GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Sep 2018, 15:26

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

Eight litres are drawn off from a vessel full of water and s

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

Hide Tags

BSchool Thread Master
User avatar
B
Joined: 13 Jul 2015
Posts: 57
Location: Singapore
GMAT 1: 730 Q50 V39
WE: Operations (Investment Banking)
Eight litres are drawn off from a vessel full of water and s  [#permalink]

Show Tags

New post 02 Oct 2015, 03:04
Bunuel wrote:
virupaksh2010 wrote:
Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight litres of the mixture are drawn off and substituted by pure milk.If the vessel now contains water and milk in the ratio 9:40, find the capacity of the vessel.

A. 21 liters
B. 22 liters
C. 20 liters
D. 14 liters
E. 28 liters


Let the capacity of the vessel be \(x\).

After the first removal there would be \(x-8\) liters of water left in the vessel. Note that the share of the water would be \(\frac{x-8}{x}\);

After the second removal, the removed mixture of 8 liters will contain \(8*\frac{x-8}{x}\) liters of water, so there will be \((x-8)-8*\frac{x-8}{x}=\frac{(x-8)^2}{x}\) liters of water left.

As the ratio of water to milk after that is \(\frac{9}{40}\), then the ratio of water to the capacity of the vessel would be \(\frac{9}{40+9}=\frac{9}{49}\).

So \(\frac{\frac{(x-8)^2}{x}}{x}=\frac{9}{49}\) --> \(\frac{(x-8)^2}{x^2}=\frac{9}{49}\) --> \(\frac{x-8}{x}=\frac{3}{7}\) --> \(x=14\).

Answer: D.


Bunuel, I understood your solution and I tried to work with milk too. what am I doing wrong?

1st pass: concentration of milk in solution: \(\frac{8}{x}\)

Removed: 8 litres of mixture --> 8 X \(\frac{8}{x}\)

Milk left: x - (8 X \(\frac{8}{x}\)) + 8 = \(\frac{x^2+8x-64}{x}\)

\(\frac{Milk}{Capacity}\) = \(\frac{x^2+8x-64}{x^2}\) = \(\frac{40}{49}\)

What am I doing wrong?
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------

update: bolded working should be Milk left: 8 - (8 X \(\frac{8}{x}\)) + 8 = \(\frac{16x-64}{x}\)

but that would lead to a very ugly quadratic equation: 10\(x^2\) - 196x + 784 = 0 --> which gives the answer x =14

so my question is, is there anything in the question that prompted you to use water instead?
Intern
Intern
avatar
B
Joined: 29 Apr 2017
Posts: 16
Re: Eight litres are drawn off from a vessel full of water and s  [#permalink]

Show Tags

New post 06 May 2017, 05:22
Hello
I am solving this que as follows:

Assume the capacity of vessel is 20l

So after first withdrawal,
Water= 12l
Milk= 8l

After second withdrawal,
Water = 20 - 12/20*8 = 12.8l
Milk = 20 - 12.8 = 7.2l

Now this ratio is equal to 9/40

I am stuck here now can anyone please help me?
Thanks

Sent from my SM-N9200 using GMAT Club Forum mobile app
Manager
Manager
avatar
B
Joined: 14 May 2015
Posts: 52
Re: Eight litres are drawn off from a vessel full of water and s  [#permalink]

Show Tags

New post 06 May 2017, 09:32
9x/49 = x((x-8)/x)^2
5x^2 - 98x + 392
x=14
Director
Director
User avatar
B
Joined: 17 Dec 2012
Posts: 637
Location: India
Eight litres are drawn off from a vessel full of water and s  [#permalink]

Show Tags

New post 10 Jun 2017, 03:07
virupaksh2010 wrote:
Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight liters of the mixture are drawn off and substituted by pure milk. If the vessel now contains water and milk in the ratio 9:40, find the capacity of the vessel.

A. 21 liters
B. 22 liters
C. 20 liters
D. 14 liters
E. 28 liters

1. We know a total of 16 L milk were added. Choice C which is 20 L capacity, implies that finally, at least 4L of water in excess was there after drawing .
2. So water is (4+x) and we know the milk added was 16L giving a ratio of (4+x)/16 which is greater than 9/40. On same reasoning all choices except D can be ruled out.
_________________

Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8104
Premium Member
Re: Eight litres are drawn off from a vessel full of water and s  [#permalink]

Show Tags

New post 29 Jun 2018, 01:58
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Eight litres are drawn off from a vessel full of water and s &nbs [#permalink] 29 Jun 2018, 01:58

Go to page   Previous    1   2   3   [ 46 posts ] 

Display posts from previous: Sort by

Eight litres are drawn off from a vessel full of water and s

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.