Three employees, A, B and C, clean a certain conference room each day.

Question

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.

sytabish · Accepted Answer

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!!

EMPOWERgmatRichC · Answer

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:  D

GMAT assassins aren't born, they're made,
Rich

chetan2u · Answer

hi Awli,
ans D..
1) statement one tells us B>A so both A and B do it in 3 hrs.. lets take the worst scenario that B is just above A or almost same so A's speed = B's speed = 6 hrs..
so C's speed = 2/5-1/6=7/30... so A,B and C can do it in 1/6+1/6+7/30=17/30.. so time taken =30/17=1 13/17 days<2 days... sufficient
2) let the worst scenario C takes 5 hrs so total time=1/3+1/5=8/15 or 15/8 days<2 days .. sufficient

EMPOWERgmatRichC · Answer

Hi sytabish,

Most Test Takers approach 'Work Formula' questions by converting data into a 'fraction of work done per hour' format or using the Work Formula (if it's two entities working on a job). Since data can be converted from one format to many different formats (fractions to decimals to percents to ratios, etc.), there is nothing wrong with what you did. It's a rather clever way to look at the data and just as valid as any other approach.

GMAT assassins aren't born, they're made,
Rich

sytabish · Answer

Thanks for the confirmation  EMPOWERgmatRichC  !
I have been trying to use the percentage approach wherever I can for Work rate problems.

AdlaT · Answer

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?

we have two equations :1) \(\frac{1}{A}+\frac{1}{B}=\frac{1}{3}\)

2) \(\frac{1}{A}+\frac{1}{C}=\frac{1}{2.5}\)

and we are asked , is \(\frac{1}{A}+\frac{1}{B}+\frac{1}{C}>\frac{1}{2}\) ?

substitute equation 1.------->\(\frac{1}{3}+\frac{1}{C}>\frac{1}{2}\)--->6+2C>3C---->is 6>C ?.

Substitute equation 2.----->\(\frac{1}{2.5}+\frac{1}{B}>\frac{1}{2}\)--->5+2B>2.5B---> is 10>B ?.

check either of the above two conditions.

Statement 1): B cleans faster than A----> B<A , and from the equation 1(\(\frac{1}{A}+\frac{1}{B}=\frac{1}{3}\)) if B cleans as fast as A then A=B=6 , But we are given that B<A then B must be less than 6 ----> B<6
Then condition, is 10>B ----> ALWAYS YES, because 10>6>B

Statement 1 SUFFICIENT

Statement 2): Working alone, C can clean the conference room in less tahn 5 hours.---> C<5
condition , is 6>C--->ALWAYS YES, because 6>5>C

Statement 2 SUFFIECIENT

ANS---> D

please correct me if i am wrong

Thanks,
Adla.

Awli · Answer

Thank you very much to all of you. I've found very useful all the approaches.

MbaRacer · Answer

This is the best way to solve DS problems

MbaRacer · Answer

Hey, 
From where do you get that 1/2(33.33)% ?

KrishnakumarKA1 · Answer

Prompt analysis
Let the rate of work done per hour for A, B, C be a,b,c respectively.According to the question:
(a+b)*3 = (b+c)*2.5 = (a+b+c)t

Superset
The answer could be YES or NO.

Translation
To find the value of t we need:
1# exact value of a, b, c.
2# some equations to find the value of t
3# any other information that will help to infer the value or range of t.

Statement analysis
St 1: b>a. lets take the worst scenario that B is just above A or almost same so A's speed = B's speed = 6 hrs..
so C's speed = 2/5-1/6=7/30... so A,B and C can do it in 1/6+1/6+7/30=17/30.. so time taken =30/17=1 13/17 days<2 days... sufficient
St 2: let the worst scenario C takes 5 hrs so total time=1/3+1/5=8/15 or 15/8 days<2 days .. sufficient 
Option D

hellosanthosh2k2 · Answer

Let Rate of A = A, Rate of B = B, Rate of C = C

Given : A + B = 1/3 (since it takes 3 hours to clean together)
A + C = 2/5 (since it takes 5/2 hours to clean together)
Question: A + B + C > 1/2 ? (does it take less than 2 hours to clean together)
1/3 + C > 1/2 ?
C > 1/6 ? or does C take less than 6 hours to clean alone?

Statement 1: B cleans faster than A.
If B were to clean at same rate as A (worst case), A + B = 1/3 => A + A = 1/3 => A = 1/6
now we have A + C = 2/5 => C = 2/5 - 1/6 (worst case) = 7/30 (greater than 1/6)
but since B cleans faster than A, A < 1/6, so above eqn C = 2/5 - (<1/6) > (7/30) (again greater than 1/6)
=> Sufficient

Statement 2: Working alone, C can clean the conference room in less than 5 hours => directly answers our question -> suff

Kudos if you like my approach, need them badly to unlock my Gmat Club Tests

Thanks

Answer (D)

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Three employees, A, B and C, clean a certain conference room each day.

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Three employees, A, B and C, clean a certain conference room each day.

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