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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

5 liters are taken off from a vessel full of water and [#permalink]
20 Oct 2005, 20:25

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct
0% (00:00) wrong based on 0 sessions

5 liters are taken off from a vessel full of water and replaced with pure milk, again, five more liters of the mixture is taken and replaced with pure milk. After this process, if the vessel contains water and milk in the ratio 9:16 what is the capacity of vessel?

Ok this is a little more calculation than I would like.

(5-5/x*5+5)/x=16/25 (equation is established for milk)
10-25/x=16/25x
16x^2-250x+25^2=0
(4x-125/4)^2-(125/4)^2+25^2=0
(4x-125/4)^2=25^2/4^2(5^2-4^2)
(4x-125/4)^2=(25*3)^2/4^2
4x-125/4=75/4
4x=200/4=50
x=12.5

Verification:
If x=12.5, after the first milk added the ratio of milk is 5/12.5=2/5. So when you get 5 of mixture out you get 2 milk out. Then you add another 5 milk. So you've got 5-2+5=8 milk left. 8/12.5=16/25. The answer seems to be correct.

Only thing is there should be an easier way to go about this. _________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Last edited by HongHu on 25 Oct 2005, 08:22, edited 1 time in total.

Verification: If x=12.5, after the first milk added the ratio of milk is 5/12.5=2/5. So when you get 5 of mixture out you get 2 milk out. Then you add another 5 milk. So you've got 5-2+5=8 milk left. 8/12.5=16/25. The answer seems to be correct.

Only thing is there should be an easier way to go about this.

in your example, the water remained constant but when you take out 5 lt and another 5 lt the the water also take out not only milk, right? i am little confused here............

x = 12.5
1st take out = 5 lt water.
now the vessel has = 12.5-5 = 7.5 water
add 5 lt milk, then vessel contains = 7.5+5 = 12.5 water and milk.
again take out 5 lt, now vessel has 7.5 water and milk

now, milk = 5 - 2 = 3 lt.
water = 7.5 -3 = 4.5

now add 5 lt milk, then total = 12.5 water and milk (water = 4.5 and milk 8)

ratio of water/milk = 4.5/8 = 9/16...hmmmmmmmm ok....... thats correct. thankxxxxxxxxxxxxxxxxxxxxxxxxxxx

i did otherway round: milk:water.

so "read and understand the question correctly. doing so is 1/2 problem solved".

Yes I didn't use water, I used the entire volume because this might be easier. However you'll have to remember to use 16/25 instead of 16/9. _________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Let's see this may be a little easier to do then the earlier approach, if you are good at manipulating ratios...

(5-5/x*5+5)/x=16/25 (same as before, equation is established for milk over total volume)
(10x-25)/x^2=16/25
(x^2-10x+25)/x^2=(25-16)/25
(x-5)^2/x^2=9/25
(x-5)/x=3/5
5/x=2/5
x=25/2

At least this gets rid of square of big numbers ... _________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Last edited by HongHu on 25 Oct 2005, 08:23, edited 2 times in total.

Let's see this may be a little easier to do then the earlier approach, if you are good at manipulating ratios...

(5+5/x*5+5)/x=16/25 (same as before, equation is established for milk over total volume) (10x-25)/x^2=16/25 (x^2-10x+25)/x^2=(25-16)/25 (x-5)^2/x^2=9/25 (x-5)/x=3/5 5/x=2/5 x=25/2

At least this gets rid of square of big numbers ...

Very clever trick to use only milk's percentage here.
Is this typo (5+5/x*5+5)/x=16/25 should it be a minus sign like
(5-5/x*5+5)/x=16/25.

There is a very handy formula to remember for these kind of questions..

If initially 'a' liters of liquid A is present in a vessel; if 'b' liters is taken from this vessel and substituted with liquid B, then 'b' liters is again taken and substituted with liquid B and this process is repeated 'n' times then after n times:

(Liquid A left in vessel / Liquid B left in vessel) =
[(a-b)/a]^n/{1-[(a-b)/a]^n}

Here, Liquid A left in vessel / Liquid B left in vessel = 9/16
b = 5, n = 2 Solve to get a = 12.5

Is this typo (5+5/x*5+5)/x=16/25 should it be a minus sign like (5-5/x*5+5)/x=16/25.

Yes, thanks! I copied the first typoed equation for my second post, which explains why I had the typo for both posts. I've corrected them both.

BumblebeeMan wrote:

Hong, can you explain how you arrived at this first equation?

Considering milk. The first time you added 5 liter milk to the vessel. So now the ratio of milk to entire volume is 5/x. Then you take 5 liter of mixtures out, there's 5/x liter milk in each liter of mixture, so 5/x*5 milk in the 5 liter mixture you take out. Then you added another 5 liter in. Now you have 5-5/x*5+5 liters of milk in the x liter mixtures. And you know the real ratio is 16/(9+16)=16/25. _________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Yes, thanks! I copied the first typoed equation for my second post, which explains why I had the typo for both posts. I've corrected them both.

BumblebeeMan wrote:

Hong, can you explain how you arrived at this first equation?

Considering milk. The first time you added 5 liter milk to the vessel. So now the ratio of milk to entire volume is 5/x. Then you take 5 liter of mixtures out, there's 5/x liter milk in each liter of mixture, so 5/x*5 milk in the 5 liter mixture you take out. Then you added another 5 liter in. Now you have 5-5/x*5+5 liters of milk in the x liter mixtures. And you know the real ratio is 16/(9+16)=16/25.

We cannot get better explanation than this. I committed this method for this kind of problems. Thanks a ton.

Wow...I'm still reeling from my HBS admit . Thank you once again to everyone who has helped me through this process. Every year, USNews releases their rankings of...

I had an interesting conversation with a friend this morning, and I realized I need to add a last word on the series of posts on my application process. Five key words:...