How long will it take for two pipes A and B to fill an empty cistern i

Question

GMATBusters’ Quant Quiz Question -1

How long will it take for two pipes A and B to fill an empty cistern if they worked alternately for an hour each? 
(1) Working alone, Pipe A can fill the cistern in 30 hours 
(2) Pipe B is one third as efficient as Pipe A

GMATBusters · Answer

Official Explanation :

St 1) No info about Pipe B 
NOT SUFFICIENT

St2) only relative rate is given. 
NOT SUFFICIENT

Combining St 1 & 2, 
The time taken by A = 30 hrs
since, Pipe B is one third as efficient as Pipe A, time taken by B = 90 hours
Let us suppose the total work is 90units (LCM of 30, 90)
Work done by A per hour = 3units
Work done by B per hour = 1 units

Now A and B are working alternatively :
in first 2 Hrs work done = (sum of work done by A and B in one hour ) = 4
hence in 44 hrs work done = 22*4 = 88
Remaining work = 2 units

Now, time required depends on whose turn is now.(the turn depends on which pipe has started the work)A or B 
if A has started, turn will be of A : remaining time = 2/3 hrs
total time = 44+2/3
if B has started, turn will be of B : work done by B in 1 hrs = 1unit.
so last 1 unit will be done by A in 1/3 hrs
total time = 44+1+1/3
hence even after combing St 1 & 2, we are unable to answer the question,

so Answer is E

shameekv1989 · Answer

How long will it take for two pipes A and B to fill an empty cistern if they worked alternately for an hour each?
(1) Working alone, Pipe A can fill the cistern in 30 hours
(2) Pipe B is one third as efficient as Pipe A

We need rates for each pipe to determine the time taken to fill an empty cistern

i) Pipe A rate = 1/30 => We don't know Pipe B rate - Insufficient
ii) Pipe B is 1/3 efficient => x for Pipe A and x/3 for pipe B  4x/3  together rate - we don't know amount of work - Insufficient

Together 
Assuming Total work needs to be done is 90 
Rate of Pipe A = 3
Rate of Pipe B = 1
Time taken by each per hour is known => 4 units every 2 hours => Therefore 22*4 = 22 hrs for the first 88 units of work. 
Then If A started - 2/3 hr would be required 
If B started - 1+ 1/3 hr would be required

Insufficient

Answer - E

monirhossain2nd · Answer

Ans is C

Stat 1
tells only about A

Stat 2
The relation between A and B
No numerical Value

Combined : Sufficient

Raxit85 · Answer

Time taken to fill the empty cistern if pipe A and B work alternately = x

1) Working alone, pipe A can fill the cistern in 30 hours
We do NOT know the filling rate of pipe B. So not sufficient.

2) Pipe B is one third as efficient as Pipe A
B = A/3, but we need to calculate the time and we do NOT have any specifics of time taken by A and B. So, not sufficient.

1) + 2)
A fills in 30 hours i.e .Time of Pipe B = 3*30 = 90 hours
We can find how much time will pipe A and B take to fill the tank as we have the exact rates of pipes. So sufficient.
Ans. C

Kinshook · Answer

Asked: How long will it take for two pipes A and B to fill an empty cistern if they worked alternately for an hour each?

(1) Working alone, Pipe A can fill the cistern in 30 hours 
Since efficiency of pipe B is unknown
NOT SUFFICIENT

(2) Pipe B is one third as efficient as Pipe A 
Since efficiency of pipe A is unknown
NOT SUFFICIENT

(1) + (2) 
(1) Working alone, Pipe A can fill the cistern in 30 hours 
(2) Pipe B is one third as efficient as Pipe A 
Pipe B can fill the cistern in 90 hours

Scenario 1: Pipe A starts working first 
1/30 + 1/90 = 4/90 = 2/45
Pipe A & Pipe B can fill 2/45th cistern in 2 hours
Pipe A & Pipe B can fill 44/45th cistern in 44 hours
Remaining 1/45th cistern can be filled by pipe A in 30/45 = 2/3 hours = 40 minutes
Pipe A & Pipe B can fill the cistern in 44 hours 40 minutes if pipe A starts working first.

Scenario 2: Pipe B starts working first 
But if pipe B starts working first
1/30 + 1/90 = 4/90 = 2/45
Pipe A & Pipe B can fill 2/45th cistern in 2 hours
Pipe A & Pipe B can fill 44/45th cistern in 44 hours
Pipe B can fill 1/90th cistern in 1 hours
Remaining 1/90th cistern can be filled by pipe A in 30/90 = 1/3 hours= 20 minutes
Pipe A and Pipe B can fill the cistern in 45 hours 20 minutes if pipe B starts working first.

Since it is not mentioned which pipe started first
NOT SUFFICIENT

IMO E

Hi  GMATBusters   Bunuel 
Unless the question specifies which pipe starts working first, the answer is E
Otherwise the answer is C.

Please clarify whether it can be assumed that pipe A starts working first.

Danchar42 · Answer

How long will it take for two pipes A and B to fill an empty cistern if they worked alternately for an hour each?
(1) Working alone, Pipe A can fill the cistern in 30 hours
(2) Pipe B is one third as efficient as Pipe A

This is a work/rate problem, and we should immediately recall that 1) work = rate * time, and 2) rates are additive. The question is asking for an answer in "hours", so we will have to have some specific values to work with.

translating the statements:
(1) the rate of Pipe A (1/30 cistern/hour)
(2) Pipe B is much slower (1/3 * Rate Pipe A cistern/hour)

individually, (1) tells us nothing about Pipe B --> insufficient --> eliminate (a) and (d)
individually, (2) tells us a relative difference between the rates of pipes A and B, but nothing concrete to use to get the time --> insufficient --> eliminate (b)
together, we have the rates of each pipe (A = 1/30, B = 1/90) --> sufficient -->  answer is (c)

kapilagarwal · Answer

The question is simply asking us to find the speed of each tap to fill the cistern.

Answer: C

Posted from my mobile device

AnirudhaS · Answer

(1) A takes 30 hours. No idea of how much B takes. And we definitely know it wont be done in 1 hour! So eliminate A & D.

(2) B is a third efficient as A. No idea of the value of A though. So eliminate B.

(1) + (2) Now we know A takes hours and B takes 90 hours to finish the job. Great we have both the rates. All we need to do is let A and B work 1 hour at a time to finish the job. We really do not need to calculate it.

Answer: C

I feel empowered!

mohagar · Answer

C : beacuse here we can get total work and also we know the ratio of their speed.

uc26 · Answer

1) We do not have the rate for pipe B. So NOT SUFFICIENT.

2) This means that pipe B takes 3 times more time as compared to pipe A. But we have no information about the time taken by pipe A to fill the cistern. So NOT SUFFICIENT.

Combining 1 and 2: We know that pipe A takes 30 hours and B takes 3 times more time as compared to A which is 90 hours. Since have the rates for both the pipes, we can find the total time required to fill the cistern.

Correct Answer: C

neharaj0001 · Answer

Both together but neither alone is sufficient. C is the answer

Posted from my mobile device

gmatway · Answer

to ans this question we need rate of both a & b pipes .
opt a and b alone are insuff .
c = opt a & b together are suff 
from 1) we have rate of pipe A from 2) we have rate of pipe B ; B=1/3A => 3B=A => 3*30 = B. pipe B takes 90 hrs to fill tank and pipe A takes 30 hrs to fill tank

bumpbot · Answer

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How long will it take for two pipes A and B to fill an empty cistern i

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How long will it take for two pipes A and B to fill an empty cistern i

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