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Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min

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Bunuel
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Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink] New post   07 Dec 2018, 02:59
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26% (01:46) correct 74% (01:49) wrong based on 152 sessions
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Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 minutes. Pump A pumps the pool for 2 minutes before pump B joins in. How may minutes will it take to empty the pool together?

A. 5
B. 32/7
C. 18/7
D. 17/7
E. 2
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B
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Re: Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink] New post   07 Dec 2018, 03:07
Total work to be done = LCM(6,8) = 24 Units.

Pump A can do 24/8 = 3 units in a minute

Pump B can do 24/6 = 4 units in a minute

Pump A works for 2 minutes then 6 units is done. Remaining is 18 units.

Together they empty 7 units in a minute.
Time taken is 18/7 minutes

C is the answer

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Re: Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink] New post   07 Dec 2018, 23:05
Bunuel, Shouldn't the answer be 18/7 and not 32/7?
Please clarify
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Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink] New post   Updated on: 08 Dec 2018, 00:04
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Bunuel wrote:
Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 minutes. Pump A pumps the pool for 2 minutes before pump B joins in. How may minutes will it take to empty the pool together?

A. 5
B. 32/7
C. 18/7
D. 17/7
E. 2



rate of pump A: x/8 and rate of pump B : x/6

combined rate of A+B: 7x/24 and work would be 24x/7

now pump A has worked for 2mins so work done by A : x/8 * 2= x/4 , x=1

work left , 1-1/4 = 3/4

w=r*t
3/4=7/24 *t
time= 18/7
since 2 mins extra are taken by A so 18/7+2 = 18+14/7 = 32/7 IMO B

Originally posted by Archit3110 on 07 Dec 2018, 23:22.
Last edited by Archit3110 on 08 Dec 2018, 00:04, edited 1 time in total.
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Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink] New post   07 Dec 2018, 23:24
Afc0892 wrote:
Bunuel, Shouldn't the answer be 18/7 and not 32/7?
Please clarify

You forgot to add the two minutes which A has already taken for completing the work.
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Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink] New post   07 Dec 2018, 23:33
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Archit3110 wrote:
Bunuel wrote:
Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 minutes. Pump A pumps the pool for 2 minutes before pump B joins in. How may minutes will it take to empty the pool together?

A. 5
B. 32/7
C. 18/7
D. 17/7
E. 2


GMATinsight :
Sir I tried solving the question , below is my working but I am not able to get the correct answer which is B..
rate of pump A: x/8 and rate of pump B : x/6

combined rate of A+B: 7x/24 and work would be 24x/7

now pump A has worked for 2mins so work done by A : x/8 * 2= x/4

work left is 24x/7-x/4 = 17x/28

w=r*t
17x/28 = (7x/24) * time
time= 17/96 ..

I am not sure where I am really going wrong.. I tired LCM method as well with it the answer is coming as option C : 18/7 but correct option is B ...

Please check and share your solution..

Archit ..


The highlighted part is a mistake

combined rate of A+B: 7x/24 means that work done by A and B together in 1 min = 7x/24 where total work = x

Hence work left after 2 min work of A = x = (x/4) = 3x/4

Now, MT/W = constant
1 / (7x/24) = time / (3x/4)

time = 18/7

Answer: Option C


My way of doing this question
If B works for t minutes
then A works for (t+2) minutes

Work done by A in (t+2) min = (t+2)/8
Work done by B in (t) min = (t)/6

Total Work Done = (t+2)/8 + (t)/6 = 1

i.e. t = 18/7

Archit3110
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Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink] New post   07 Dec 2018, 23:41
Let x be the time it takes A and B to empty the pool
Rate of Pump A = 1/8
Rate of Pump B = 1/6
Pump A pumps the pool for 2 minutes => 1/8* 2 = 1/4
Pump B joins in to empty the pool => 1/4 + [(1/8 + 1/6)*x] = 1
(7/24)x = 1 - 1/4 = 3/4
x = 18/7
Total time to empty the pool => 18/7 + 2 = 32/7
Answer = B
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Re: Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink] New post   07 Dec 2018, 23:48
GMATinsight wrote:
Archit3110 wrote:
Bunuel wrote:
Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 minutes. Pump A pumps the pool for 2 minutes before pump B joins in. How may minutes will it take to empty the pool together?

A. 5
B. 32/7
C. 18/7
D. 17/7
E. 2


GMATinsight :
Sir I tried solving the question , below is my working but I am not able to get the correct answer which is B..
rate of pump A: x/8 and rate of pump B : x/6

combined rate of A+B: 7x/24 and work would be 24x/7

now pump A has worked for 2mins so work done by A : x/8 * 2= x/4

work left is 24x/7-x/4 = 17x/28

w=r*t
17x/28 = (7x/24) * time
time= 17/96 ..

I am not sure where I am really going wrong.. I tired LCM method as well with it the answer is coming as option C : 18/7 but correct option is B ...

Please check and share your solution..

Archit ..


The highlighted part is a mistake

combined rate of A+B: 7x/24 means that work done by A and B together in 1 min = 7x/24 where total work = x

Hence work left after 2 min work of A = x = (x/4) = 3x/4

Now, MT/W = constant
1 / (7x/24) = time / (3x/4)

time = 18/7

Answer: Option C


My way of doing this question
If B works for t minutes
then A works for (t+2) minutes

Work done by A in (t+2) min = (t+2)/8
Work done by B in (t) min = (t)/6

Total Work Done = (t+2)/8 + (t)/6 = 1

i.e. t = 18/7

Archit3110


GMATinsight : thank you sir... I have understood where I went wrong.. :) ,
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Re: Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink] New post   08 Dec 2018, 06:07
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I feel the question is poorly worded... it's says how many minutes to empty the pool "together". However, I would like to ask: Can the GMAT use such subtle wording that allows ambiguity, in wording an official question? Bunuel...

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Re: Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink] New post   08 Dec 2018, 07:44
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Kem12 wrote:
I feel the question is poorly worded... it's says how many minutes to empty the pool "together". However, I would like to ask: Can the GMAT use such subtle wording that allows ambiguity, in wording an official question? Bunuel...

Posted from my mobile device

Gmat questions are not ambiguous. This question is either poorly worded or the provided OA is incorrect.
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Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink] New post   13 Aug 2020, 09:51
How may minutes will it take to empty the pool together?

together might also mean just = \(\frac{1}{1/6+1/8} = \frac{24}{7}\)

It makes sense to me that answer is C, not B. Because the first 2 minutes of work are not done together.
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Re: Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink] New post   13 Aug 2020, 10:04
This question is asking for the time taken by both A and b together, not together+ A separately. So and should be c, not b.
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Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink] New post   13 Aug 2020, 10:05
Bunuel wrote:
Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 minutes. Pump A pumps the pool for 2 minutes before pump B joins in. How may minutes will it take to empty the pool together?

A. 5
B. 32/7
C. 18/7
D. 17/7
E. 2


Umm seems wrong but I am still learning so let me know.

Machine A \(\frac{1}{8} * 2 + t = \frac{2+t}{8}\)
Machine B \(\frac{1}{6} * t = \frac{t}{6}\)

So finally:

\(\frac{2+t}{8 }+ \frac{t}{6} = 1\)

To solve and we get \(\frac{18}{7}\) Minutes

Ans : C

How is B the right answer?

A worked for 2 minutes then B joined. Thus A worked for 2 + t minutes and b worked for t minutes.
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Re: Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink] New post   13 Aug 2020, 18:28
TBH i don't think the question is worded explicit enough.
The question states "How may minutes will it take to empty the pool together?". That can either mean "how long do A and B work together" or "what is the total time taken to empty the pool".

If you're asking for the total time - you should just say "How long will it take to empty the pool" or "What is the total time taken to empty the pool" and not use language that can be interpreted multiple ways.
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Re: Pump A can empty a pool in 8 minutes. Pump B can empty a pool in 6 min [#permalink]
13 Aug 2020, 18:28
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