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M22-17

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M22-17  [#permalink]

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New post 16 Sep 2014, 01:16
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Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of \(K\) gallons per minute and water is being added to tank Y at a rate of \(M\) gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?

A. \(\frac{5}{M + K}\text{ hours}\)
B. \(6(M + K)\text{ hours}\)
C. \(\frac{300}{M + K}\text{ hours}\)
D. \(\frac{300}{M - K}\text{ hours}\)
E. \(\frac{60}{M - K}\text{ hours}\)

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Re M22-17  [#permalink]

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New post 16 Sep 2014, 01:16
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Official Solution:

Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of \(K\) gallons per minute and water is being added to tank Y at a rate of \(M\) gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?

A. \(\frac{5}{M + K}\text{ hours}\)
B. \(6(M + K)\text{ hours}\)
C. \(\frac{300}{M + K}\text{ hours}\)
D. \(\frac{300}{M - K}\text{ hours}\)
E. \(\frac{60}{M - K}\text{ hours}\)

Say \(t\) minutes are needed the two tanks to contain equal amounts of water, then we would have that \(500-kt=200+mt\). Find \(t\): \(t=\frac{300}{m+k}\) minutes or \(\frac{1}{60}*\frac{300}{m+k}=\frac{5}{m+k}\) hours.

Answer: A
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Re: M22-17  [#permalink]

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New post 23 Jan 2017, 20:44
Is a viable method to sub in gallon amounts for M and K, determine the time, t, when the volumes are equal, and then plug in to see which answer gives the correct value? E.g.

If M=100 and K=50, after 1h X has 400 gallons and Y has 250 gallons. After 2h, X has 300 gallons and Y has 300 gallons. So t=2h.

Answer A gives the correct time of 2h, when plugging in (5/3 for M and 5/6 for K). Note that M and K are converted to gallons/min.
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Re: M22-17  [#permalink]

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New post 23 Jan 2017, 20:45
Bunuel wrote:
Official Solution:

Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of \(K\) gallons per minute and water is being added to tank Y at a rate of \(M\) gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?

A. \(\frac{5}{M + K}\text{ hours}\)
B. \(6(M + K)\text{ hours}\)
C. \(\frac{300}{M + K}\text{ hours}\)
D. \(\frac{300}{M - K}\text{ hours}\)
E. \(\frac{60}{M - K}\text{ hours}\)

Say \(t\) minutes are needed the two tanks to contain equal amounts of water, then we would have that \(500-kt=200+mt\). Find \(t\): \(t=\frac{300}{m+k}\) minutes or \(\frac{1}{60}*\frac{300}{m+k}=\frac{5}{m+k}\) hours.

Answer: A



Hi. Is a viable method to sub in gallon amounts for M and K, determine the time, t, when the volumes are equal, and then plug in to see which answer gives the correct value? E.g.

If M=100 and K=50, after 1h X has 400 gallons and Y has 250 gallons. After 2h, X has 300 gallons and Y has 300 gallons. So t=2h.

Answer A gives the correct time of 2h, when plugging in (5/3 for M and 5/6 for K). Note that M and K are converted to gallons/min.
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Re: M22-17  [#permalink]

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New post 12 Mar 2018, 23:32
Hi,

Why do you assume that both tanks need the same amount of time? Should this be not stated in the question?
Because for example if the first tank needs 30 minutes because he has a much higher rate and the second one needs 60 minutes because of a lower rate, the time needed to reach the same level is 60 minutes.

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Re: M22-17  [#permalink]

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New post 12 Mar 2018, 23:59
MarFel wrote:
Hi,

Why do you assume that both tanks need the same amount of time? Should this be not stated in the question?
Because for example if the first tank needs 30 minutes because he has a much higher rate and the second one needs 60 minutes because of a lower rate, the time needed to reach the same level is 60 minutes.

BR


I think you misunderstood the question.

We have two tanks, X and Y, containing 500 and 200 gallons of water. Water is being pumped out of tank X at some rate and water is being added to tank Y at some rate. Now, obviously, after some time both tanks will have equal amount of water. The question asks to find that amount of time.

Hope it's clear.
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Re: M22-17  [#permalink]

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New post 13 Mar 2018, 00:14
Bunuel wrote:
MarFel wrote:
Hi,

Why do you assume that both tanks need the same amount of time? Should this be not stated in the question?
Because for example if the first tank needs 30 minutes because he has a much higher rate and the second one needs 60 minutes because of a lower rate, the time needed to reach the same level is 60 minutes.

BR


I think you misunderstood the question.

We have two tanks, X and Y, containing 500 and 200 gallons of water. Water is being pumped out of tank X at some rate and water is being added to tank Y at some rate. Now, obviously, after some time both tanks will have equal amount of water. The question asks to find that amount of time.

Hope it's clear.


Thx for your reply!
Still dont get it.

Your solutions says that:
500−kt=200+mt

My point is that t must not be equal on both sides because they can have different rates at which water is pumped out or in and need thus different amounts of time.
So my formula would be: 500-k*t1=200+m*t2
Which can not be solved for a valid solution.
To be more precise if water is pumped out of Tank X at a rate of 30 gallons per minute and water is pumped into Tank Y at 50 gallons per minute.
Tank X needs to loose 150 gallons and needs thus 150/30= 5 minutes and Tank Y needs to gain 150 gallons and thus 150/50=3 minutes. Thus the time is not equal.

Ahh okay got it now will leave it for others though.
The amount of water is not fixed we will just pump water out of tank X until it reaches the same level of tank Y. And that level is somewhere between 500 and 200.
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Re: M22-17  [#permalink]

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New post 05 May 2018, 14:26
The explanation is very good and awesome.
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Re: M22-17  [#permalink]

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New post 22 Sep 2018, 04:06
Bunuel wrote:
Official Solution:

Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of \(K\) gallons per minute and water is being added to tank Y at a rate of \(M\) gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?

A. \(\frac{5}{M + K}\text{ hours}\)
B. \(6(M + K)\text{ hours}\)
C. \(\frac{300}{M + K}\text{ hours}\)
D. \(\frac{300}{M - K}\text{ hours}\)
E. \(\frac{60}{M - K}\text{ hours}\)

Say \(t\) minutes are needed the two tanks to contain equal amounts of water, then we would have that \(500-kt=200+mt\). Find \(t\): \(t=\frac{300}{m+k}\) minutes or \(\frac{1}{60}*\frac{300}{m+k}=\frac{5}{m+k}\) hours.

Answer: A





my doubt is 500-kt = 200+mt

if 300 gallons has flowed out of tank x and 300 gallons had to flow into tank y

now 200 = 500?

pl explain if i missed out anything?
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Re: M22-17  [#permalink]

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New post 23 Sep 2018, 04:04
sdgmat89 wrote:
Bunuel wrote:
Official Solution:

Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of \(K\) gallons per minute and water is being added to tank Y at a rate of \(M\) gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?

A. \(\frac{5}{M + K}\text{ hours}\)
B. \(6(M + K)\text{ hours}\)
C. \(\frac{300}{M + K}\text{ hours}\)
D. \(\frac{300}{M - K}\text{ hours}\)
E. \(\frac{60}{M - K}\text{ hours}\)

Say \(t\) minutes are needed the two tanks to contain equal amounts of water, then we would have that \(500-kt=200+mt\). Find \(t\): \(t=\frac{300}{m+k}\) minutes or \(\frac{1}{60}*\frac{300}{m+k}=\frac{5}{m+k}\) hours.

Answer: A





my doubt is 500-kt = 200+mt

if 300 gallons has flowed out of tank x and 300 gallons had to flow into tank y

now 200 = 500?

pl explain if i missed out anything?


Please notice that you do not get 200 = 500, because kt and mt are not the same and they don't cancel out.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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