = (1/24 + 1/40+ 1/60) *2
A and C Working together for next 5 days = (1/24 + 1/60) *5
A working alone for rest of the days = (1/24)*x

(1/24 + 1/40+ 1/60) *2 + (1/24 + 1/60) *5 + (1/24)*x = 1

AND WE CAN FIND x by this?

Please tell me if i solved it right or wrong:?
Manager  B
Joined: 04 Oct 2017
Posts: 79
Re: A, B and C can complete a piece of work in 24 days, 40 days and 60 day  [#permalink]

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Luckisnoexcuse wrote:
Bunuel wrote:
A, B and C can complete a piece of work in 24 days, 40 days and 60 days, respectively. In how many days was the piece of work completed?

(1) A, B and C started working together, and A continued to work till the end.
(2) A, B and C started working together, B and C left the work 2 days and 7 days, respectively, before the completion of the work.

A does 1/24 of work in 1 day
B does 1/40 of work in 1 day
C does 1/60 of work in 1 day

(1) gives us A+B+C started together and A continued till the end but we do not know for how many days B & C worked
Not sufficient

(2) A+B+C started together, B worked for 2 days and C worked for 7 Days

We can say that

For 2 days (A+B+C)
For 5 days (A+C)
For the rest of days A alone

Lets assume the work to be 240 units
A works for 10 units/day
B works for 6 units/day
C works for 4 units/day

A+B+C = 20 units/day
A+C = 14 units/day

But we don't know if A continued till the end (Cannot assume that A completed the work after 7 days) hence Not sufficient
On combining both we can form the equation

2*20 + 5*14 + x*10 = 240

We can find x and add 7 days to it to get the answer

Hence C

I too arrived at C. How can I conclude A worked till the end using statement 2???
Manager  S
Status: Victory is never a one time thing.
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Posts: 54
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Concentration: Finance, Marketing
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Re: A, B and C can complete a piece of work in 24 days, 40 days and 60 day  [#permalink]

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1
Kezia9 wrote:
Luckisnoexcuse wrote:
Bunuel wrote:
A, B and C can complete a piece of work in 24 days, 40 days and 60 days, respectively. In how many days was the piece of work completed?

(1) A, B and C started working together, and A continued to work till the end.
(2) A, B and C started working together, B and C left the work 2 days and 7 days, respectively, before the completion of the work.

A does 1/24 of work in 1 day
B does 1/40 of work in 1 day
C does 1/60 of work in 1 day

(1) gives us A+B+C started together and A continued till the end but we do not know for how many days B & C worked
Not sufficient

(2) A+B+C started together, B worked for 2 days and C worked for 7 Days

We can say that

For 2 days (A+B+C)
For 5 days (A+C)
For the rest of days A alone

Lets assume the work to be 240 units
A works for 10 units/day
B works for 6 units/day
C works for 4 units/day

A+B+C = 20 units/day
A+C = 14 units/day

But we don't know if A continued till the end (Cannot assume that A completed the work after 7 days) hence Not sufficient
On combining both we can form the equation

2*20 + 5*14 + x*10 = 240

We can find x and add 7 days to it to get the answer

Hence C

I too arrived at C. How can I conclude A worked till the end using statement 2???

Hi Kezia9
I think you may have not read the second statement's complete sentence. The last part of the sentence states "Before the completion of work". Simplifying, you can say something like "X left 6 days before the completion of work" for example.

By this interpretation, since B and C left before completion of work, the only logical way to complete the work is when A stays till the end to complete the work.

Let's assume total days required was T days. Hence, A would have worked for T days, B for T-2 days and C for T-7 days. With this you can now form the equation and arrive at the solution, thereby making the statement 2 alone sufficient for this problem.

Hope my answer has helped you. Please leave a kudos in case you liked! Intern  B
Joined: 13 Mar 2018
Posts: 14
Re: A, B and C can complete a piece of work in 24 days, 40 days and 60 day  [#permalink]

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Bunuel wrote:
A, B and C can complete a piece of work in 24 days, 40 days and 60 days, respectively. In how many days was the piece of work completed?

(1) A, B and C started working together, and A continued to work till the end.
(2) A, B and C started working together, B and C left the work 2 days and 7 days, respectively, before the completion of the work.

Hi Bunnel,

I have one doubt here, in st. (b) do we have to assume that A continued to work till the work was completed. Because it is always advised for DS qstns, never assume anything. My doubt arose because in st. (2) its not given that A continued to wrk till end, but if we combine it with st. (A) then we can confidently calculate no. of dys.

Kindly explain...Thanks Re: A, B and C can complete a piece of work in 24 days, 40 days and 60 day   [#permalink] 21 Feb 2019, 07:54
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