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26 Feb 2015, 11:36
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
26% (02:46) correct
74%
(02:45)
wrong
based on 729
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Three employees, A, B and C, clean a certain conference room each day. Working together, A and B can clean the conference room in 3 hours, whereas A and C together can do it in 2 and 1/2 hours. Can A, B and C working together clean the conference room in less than 2 hours?
1) B cleans faster than A.
2) Working alone, C can clean the conference room in less tahn 5 hours.
1) B cleans faster than A.
2) Working alone, C can clean the conference room in less tahn 5 hours.
12 Mar 2015, 19:27
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Awli
Three employees, A, B and C, clean a certain conference room each day. Working together, A and B can clean the conference room in 3 hours, whereas A and C together can do it in 2 and 1/2 hours. Can A, B and C working together clean the conference room in less than 2 hours?
1) B cleans faster than A.
2) Working alone, C can clean the conference room in less than 5 hours.
1) B cleans faster than A.
2) Working alone, C can clean the conference room in less than 5 hours.
A + B , Time = 3 hrs, so per hr work = 33.33% of total work.
A + C , Time = 2.5 hrs, so per hr work = 40% of total work.
Need to know, whether A+B+C can complete in less than 2 hrs. or A+B+C can do more than 50% work per hr.
1) Rate of B faster than A.
Therefore, B will do work which is greater than 1/2(33.33)% , i.e. greater than 16.5 %
Now add B's effort in A+C's effort(40%). We get A+B+C's effort > 50 %
Suff.
2) C can do more than 20% of the job per hr.
Now add C's effort with A+B( 33.33%), i.e. A+B+C can do more than 50% of the work per hr.
Suff.
Hence (D)
Please lemme know if there's anything wrong in my logic.
Thanks!!
28 Feb 2015, 00:40
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Hi Awli,
The prompt is "layered" and more difficult than typical "Work" questions, but if you are comfortable converting the data into "work per hour" then you can get to the correct answer with a bit of effort. Knowing the 'Work Formula' will also help you when dealing with Fact 2.
We're given 2 rates for 2 groups of people:
1) A and B can clean the room in 3 hours
2) A and C can clean the room in 2.5 hours
We're asked if A, B and C can clean the room in UNDER 2 hours. This is a YES/NO question.
Fact 1: B cleans faster than A
Since A and B can clean the room in 3 hours, and we're told that B cleans FASTER than A, then that means that B does MORE than 1/2 of the work in that 3 hours:
> 1/2 the work in 3 hours =
> 3/6 of the work in 3 hours =
> 1/6 of the work in 1 hour
We now know that B can clean MORE than 1/6 of the room in 1 hour....
We also know that A and C can clean the room in 2.5 hours:
1/1 of the work in 2.5 hours =
2/5 of the work in 1 hour
NOW we know how much gets done per hour:
A and C get 2/5 of the room cleaned
B gets MORE than 1/6 of the room cleaned
2/5 + (more than 1/6) =
12/30 + (more than 5/30) =
MORE than 17/30 of the room is cleaned in 1 hour. By extension, 34/30 of the room would be cleaned in 2 hours (which is more cleaning than is necessary). This PROVES that the room will take LESS than 2 hours to clean and the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.
Fact 2: C can clean the room in LESS than 5 hours.
Here, we can use the Work Formula to our advantage....
Work = (X)(Y)/(X+Y) where X and Y are the times it takes to clean the room individually.
Here, we'll call....
X = the time for A and B to clean the room = 3 hours
Y = the time for C to clean the room = less than 5 hours
(3)(less than 5)/(3 + less than 5) = (less than 15)/(less than 8) = less than 15/8 = less than 2 hours and the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
The prompt is "layered" and more difficult than typical "Work" questions, but if you are comfortable converting the data into "work per hour" then you can get to the correct answer with a bit of effort. Knowing the 'Work Formula' will also help you when dealing with Fact 2.
We're given 2 rates for 2 groups of people:
1) A and B can clean the room in 3 hours
2) A and C can clean the room in 2.5 hours
We're asked if A, B and C can clean the room in UNDER 2 hours. This is a YES/NO question.
Fact 1: B cleans faster than A
Since A and B can clean the room in 3 hours, and we're told that B cleans FASTER than A, then that means that B does MORE than 1/2 of the work in that 3 hours:
> 1/2 the work in 3 hours =
> 3/6 of the work in 3 hours =
> 1/6 of the work in 1 hour
We now know that B can clean MORE than 1/6 of the room in 1 hour....
We also know that A and C can clean the room in 2.5 hours:
1/1 of the work in 2.5 hours =
2/5 of the work in 1 hour
NOW we know how much gets done per hour:
A and C get 2/5 of the room cleaned
B gets MORE than 1/6 of the room cleaned
2/5 + (more than 1/6) =
12/30 + (more than 5/30) =
MORE than 17/30 of the room is cleaned in 1 hour. By extension, 34/30 of the room would be cleaned in 2 hours (which is more cleaning than is necessary). This PROVES that the room will take LESS than 2 hours to clean and the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.
Fact 2: C can clean the room in LESS than 5 hours.
Here, we can use the Work Formula to our advantage....
Work = (X)(Y)/(X+Y) where X and Y are the times it takes to clean the room individually.
Here, we'll call....
X = the time for A and B to clean the room = 3 hours
Y = the time for C to clean the room = less than 5 hours
(3)(less than 5)/(3 + less than 5) = (less than 15)/(less than 8) = less than 15/8 = less than 2 hours and the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
