a PS from Gmat

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Sun Nov 13, 2011 10:27 am

15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container?

A:45
B:25
C:37.5
D:36
E:42

to be honest, i dont understand this question much, it says 15lts moved out from a container in which there are A and B or 15 lts are taking out from A?

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Source: Beat The GMAT — Problem Solving | Sun Nov 13, 2011 10:27 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Sun Nov 13, 2011 10:36 am

I posted a solution earlier
https://www.beatthegmat.com/container-t92063.html

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vaibhavgupta: Master | Next Rank: 500 Posts; Posts: 416; Joined: Tue Aug 30, 2011 2:18 pmFollowed by: 9 members; Location: Delhi, India; Thanked: 13 times

by vaibhavgupta » Sun Nov 13, 2011 11:24 am

diebeatsthegmat wrote:15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container?

A:45
B:25
C:37.5
D:36
E:42

to be honest, i dont understand this question much, it says 15lts moved out from a container in which there are A and B or 15 lts are taking out from A?

IMO C

OA?

If OA is A, IMO B
If OA is B, IMO C
If OA is C, IMO D
If OA is D, IMO E
If OA is E, IMO A

FML!! :/

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Nov 13, 2011 1:17 pm

diebeatsthegmat wrote:15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container?

A:45
B:25
C:37.5
D:36
E:42

to be honest, i dont understand this question much, it says 15lts moved out from a container in which there are A and B or 15 lts are taking out from A?

We can plug in the answers, which represent the volume of the container.

Answer choice C: 37.5 liters.
After the first mixing, the amount of A remaining in the container = 37.5 - 15 = 22.5 liters.
15 liters of the resulting solution are to be replaced with pure B.
Since 15/37.5 = 40%, the second mixing will replace 40% of the remaining 22.5 liters of A.
Thus, the amount of A left after the second mixing = .6(22.5) = 13.5 liters.
The amount of B after the second mixing = 37.5-13.5 = 24 liters.
A:B = 13.5 : 24 = 27:48 = 9:16.
Success!

The correct answer is C.

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subhakam: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Mon Jun 21, 2010 12:37 pm

by subhakam » Tue Feb 12, 2013 8:37 pm

GMATGuruNY wrote:
diebeatsthegmat wrote:15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container?

A:45
B:25
C:37.5
D:36
E:42

to be honest, i dont understand this question much, it says 15lts moved out from a container in which there are A and B or 15 lts are taking out from A?
We can plug in the answers, which represent the volume of the container.

Answer choice C: 37.5 liters.
After the first mixing, the amount of A remaining in the container = 37.5 - 15 = 22.5 liters.
15 liters of the resulting solution are to be replaced with pure B.
Since 15/37.5 = 40%, the second mixing will replace 40% of the remaining 22.5 liters of A.
Thus, the amount of A left after the second mixing = .6(22.5) = 13.5 liters.
The amount of B after the second mixing = 37.5-13.5 = 24 liters.
A:B = 13.5 : 24 = 27:48 = 9:16.
Success!

The correct answer is C.

Sorry GMAT Guru - I still do not get it

Can you show it algebraically? I really get confused on the second mixing.
if I make a column below and try to track the amount of both A and B - how do i do it ?

A B
37.5 0
First take out - 15 liters
37.5-15 +15
= 22.5 15
Can you explain what happens after another 15 are removed - what i get confused about is not only A being reduced but B is being reduced as well (when 15 is being removed the 2nd time)

Thanks

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Feb 13, 2013 5:40 am

subhakam wrote:
GMATGuruNY wrote:
diebeatsthegmat wrote:15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container?

A:45
B:25
C:37.5
D:36
E:42
Sorry GMAT Guru - I still do not get it
Can you show it algebraically? I really get confused on the second mixing.
Let the capacity of the container = x.
Every time 15 liters are removed, the volume of liquid inside the container decreases by 15/x.
To illustrate:
If x=30, removing 15 liters from the container -- 1/2 of the volume -- is equivalent to reducing the volume by 15/x = 15/30 = 1/2.
If x=45, removing 15 liters from the container -- 1/3 of the volume -- is equivalent to reducing the volume by 15/x = 15/45 = 1/3.
Thus, every time 15 liters are removed, the volume of A inside the container decreases by 15/x.

At the start, the container is full of A.
Thus, the original amount of A = x.
When 15 liters are removed, the decrease in A = (15/x)x = 15.
Remaining amount of A = x-15.
When 15 more liters are removed, the decrease in A = (15/x)(x-15).
Remaining amount of A = (x-15) - (15/x)(x-15) = (x-15)*(1 - 15/x) = (x-15)*(x-15)/x.

At the end of the process, A:B = 9:16.
Since 9+16 = 25, liquid A constitutes 9 of every 25 liters inside the container, implying that A = (9/25)x.

Since both expressions in red above represent the amount of A at the end of the process, we get:
(x-15)*(x-15)/x = (9/25)x

(x-15)Â² = (9/25)xÂ²

x-15 = (3/5)x

5x - 75 = 3x

2x = 75

x = 37.5.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Feb 13, 2013 9:12 am

diebeatsthegmat wrote:15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container?

A:45
B:25
C:37.5
D:36
E:42

We could also use the formula for REPEATED FRACTIONAL CHANGE.
If amount x DECREASES by fraction a/b exactly n times:

Final amount = x * (1 - a/b)^n.

In the problem at hand (as noted in my post above):
The original amount of A = x.
The final amount = (9/25)x.
The fractional decrease = 15/x.
Since the volume decreases TWICE, n = 2.
Plugging these values into the formula, we get:

(9/25)x = x * (1 - 15/x)Â²

9/25 = (1 - 15/x)Â²

3/5 = 1 - 15/x

15/x = 2/5

2x = 75

x = 37.5.

Note that if amount x INCREASES by fraction a/b exactly n times, the formula is as follows:
Final amount = x * (1 + a/b)^n.

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subhakam: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Mon Jun 21, 2010 12:37 pm

by subhakam » Thu Feb 14, 2013 6:36 pm

Thank you so much!! It finally makes sense- come to think of it; we deal with such problems in daily life but never come to stop and think how actually it formulates. Thank you once again for the clarification!!

One quick question - the formula that you posted on your second posting - it is only valid if the same quantity is removed/added repeatedly correct? So, for example we could not have used the direct formula if instead of 15 , 10 liters wee taken out.
Final amount = x * (1 - a/b)^n.
All help greatly appreciated

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Feb 15, 2013 8:34 am

subhakam wrote:Thank you so much!! It finally makes sense- come to think of it; we deal with such problems in daily life but never come to stop and think how actually it formulates. Thank you once again for the clarification!!

One quick question - the formula that you posted on your second posting - it is only valid if the same quantity is removed/added repeatedly correct? So, for example we could not have used the direct formula if instead of 15 , 10 liters wee taken out.
Final amount = x * (1 - a/b)^n.
All help greatly appreciated

Correct: the fractional change -- (amount removed)/(total volume) -- must be the same in each case.

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