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With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. What is the capacity of the pool if every minute the second valve admits 50 cubic meters of water more than the first? (A) 9000 cubic meters (B) 10500 cubic meters (C) 11750 cubic meters (D) 12000 cubic meters (E) 12500 cubic meters Source: GMAT Club Tests - hardest GMAT questions I sweated when time gone!
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Manager
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I get D
let x mcube be the vol
then
60*x/(x+3000) = 48
=> x = 12000
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sondenso wrote: With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. What is the capacity of the pool if every minute the second valve admits 50 cubic meters of water more than the first?
9000 cubic meters
10500 cubic meters
11750 cubic meters
12000 cubic meters
12500 cubic meters
I sweated when time gone! let first taps speed be x cu/min then second taps speed be x+50 cu/min then 48(x+(x+50))= total capacity---------(1) since first tap can fill in 2 hrs 60*2(x) is total capacity------------(2) equating x=100 total capacity=100*2*60 =12000 hope this is clear
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I'm confused here:
Shouldn't we add the quantity of valve1 + quantity of valve2 = total quantity? Please tell me where I'm going wrong.
For example:
This is what I did:
1. Figure out the time Valve 2 took to fill the pool by itself
1/Valve1 + 1/Valve2 = 1/48
1/120 mins (or 2 hours) + 1/Valve2 = 1/48 mins
Valve2 = 80 mins
2. Find the Quantity to fill the pool X
120(X) + 80 (X+50) = 48 (2x + 50)
So this is where it goes down hill...
not sure why we don't include 80 (X+50) in the equation?
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bigfernhead wrote: I'm confused here:
Shouldn't we add the quantity of valve1 + quantity of valve2 = total quantity? Please tell me where I'm going wrong.
For example:
This is what I did:
1. Figure out the time Valve 2 took to fill the pool by itself
1/Valve1 + 1/Valve2 = 1/48
1/120 mins (or 2 hours) + 1/Valve2 = 1/48 mins
Valve2 = 80 mins
2. Find the Quantity to fill the pool X
120(X) + 80 (X+50) = 48 (2x + 50)
So this is where it goes down hill...
not sure why we don't include 80 (X+50) in the equation? Step 1 is correct in that you found that Valve 2 can fill a tank in 80 min. Step 2 is wrong. Valve 1 can fill the tank in 120 Min with x being the volume filled per min - So total volume = 120*x ----> Eq1 Valve 2 can fill the tank in 80 min with (x+50) being the volume filled per min. So the total volume = 80(x+50) ---> Eq2 Together can fill the tank in 48 min with (x + (x + 5)) being the volume filled per min. So the total volume = 48(x + (x + 5)) ---> Eq 3. To solve for x, pick any of the 2 of the 3 eq, ie either equate Eq 1 = Eq 2 or Eq 1 = Eq 3 or Eq2 = Eq 3 and get the ie 120X = 80(x + 50) ==> x = 100. We get x = 100. Now substitute value of x in any of the 3 eq and you should get the total volume.
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sondenso wrote: rohit929 wrote: sondenso wrote: With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. What is the capacity of the pool if every minute the second valve admits 50 cubic meters of water more than the first?
9000 cubic meters
10500 cubic meters
11750 cubic meters
12000 cubic meters
12500 cubic meters
I sweated when time gone! let first taps speed be x cu/min then second taps speed be x+50 cu/min then 48(x+(x+50))= total capacity---------(1) since first tap can fill in 2 hrs 60*2(x) is total capacity------------(2) equating x=100 total capacity=100*2*60 =12000 hope this is clear So sooooooo great, rohit! Thanks! I lost many basic, I think. I approach this by using work rate = work/time. And stucked!  Indeed "rate = work/time" approach is same as rohit used. capacity=work = rate*time = (x +x+50)*48 capacity= rate*time = x*120
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Here is how I solved the problem:
9. With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. What is the capacity of the pool if every minute the second valve admits 50 cubic meters of water more than the first?
* 9000 cubic meters
* 10500 cubic meters
* 11750 cubic meters
* 12000 cubic meters
* 12500 cubic meters
let B = # of mins for the second valve alone to fill the pool
1/(time it takes first valve to fill the pool) + 1/B = 1/(total time its takes to fill the pool)
1/120 + 1/B = 1/48
B = 80
let C = the capacity of the pool
C/80 - C/120 = 50
C = 12000
ANSWER: D. 12000
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Here x and x+50 are nothing but the rates of the pipes.
R1 + R2 = R ( R=combined rate )
x+x+50 = Capacity/48, Now capacity = 120x
=> 2x+50 = 120x/48
=> x=100
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48 min = 0.8 hrs, then if x is pool's volume
both pipes open
for 0.8 hrs - x cubic m (multiply both sides by 5)
for 4 hrs - 5x cubic m
Within 4 hrs
the first pipe alone could fill 2 pools,
the second 3 pools.
So, the second could fill one pool more than the 1st being open for 4hrs.
x=4*60*50=12000 (D).
Last edited by nvgroshar on 26 Jan 2011, 11:03, edited 1 time in total.
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It's actually an easy word question - just take your time to set up the x variable - let x be the amount of water in cube meter the first valve admits per minute, x+50 will be for the second valve 48(x+(x+50))=60*2x => x=100 substitute back to the right hand side of the equation => total capacity=100*120 =12,000 Usually when I have enough time, I put the x value in the left side to see if I get 12,000 as well - just for sanity check
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from the given info we know that
1/x+1/y=48 ( both valve will fill in 48 mins)
1/x=1/120 (fist valve will fill in 2 hrs or 120 mins)
so by solving
1/y=1/80 (second valve will take 80 mins)
first valve =1/120
second valve =1/80
if the tank can be filled by first valve in 120 minutes and the second one by 80 mins
then answer should be exactly divided by 120 and 80 only choice D satisfies this criterion so I picked ans D ( of courseif it contains more than one choice divisble by 120 and 80 then you'll have to solve it precisely)
or you can solve this by solving for x tradionaly by applying formula as everyone stated above
1/120(x)+1/80(x+5)=1/48(2x+5)
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With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity of the pool?
(C) 2008 GMAT Club - m12#10
* 9000 cubic meters
* 10500 cubic meters
* 11750 cubic meters
* 12000 cubic meters
* 12500 cubic meters |
still puzzled how to do it my way.... found out that the rate of V1 is 1/120 and V2 is 1/100....correct? if yes, then how to find volume? thanks.....
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zisis wrote: With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity of the pool?
(C) 2008 GMAT Club - m12#10
* 9000 cubic meters
* 10500 cubic meters
* 11750 cubic meters
* 12000 cubic meters
* 12500 cubic meters |
still puzzled how to do it my way.... found out that the rate of V1 is 1/120 and V2 is 1/100....correct? if yes, then how to find volume? thanks..... Let the rate of the first valve be x cubic meters per minute, then the rate of the second valve will be x+50 cubic meters per minute. As both valves open fill the pool in 48 minutes then the capacity of the pool equals to C=time*combined \ rate=48(x+x+50)=48(2x+50); But as the first valve alone fills the pool in 2 hours (120 minutes) then the capacity of the pool also equals to C=time*rate=120x; So, 120x=48(2x+50) --> x=100 --> C=120x=12,000. Answer: D. Hope it's clear.
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Total Volume = x First valve and second valve take 48 minutes to fill the pool The both valves filled x/48 in 1 minute First valve filled x/120 part in 1 minute So, Second valve filled in 1 minute = x/48 - x/120 = 3x/240 part Given that 3x/240 - x/120 = 50 x =12000 Ans. D.
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good question..........and an amazing explanation
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Gurus,
With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. What is the capacity of the pool if every minute the second valve admits 50 cubic meters of water more than the first?
(A) 9000 cubic meters
(B) 10500 cubic meters
(C) 11750 cubic meters
(D) 12000 cubic meters
(E) 12500 cubic meters
I tried this question and tried this approach but did not get me the answer? Please could you tell me what I did wrong?
W= RT
R=w/t
c/120 +x =C/48
X( rate at which second valve fills up) .I got stuck here cos i had two many unknowns
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Jiggyjee1
X is C/120+50 which is given so only 1 unknown.
+1 D
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We can use plugin approach also here.
From the options given, assume that capacity of tank is = 12000
Tap 1 fills 12000 in 2 hrs. In 1 min = 100 cu/m
Tap 2 in 1 min = 100 + 50 = 150.
So in 48 mins = 48(100 (t1) + 150 (t2) = 12000.
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Consider the time the second pipe takes to fill the tank as 1/x = 1/48 - 1/120
= 1/80 .
therefore x takes 80 mins to fill the pipe . But since each minute pipe B fills in an extra 50 from A using a smart number 100
B takes = 80 * 150 = 12000 would be the capacity
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