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Manager  Joined: 03 Feb 2010
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Working together at their constant rates, A and B can fill  [#permalink]

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Question Stats: 64% (01:15) correct 36% (01:09) wrong based on 806 sessions

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Working together at their constant rates, A and B can fill an empty tank to capacity in 1/2 hours. What is the constant rate of pump B?

(1) A's constant rate is 25 LTS / min
(2) The tanks capacity is 1200 lts.

Originally posted by ksharma12 on 15 Jul 2010, 15:50.
Last edited by Bunuel on 09 Nov 2012, 05:16, edited 1 time in total.
Edited the question.
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Re: Data sufficiency work rate problem  [#permalink]

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ksharma12 wrote:
15. working together at their constant rates , A and B can fill an empty tank to capacity in1/2 hr.what is the constant rate of pump B?
1) A's constant rate is 25LTS / min
2) the tanks capacity is 1200 lts.

Can someone solve this beyond just showing what is sufficient?

I know the answer is A but I need to know how to solve to fully grasp the concept of only needing the first statement.

Thank you

Answer to this question is C not A.

$$rate*time=job$$.

We are told that $$(A+B)*30=C$$, where $$A$$ is the rate of pump A in lts/min, $$B$$ is the rate of pump B in lts/min and C is the capacity of the tank in liters.

Question: $$B=?$$

(1) $$A=25$$ --> $$(25+B)*30=C$$ --> clearly insufficient (two unknowns), if $$C=1200$$, then $$B=15$$ but of $$C=1500$$, then $$B=25$$.

(2) $$C=1200$$. $$(A+B)*30=1200$$ --> $$A+B=40$$. Also insufficient.

(1)+(2) $$A=25$$ and $$A+B=40$$ --> $$B=15$$. Sufficient.

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Re: Data sufficiency work rate problem  [#permalink]

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ksharma12 wrote:
15. working together at their constant rates , A and B can fill an empty tank to capacity in1/2 hr.what is the constant rate of pump B?
1) A's constant rate is 25LTS / min
2) the tanks capacity is 1200 lts.

Can someone solve this beyond just showing what is sufficient?

I know the answer is A but I need to know how to solve to fully grasp the concept of only needing the first statement.

Thank you

Question: If A and B can fill 2 tanks in 1 hour together, then how many tanks can B fill up in 1 hour alone?

I'm setting this up as ratios of "x tanks per 1 hour" :
$$\frac{a}{1hr}+\frac{b}{1hr}= \frac{2}{1hr}$$

1) This does NOT give you "a" because you need to know the size of the tanks. As we stated above, the ratios above show how many TANKS per hour each can fill, not how many gallons or liters. NOT sufficient

2) This gives you the tank's capacity, which is valuable in combination with 1). However, just knowing the tank's volume isn't useful since we don't know the flow rate of A. NOT sufficient

Now that we have both the flow rate and the volume of the tank, we can easily find the value of "a" in the above equation. Both statements together are sufficient.

Are you sure the answer is A? I definitely think it is C. Where is this question from?
Manager  Joined: 03 Feb 2010
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Re: Data sufficiency work rate problem  [#permalink]

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Yea i thought it was c too.

but its not.

This question is from the work/rate made easy thread in the beginning of the quant forum.

I figured knowing the rate per minute was not sufficient unless we knew the total.
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Re: Data sufficiency work rate problem  [#permalink]

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I'm definitely agreeing with you here. Must be a typo -- or we're both missing something obvious!
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Re: Data sufficiency work rate problem  [#permalink]

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(1/A+1/B)*0.5=1
It means that the work is done by 2 employees.
From (1) we have A, so we can solve for B.
That's all.
(A)
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Re: working together at their constant rates , A and B can fill  [#permalink]

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Can't we do this question using unitary method ?
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smartmanav wrote:
Can't we do this question using unitary method ?

Hi Smartmanav,

I guess this cannot be done by Unitary method as we are given the Constant rate of A i.e 25L/min. Now does it tell you the time A will take alone to fill the tank. No, because we do not the volume/size of the tank.

That is why method suggested by Bunuel of Rate*Time =Work

Thanks
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The standard formula for solving this problem is AB/A+B=1/2 hrs
we need A to get to B, where A is the time taken by Pipe A to fill ENTIRE tank alone
from options the time taken by Pipe A to fill ENTIRE tank alone=1200/25=48 minutes
substitute in equation above to get value of B. SIMPLE!
Intern  Joined: 21 Apr 2014
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So let's put this into an equation. We know that (Arate+Brate)30min=T, if T= the tank's capacity.

(1) now we know that Arate=25lirer/min, so we can plug that into the equation and we get (25lit/min+Brate)30min=T

This is not sufficient, because there are still too many unkowns. For example, it T=900 liters then Brate would equal 5 liters/min. But if T=9,000 then Brate would equal 275 liters/min

(2) now we know that T= 1200 liters, plugging that into the equation we get (Arate+Brate)30min=1200 liters

This is also not sufficient, because there are a variety of different combinations of Arate and Brate that can fit this equation. For example, Arate could be 10 liters per min and Brate could be 30 liters per min OR vice versa.

Now lets try them both together by plugging (1) and (2) into the equation:

(25lit/min+Brate)30min=1200 liters

divide both sides by 30 min and we get: 25 liters/min+Brate=40liters/min

that means Brate equals 15 liters, so the answer is (C) both together are sufficient

In the actual GMAT, you would not need to go so far as to figure out exactly what B rate. That would be a waste of time. As soon as you know what you CAN solve it with both, which can be determined by the fact that there is only 1 unknown then you should select C and move on.
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GMAT 1: 750 Q49 V43 Re: Working together at their constant rates, A and B can fill  [#permalink]

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ksharma12 wrote:
Working together at their constant rates, A and B can fill an empty tank to capacity in 1/2 hours. What is the constant rate of pump B?

(1) A's constant rate is 25 LTS / min
(2) The tanks capacity is 1200 lts.

ksharma12 wrote:
Working together at their constant rates, A and B can fill an empty tank to capacity in 1/2 hours. What is the constant rate of pump B?

(1) A's constant rate is 25 LTS / min
(2) The tanks capacity is 1200 lts.

Let the rate of A be a and the rate of B be b

(1) A's constant rate is 25 LTS / min
(a+b)time = Volume of tank
(25+b)*30 minutes = Volume of tank
750+30b = volume of tank
Rate of B and the volume of tank is not known
INSUFFICIENT

(2) The tanks capacity is 1200 lts.
(a+b)*time = 1200
(a+b)*30 minutes = 1200
30a+30b=1200
Rate of A and rate of B is not known
INSUFFICIENT

MERGE BOTH
750 + 30b= 30a+30b {since both equations are equal to 1200}
30a=750
a=750/30 = 25

Now rate of A is known. Rate of B can be easily calculated by putting value of in any equation
for example 30a+30b =1200
750+30b=1200
30b=450
b= 15

SUFFICIENT

we need both statements together

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Re: Working together at their constant rates, A and B can fill  [#permalink]

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Imo C
At first sight the answer seems to be statement 1 but on closer inspection we come to know about its flaw as the rate is given in 25 liters per minute and from the question stem we have been given only the completion time ,So we need the capacity of the tank .
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_________________ Re: Working together at their constant rates, A and B can fill   [#permalink] 08 Oct 2018, 01:00
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