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Intern  Joined: 02 Jun 2013
Posts: 18
Three men A, B and C working together can do a work in 30 da  [#permalink]

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5 00:00

Difficulty:   95% (hard)

Question Stats: 30% (03:26) correct 70% (03:24) wrong based on 164 sessions

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Three men A, B and C working together can do a work in 30 days. They start the work together and A works for 3 days and takes rest on the fourth day, B works for 5 days and takes rest on the next two days and C works for 7 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate)

A. 39
B. 40
C. 42
D. 41
E. 45
Math Expert V
Joined: 02 Sep 2009
Posts: 59021
Re: Three men A, B and C working together can do a work in 30 da  [#permalink]

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abhishekkhosla wrote:
Three men A, B and C working together can do a work in 30 days. They start the work together and A works for 3 days and takes rest on the fourth day, B works for 5 days and takes rest on the next two days and C works for 7 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate)

A. 39
B. 40
C. 42
D. 41
E. 45

Total work is 3*30 = 90 units.

A's schedule WWWR 3 workdays in 4.
B's schedule WWWWWRR 5 workdays in 7.
C's schedule WWWWWWWRRR 7 workdays in 10.

Test the options. In 40 days:
A will do 10*3=30 units (10 complete cycles).
B will do 5*5+5=30 units (5 complete cycles and 5 days of work).
C will do 4*7=28 units (4 complete cycles).

Total = 88 units.

On 41st day, A and C will work and do 2 units of work, so in 41 days 88+2=90 units of work will be done.

P.S. Not a GMAT question.
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Intern  Joined: 02 Jun 2013
Posts: 18
Re: Three men A, B and C working together can do a work in 30 da  [#permalink]

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Hi bunnel,

I am not able to understand how you took the cycles part

Test the options. In 40 days:
A will do 10*3=30 units (10 complete cycles).
B will do 5*5+5=30 units (5 complete cycles and 5 days of work).
C will do 4*7=28 units (4 complete cycles).

Math Expert V
Joined: 02 Sep 2009
Posts: 59021
Re: Three men A, B and C working together can do a work in 30 da  [#permalink]

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abhishekkhosla wrote:
Hi bunnel,

I am not able to understand how you took the cycles part

Test the options. In 40 days:
A will do 10*3=30 units (10 complete cycles).
B will do 5*5+5=30 units (5 complete cycles and 5 days of work).
C will do 4*7=28 units (4 complete cycles).

For A: one cycle is 4 days. In 40 days there are 40/4=10 cycles. In each cycle A works for 3 days, thus in 40 days A does 3*10=30 units.
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Intern  Joined: 02 Jun 2013
Posts: 18
Re: Three men A, B and C working together can do a work in 30 da  [#permalink]

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Hi Bunnel,

How did you got this B will do 5*5+5=30 units (5 complete cycles and 5 days of work).

40/7=5.714 so i understood that he completed 5 cycles so are you trying to say that the statement is like this (35/7)5 + (40-35)
Math Expert V
Joined: 02 Sep 2009
Posts: 59021
Re: Three men A, B and C working together can do a work in 30 da  [#permalink]

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abhishekkhosla wrote:
Hi Bunnel,

How did you got this B will do 5*5+5=30 units (5 complete cycles and 5 days of work).

40/7=5.714 so i understood that he completed 5 cycles so are you trying to say that the statement is like this (35/7)5 + (40-35)

5 complete cycles is 35 days and then 5 days of work!
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Manager  B
Joined: 31 Mar 2013
Posts: 60
Location: India
GPA: 3.02
Re: Three men A, B and C working together can do a work in 30 da  [#permalink]

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2
1
1
Bunuel wrote:
abhishekkhosla wrote:
Three men A, B and C working together can do a work in 30 days. They start the work together and A works for 3 days and takes rest on the fourth day, B works for 5 days and takes rest on the next two days and C works for 7 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate)

A. 39
B. 40
C. 42
D. 41
E. 45

Total work is 3*30 = 90 units.

A's schedule WWWR 3 workdays in 4.
B's schedule WWWWWRR 5 workdays in 7.
C's schedule WWWWWWWRRR 7 workdays in 10.

Test the options. In 40 days:
A will do 10*3=30 units (10 complete cycles).
B will do 5*5+5=30 units (5 complete cycles and 5 days of work).
C will do 4*7=28 units (4 complete cycles).

Total = 88 units.

On 41st day, A and C will work and do 2 units of work, so in 41 days 88+2=90 units of work will be done.

P.S. Not a GMAT question.

I took a slightly different approach and got C as the answer. Here it goes:

A's schedule lasts 4 days, B's schedule lasts 7 days, C's schedule lasts 10 days. Now, LCM of 4,10 and 7 is 140 days.

For A: In 4 days, A works for 3 days. Therefore in 140 days, A will work for $$105 days$$.

For B: In 7 days, B works for 5 days. Therefore in 140 days, B will work for $$100 days$$.

For C: In 10 days, C works for 7 days. Therefore in 140 days, C will work for $$98 days$$.

Now, the total days worked = $$(105 + 100 + 98)= 303 workdays$$

To achieve 303 workdays we need 140 days. Therefore to achieve 90 workdays we need $$\frac{90*140}{303}$$= 41.6(approx) = 42 days.
Intern  Joined: 17 Sep 2013
Posts: 24
Location: United States
Concentration: Economics, Statistics
Schools: CBS '18 (M)
GMAT 1: 770 Q51 V45 GPA: 3.36
WE: Analyst (Health Care)
Re: Three men A, B and C working together can do a work in 30 da  [#permalink]

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Sorry, but this is a confusing and poorly-written question. You can get an answer that isn't even on the list if you interpret a certain way. The question doesn't specify whether this work schedule is cyclical or it just happened one time.

I interpreted it as if it happened one time:

Each worker completes 1/90 of a work per day individually.

Days 1-3: All three work together so they complete 3*(3/90) = 9/90
Day 4: A takes a break, B and C work together so they complete 1*(2/90) = 2/90
Day 5: All three work together again so they complete 1*(3/90) = 3/90
Day 6-7: Worker B takes a break so they complete 2*(2/90) = 4/90
Day 8-10: Worker C takes a break, A and B work together and complete 3*(2/90) = 6/90

So for the first 10 days they complete a total of 9 + 2 + 3 + 4 + 6 = 24/90 of the work, which means that they have an additional 66/90 to complete.

This is where the question breaks down. You can assume that they will go through the same cycle again OR you can assume that they will work together for the remainder of the time. If they work together they must complete (3/30)*x = 66/90 works. If you solve for x, you get x = 22. Add that to the first 10 days and the total is 32, which is not a choice.
Manager  Joined: 26 Sep 2013
Posts: 182
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41 Re: Three men A, B and C working together can do a work in 30 da  [#permalink]

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Problem took me 3 minutes, not because it was difficult, there was just a ton of drudgery as far as adding everything. Re: Three men A, B and C working together can do a work in 30 da   [#permalink] 21 Nov 2013, 10:55
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