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# Three workers A,B,C working individually can complete a task in 30 day

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VP
Joined: 31 Oct 2013
Posts: 1138
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Three workers A,B,C working individually can complete a task in 30 day  [#permalink]

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Updated on: 09 Feb 2019, 03:06
00:00

Difficulty:

65% (hard)

Question Stats:

18% (01:46) correct 82% (02:07) wrong based on 17 sessions

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Three workers A,B,C working individually can complete a task in 30 days, 15 days, 10 days respectively. If A starts the task alone, and B and C helps A on every 2nd and 3rd days respectively, on which day will the task yo be completed?

A)10th
B)11th
C)12th
D)15th
E)16th

Originally posted by selim on 08 Feb 2019, 13:54.
Last edited by chetan2u on 09 Feb 2019, 03:06, edited 1 time in total.
Corrected the choices and the OA
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: Three workers A,B,C working individually can complete a task in 30 day  [#permalink]

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08 Feb 2019, 21:29
selim wrote:
Three workers A,B,C working individually can complete a task in 30 days, 15 days, 10 days respectively. If A starts the task alone, and B and C helps A on every 2nd and 3rd days respectively, on which day will the task yo be completed?

A)10th
B)12th
C)14th
D)15th
E)11$$\frac{1}{4}$$th

Four scenarios..
1) A working alone - 1/30 the of work....On odd days except multiple of 3------+--- 1,5,7, so 3 days in first 10
2) A and B working together - 1/30+1/15=1/10th of work.....on all even days except multiple of 3----------2,4,8,10, so 4 days
3) A and C working together - 1/30+1/10=2/15th of work....on all odd multiple of 3........3,9, so 2 days
4) All three together - 1/30+1/15+1/10=1/5th of work...on all even multiple of 3........6, so 1 day..

Thus in 10 days, work done is 3*(1/30)+4*(1/10)+2*(2/15)+1/5=(1/10)+(2/5)+(4/15)+1/5=(3+12+8+6)/30=29/30

Now on 11th day A works alone so does 1/30 of work and 29/30+1/30=30/30

So the work gets over in 11 days..

selim, the options does not show 11 as an answer.
Also since the question is WHICH day, it cannot be 11 1/4, because that will come as 12th day.
Or the question should have asked--"How much time?"
_________________

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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Posts: 1001
Location: India
Re: Three workers A,B,C working individually can complete a task in 30 day  [#permalink]

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Updated on: 08 Feb 2019, 22:02
selim wrote:
Three workers A,B,C working individually can complete a task in 30 days, 15 days, 10 days respectively. If A starts the task alone, and B and C helps A on every 2nd and 3rd days respectively, on which day will the task yo be completed?

A)10th
B)12th
C)14th
D)15th
E)11$$\frac{1}{4}$$th

IMO E(some discrepancy is there)

Let the total work be 30 units.

Now if i understood this part correctly
B and C helps A on every 2nd and 3rd days respectively, this means that 2nd day work done will be 3 units, 3rd day work done will be 4 units

Rate of A = 1 unit
rate of B = 2 units
rate of C = 3 units

Now if A starts on 1st day and he is helped by B and C
1,3,4
8 units will be done in 3 days
30 units will be done in 3/8 * 30

= 45/4 days

11.25, 11 * 1/4
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Originally posted by KanishkM on 08 Feb 2019, 21:57.
Last edited by KanishkM on 08 Feb 2019, 22:02, edited 2 times in total.
Intern
Joined: 17 Dec 2018
Posts: 21
Re: Three workers A,B,C working individually can complete a task in 30 day  [#permalink]

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08 Feb 2019, 22:00
Goal = 30
Day 1: A = 1
Day 2: A and B = 3
Day 3: A and C = 4
Day 4: A and B = 3
Day 5: A = 1
Day 6: A and B and C = 6
Day 7: A = 1
Day 8: A and B = 3
Day 9: A and C = 4
Day 10:A and B = 3
Day 11: A = 1

11 days to reach 30 but this is not an option

It is a 6 day pattern: 1, 3, 4, 3, 1, 6... repeat

Posted from my mobile device
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: Three workers A,B,C working individually can complete a task in 30 day  [#permalink]

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08 Feb 2019, 22:09
KanishkM wrote:
selim wrote:
Three workers A,B,C working individually can complete a task in 30 days, 15 days, 10 days respectively. If A starts the task alone, and B and C helps A on every 2nd and 3rd days respectively, on which day will the task yo be completed?

A)10th
B)12th
C)14th
D)15th
E)11$$\frac{1}{4}$$th

IMO E(some discrepancy is there)

Let the total work be 30 units.

Now if i understood this part correctly
B and C helps A on every 2nd and 3rd days respectively, this means that 2nd day work done will be 3 units, 3rd day work done will be 4 units

Rate of A = 1 unit
rate of B = 2 units
rate of C = 3 units

Now if A starts on 1st day and he is helped by B and C
1,3,4
8 units will be done in 3 days
30 units will be done in 3/8 * 30

= 45/4 days

11.25, 11 * 1/4

You are missing out the point that 6th day all three will work together..
1- A, 2-AB, 3-AC, 4-AB, 5-A, 6-ABC, 7-A, 8-AB, 9-AC
_________________

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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

VP
Joined: 09 Mar 2018
Posts: 1001
Location: India
Re: Three workers A,B,C working individually can complete a task in 30 day  [#permalink]

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09 Feb 2019, 02:33
chetan2u wrote:
KanishkM wrote:

You are missing out the point that 6th day all three will work together..
1- A, 2-AB, 3-AC, 4-AB, 5-A, 6-ABC, 7-A, 8-AB, 9-AC

Hi chetan2u

Thank you for addressing my discrepancy.

Am i correct at saying that this question even tested on identifying that:

Days can be multiples of 2,3 and 6 respectively.
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Re: Three workers A,B,C working individually can complete a task in 30 day   [#permalink] 09 Feb 2019, 02:33
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# Three workers A,B,C working individually can complete a task in 30 day

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