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# M and N working together, can finish a job in 6 days

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2438
M and N working together, can finish a job in 6 days  [#permalink]

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Updated on: 27 Aug 2018, 02:09
00:00

Difficulty:

25% (medium)

Question Stats:

87% (01:52) correct 13% (02:17) wrong based on 71 sessions

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M and N working together, can finish a job in 6 days. With the help of P, they completed the job in 4 days. If Q joined them, all 4 together would have completed the job in 3$$\frac{1}{3}$$ days. If all work at their respective constant rate, then in how many days Q alone can complete the work?

A. 10
B. 12
C. 15
D. 18
E. 20

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Originally posted by EgmatQuantExpert on 27 Aug 2018, 01:51.
Last edited by EgmatQuantExpert on 27 Aug 2018, 02:09, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7200
M and N working together, can finish a job in 6 days  [#permalink]

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27 Aug 2018, 01:59
1
1
EgmatQuantExpert wrote:
M and N working together, can finish a job in 6 days. With the help of P, they completed the job in 4 days. If Q joined them, all 4 together would have completed the job in 31/3 days. If all work at their respective constant rate, then in how many days Q alone can complete the work?

A. 10
B. 12
C. 15
D. 18
E. 20

All four can complete the job in 3 and 1/3 days or 10/3 , so 1 day work =3/10
All except Q can complete job in 4 days, so their 1 day work=1/4

So 1 day work of Q = 3/10-1/4=(12-10)/40=1/20
So total work in 20 days..

E

EgmatQuantExpert, how can 3 people finish faster in 4 days as compared to a situation when a fourth person joins them and now in 31/3=10 days ?????
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: M and N working together, can finish a job in 6 days  [#permalink]

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27 Aug 2018, 02:13
chetan2u wrote:

All four can complete the job in 31/3 days , so 1 day work =3/31
All except Q can complete job in 4 days, so their 1 day work=1/4

EgmatQuantExpert, how can 3 people finish faster in 4 days as compared to a situation when a fourth person joins them and now in 31/3=10 days ?????

It was a tagging error. It should be 3$$\frac{1}{3}$$ days not 31/3.
We have corrected it.
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Ace GMAT quant
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Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
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Posts: 1287
Re: M and N working together, can finish a job in 6 days  [#permalink]

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27 Aug 2018, 06:12
1
chetan2u wrote:
EgmatQuantExpert wrote:
M and N working together, can finish a job in 6 days. With the help of P, they completed the job in 4 days. If Q joined them, all 4 together would have completed the job in 31/3 days. If all work at their respective constant rate, then in how many days Q alone can complete the work?

A. 10
B. 12
C. 15
D. 18
E. 20

All four can complete the job in 3 and 1/3 days or 10/3 , so 1 day work =3/10All except Q can complete job in 4 days, so their 1 day work=1/4

So 1 day work of Q = 3/10-1/4=(12-10)/40=1/20
So total work in 20 days..

E

EgmatQuantExpert, how can 3 people finish faster in 4 days as compared to a situation when a fourth person joins them and now in 31/3=10 days ?????

what is the reason you switched 10/3 to 3/10 ?
Math Expert
Joined: 02 Aug 2009
Posts: 7200
Re: M and N working together, can finish a job in 6 days  [#permalink]

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27 Aug 2018, 06:23
1
dave13 wrote:
chetan2u wrote:
EgmatQuantExpert wrote:
M and N working together, can finish a job in 6 days. With the help of P, they completed the job in 4 days. If Q joined them, all 4 together would have completed the job in 31/3 days. If all work at their respective constant rate, then in how many days Q alone can complete the work?

A. 10
B. 12
C. 15
D. 18
E. 20

All four can complete the job in 3 and 1/3 days or 10/3 , so 1 day work =3/10All except Q can complete job in 4 days, so their 1 day work=1/4

So 1 day work of Q = 3/10-1/4=(12-10)/40=1/20
So total work in 20 days..

E

EgmatQuantExpert, how can 3 people finish faster in 4 days as compared to a situation when a fourth person joins them and now in 31/3=10 days ?????

what is the reason you switched 10/3 to 3/10 ?

dave13
If someone can do a job in 10 days so each day he does 1/10 th of work..
So here also they complete the work in 10/3 days, thus in one day they can do 3/10th of work as 1/(10/3)=1*3/10=3/10

If A is doing 1/2 of the work in one day, A will complete full work in 2 days as 1/(1/2)=1*2/1=2
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: M and N working together, can finish a job in 6 days &nbs [#permalink] 27 Aug 2018, 06:23
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