It is currently 20 Nov 2017, 07:01

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Tanks X and Y contain 500 and 200 gallons of water respectively. If

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7738

Kudos [?]: 17814 [2], given: 235

Location: Pune, India
Re: Tanks X and Y contain 500 and 200 gallons of water respectively. If [#permalink]

Show Tags

New post 27 Jul 2015, 21:42
2
This post received
KUDOS
Expert's post
dhawalbp wrote:
VeritasPrepKarishma wrote:
PareshGmat wrote:
I started up like this;
We require both tanks to have same amount of water i.e 350 gallons
means 150 gallons have to be removed from Tank X & 150 gallons have to be added to Tank Y

It will take \(\frac{150}{60K}\) Hrs to remove water from Tank X & \(\frac{150}{60M}\) Hrs to add water to Tank Y

I stuck at this point; Bunuel / Karishma can you please suggest how to continue using this approach


Your starting point is the problem Paresh. Think about it. There are two people standing on a number line, one at 200 and the other at 500. They have a distance of 300 steps between them. They want to meet by walking towards each other and hence be at the same point. Will they necessarily meet at the center point? No. It depends on their speed where they meet. If the person at 200 is very slow and the other very fast, they will meet very close to 200 because the person at 200 would not have covered much distance and most distance will be covered by the person at 500. Hence the assumption that both need to have 350 ml is incorrect. Perhaps the filling up of 200 gallon tank is very slow while the emptying of 500 gallon is very fast. Then they both might have equal volumes of 250 gallons.

Check out the posts above for alternative solutions.

karishma: What PareshGmat did was pretty right....The catch is if both tank X and y are taking same time say, t hr to equal the level that means rate M=K...so time taken t=150/(K*60)=5/(2K)=5/(K+M)


Did you read the explanation I gave to him on why his logic is not sound?
Having equal level of water does not mean they did equal work. After some time, they both could have been at 300 gallons. So the tank with 200 gallons would have increased its water level by 100 gallons and tank with 500 gallons would have decreased its water level by 200 gallons. Note that the second tank would have done twice the work as done by first tank in the same amount of time so in this case, its rate would be twice the rate of first tank.
They do have equal level at the end but to reach there, they might have done different amount of work. So their rate need not be equal. This is the catch of this question.
Kindly go through my explanation given above and then check out the solutions given here:

tanks-x-and-y-contain-500-and-200-gallons-of-water-respectiv-101762.html#p789043
tanks-x-and-y-contain-500-and-200-gallons-of-water-respectiv-101762.html#p1346155
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17814 [2], given: 235

Current Student
User avatar
Joined: 12 Aug 2015
Posts: 300

Kudos [?]: 580 [0], given: 1474

Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
Re: Tanks X and Y contain 500 and 200 gallons of water respectively. If [#permalink]

Show Tags

New post 18 Jan 2016, 00:18
Plug-in SMART numbers and test options.

M=20 and K=5, hence \(\frac{(500-200)}{(20+5)}\) = 12 minutes to equalize the both which is 1/5 h. Answer A works
_________________

KUDO me plenty

Kudos [?]: 580 [0], given: 1474

Expert Post
Math Expert
User avatar
P
Joined: 02 Aug 2009
Posts: 5211

Kudos [?]: 5851 [0], given: 117

Re: Tanks X and Y contain 500 and 200 gallons of water respectively. If [#permalink]

Show Tags

New post 18 Jan 2016, 01:22
ichha148 wrote:
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. \(\frac{60}{M - K}\text{ hours}\)

m22 q17



Hi,
the Q can be done in two steps...
the total change, both filling in one and draining in other, equals 500-200=300..
what are the rates working towards it .. M+K gallons per minute or (M+K)*60 gallons per hour...
\(answer =\frac{300}{{(M+K)*60 }}=\frac{5}{{M+K}}\)..
A
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5851 [0], given: 117

Intern
Intern
avatar
Joined: 02 Jul 2015
Posts: 38

Kudos [?]: 3 [0], given: 1

WE: Investment Banking (Investment Banking)
Re: Tanks X and Y contain 500 and 200 gallons of water respectively. If [#permalink]

Show Tags

New post 18 Jan 2016, 02:01
Plug in numbers to find an answer.

Lets take 250 gallons as the common amount that we need to reach with each tank.

If water is pumped out of X at 5 gallons per min, it will take 50 mins to pump out 250 gallons (500 - 250 = 250 gallons left). If water is pumped into Y at 1 gallon per min, then in 50 mins, 50 gallons will be pumped in. Hence Y will also reach 250.

It will take 50 mins or 5/6 hours for both of them to reach an equal level.

M = 5, N = 1. Answer A = 5/6.

Kudos [?]: 3 [0], given: 1

Intern
Intern
User avatar
Joined: 18 Jul 2015
Posts: 43

Kudos [?]: 13 [0], given: 33

Location: Brazil
Concentration: General Management, Strategy
GMAT 1: 640 Q39 V38
GMAT 2: 700 Q47 V38
Re: Tanks X and Y contain 500 and 200 gallons of water respectively. If [#permalink]

Show Tags

New post 05 Feb 2016, 12:00
Here is how I solve it:

500 gallons - 60K gallons per hour x HOUR = 200 gallons + 60M gallons per hour x HOUR

Translating:
500-60kH=200+60mH
500-200=60mH+60kH
300=60H(m+k)
300/60(m+k)=H - simplify
5/(m+k)=h

ANSWER A

Kudos [?]: 13 [0], given: 33

Intern
Intern
avatar
Joined: 30 Oct 2013
Posts: 38

Kudos [?]: [0], given: 51

Re: Tanks X and Y contain 500 and 200 gallons of water respectively. If [#permalink]

Show Tags

New post 05 Feb 2016, 20:10
Bunuel wrote:
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.

This approach is the one I can formulate easiest, however I do have two questions.

1) W = RT, which is why we take k*t and m*t is that correct?
2) Why do we use k and m, rather than 1/k and 1/m? Are we not supposed to use rates? Perhaps I'm missing what kt and mt really mean.

Thanks

Kudos [?]: [0], given: 51

Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3098

Kudos [?]: 1115 [0], given: 327

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: Tanks X and Y contain 500 and 200 gallons of water respectively. If [#permalink]

Show Tags

New post 06 Feb 2016, 10:22
ichha148 wrote:
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. \(\frac{60}{M - K}\text{ hours}\)

m22 q17


Good One , loved solving it !!

I am attaching 2 Pics ( hope it helps)

Attachment:
Capacity.PNG
Capacity.PNG [ 3.4 KiB | Viewed 593 times ]


Attachment:
Calculations.PNG
Calculations.PNG [ 3.01 KiB | Viewed 593 times ]


Hence IMHO (A)


_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1115 [0], given: 327

Intern
Intern
avatar
Joined: 30 Nov 2012
Posts: 10

Kudos [?]: 2 [0], given: 1

Re: Tanks X and Y contain 500 and 200 gallons of water respectively. If [#permalink]

Show Tags

New post 12 Oct 2016, 19:11
Bunuel wrote:
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.

BUNUEL,
pls explain me why t should be equal for both tanks. Why cant one tank take 10 min more to reach the same amount of water that another tank already has?

Kudos [?]: 2 [0], given: 1

Intern
Intern
avatar
Joined: 30 Nov 2012
Posts: 10

Kudos [?]: 2 [0], given: 1

Re: Tanks X and Y contain 500 and 200 gallons of water respectively. If [#permalink]

Show Tags

New post 12 Oct 2016, 19:21
VeritasPrepKarishma wrote:
ichha148 wrote:
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. \(\frac{60}{M - K}\text{ hours}\)

m22 q17



This is a relative speed question.

Distance to be covered together = 300 gallons (= 500 gallons - 200 gallons)
Relative speed (rate of work) = (K+M) gallons per minute OR 60*(K+M) gallons per hour (The rates get added because they are working in opposite directions)

Time taken = 300/60(K+M) hours = 5/(K+M) hours


honestly, I didnt realize it is this type of question. Can you explain pls how to spot relative speed questions , especially in a different context like this one.
thank you

Kudos [?]: 2 [0], given: 1

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7738

Kudos [?]: 17814 [1], given: 235

Location: Pune, India
Re: Tanks X and Y contain 500 and 200 gallons of water respectively. If [#permalink]

Show Tags

New post 14 Oct 2016, 01:19
1
This post received
KUDOS
Expert's post
alesia257 wrote:
VeritasPrepKarishma wrote:
ichha148 wrote:
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. \(\frac{60}{M - K}\text{ hours}\)

m22 q17



This is a relative speed question.

Distance to be covered together = 300 gallons (= 500 gallons - 200 gallons)
Relative speed (rate of work) = (K+M) gallons per minute OR 60*(K+M) gallons per hour (The rates get added because they are working in opposite directions)

Time taken = 300/60(K+M) hours = 5/(K+M) hours


honestly, I didnt realize it is this type of question. Can you explain pls how to spot relative speed questions , especially in a different context like this one.
thank you


It is not necessary to do it using the relative speed concept. You can do it using algebra too.
But it is good if you recognise that there is an equivalence in time-speed-distance and work-rate-time. In fact, time-speed-distance is just a special case of work-rate-time.
In this case, work done is the 'distance covered' and rate is the 'speed'. So the concepts of TSD can be applied to the generic work-rate case too.

Distance covered is work done (300 gallons)
Relative speed is relative rate of work = 60(K+M)
So time taken = Distance/Speed = 300/60*(K+M) = 5/(K+M) hrs
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17814 [1], given: 235

Director
Director
avatar
G
Joined: 07 Dec 2014
Posts: 836

Kudos [?]: 266 [0], given: 15

Re: Tanks X and Y contain 500 and 200 gallons of water respectively. If [#permalink]

Show Tags

New post 14 Oct 2016, 14:00
ichha148 wrote:
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. \(\frac{60}{M - K}\text{ hours}\)

m22 q17


let h=number of hours
200+h*60M=500-h*60K
h*(60M+60K)=300
h=300/(60M+60K)
h=5/(M+K)
A.

Kudos [?]: 266 [0], given: 15

Manager
Manager
avatar
B
Joined: 24 Jun 2017
Posts: 110

Kudos [?]: 14 [0], given: 125

Re: Tanks X and Y contain 500 and 200 gallons of water respectively. If [#permalink]

Show Tags

New post 14 Aug 2017, 14:59
work rate in hours for both 60(k+m)
total amount of work to be performed 500-200 = 300
then:
60(k+m) *x hours = 300
X hours = 300/60(k+m) = 5/(k+m)

Kudos [?]: 14 [0], given: 125

Re: Tanks X and Y contain 500 and 200 gallons of water respectively. If   [#permalink] 14 Aug 2017, 14:59

Go to page   Previous    1   2   [ 32 posts ] 

Display posts from previous: Sort by

Tanks X and Y contain 500 and 200 gallons of water respectively. If

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.