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# A certain quantity of 40% solution is replaced with 25% solu

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Senior Manager
Joined: 30 Aug 2003
Posts: 313
Location: dallas , tx
A certain quantity of 40% solution is replaced with 25% solu  [#permalink]

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24 Dec 2003, 20:28
17
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Difficulty:

55% (hard)

Question Stats:

65% (01:47) correct 35% (01:49) wrong based on 605 sessions

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A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?

(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4

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shubhangi

Veritas Prep GMAT Instructor
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Re: Mixture problem  [#permalink]

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22 Jul 2011, 02:30
6
2
gmatprep09 wrote:
A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?

(A) 1/4

(B) 1/3

(C) 1/2

(D) 2/3

(E) 3/4

Or use our standard mixtures formula for replacements too. In a certain quantity of 40% solution, 25% solution is added to give 35% solution.
w1/w2 = (A2 - Aavg)/(Aavg - A1) = (40 - 35)/(35 - 25) = 1/2
So quantity of 40% sol:25% solution = 2:1
This means the initial total solution was 3 and the fraction of 25% now in the mixture is 1. Therefore, 1/3 of the 40% solution was removed and replaced with 25% solution.

For explanation of the formula, see:
http://www.veritasprep.com/blog/2011/03 ... -averages/
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Senior Manager
Joined: 05 May 2003
Posts: 412
Location: Aus

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25 Dec 2003, 14:07
4
5
I find it difficult to explain it in words. So, I am pasting the way i did it.
Attachments

mixture problem.JPG [ 26.98 KiB | Viewed 12865 times ]

##### General Discussion
Director
Joined: 14 Oct 2003
Posts: 567
Location: On Vacation at My Crawford, Texas Ranch

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Updated on: 25 Dec 2003, 16:04
1
Ok Shabang, I'll try to explain this to you since it appears most people are away celebrating x-mas. Studying for the GMAT is how I'm celebrating X-mas this year.

I would pick numbers here and scan the answer choices (also think logically - the difference in the percentage of the solution declines by only 5% when added with the diluted solution - thus I would get rid of answer choices c,d,e - so I'm left with a and b) I chose b off the bat:

Pick 60 (ml, oz, whatever) as the total mixture - it works well with 3, 4, and 5.

You have a mixture that is 40% solution: 2:5=x:60 thus x = 24 solution : 60 total mixture

Using answer choice B 1/3 - plug it in. 1/3 of 60 is 20 so you're left with 40 oz of the solution. Thus the new solution is 2:5=x:40 x=16 solution: 40 total mixture. You're adding 20 oz of a diluted mixture. thus 1/4 = x/20 = 5 solution: 20 total mixture. Add them together you have: 21 solution : 60 total mixture or 21/60 = 35%.

I'm a little buzzed - I hoep ti amkes sense.

Originally posted by Titleist on 25 Dec 2003, 13:51.
Last edited by Titleist on 25 Dec 2003, 16:04, edited 1 time in total.
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Joined: 15 Dec 2003
Posts: 4153

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25 Dec 2003, 14:43
5
2
Indeed, not easy to explain with words. My explanation is:

Let's say that the total original mixture A is 100ml

The original mixture A thus has 40ml of alcohol out of 100ml of solution
You want to replace some of that original mixture A with another mixture B that contains 25ml of alcohol per 100ml. Thus, the difference between 40ml and 25ml is 15ml per 100ml of mixture. This means that everytime you replace 100ml of the original mixture A by 100ml of mixture B, the original alcohol concentration will decrease by 15%. The question says that the new mixture, let's call it C, must be 35% alcohol, a decrease of only 5%. Therefore, 5 out of 15 is 1/3 and B is the answer. Was that clear?[/b]
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Joined: 04 Dec 2003
Posts: 4
Location: US

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26 Dec 2003, 11:43
8
Yet another way:

Initial solution = x
concentration of solvent = .4x

Lets remove 'y' from the total solution
Solvent in the removed solution = .4y

We add back 'y' into the solution
Solvent in the added solution = .25y
___________________________________________________
Total solution = x-y+y = x
Solvent = .4x - .4y + .25y = .4x - .15y

Now,
.4x - .15y = .35x (new concentration)

Solve for y = 1/3 of x.
Senior Manager
Joined: 22 May 2003
Posts: 318
Location: Uruguay

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26 Dec 2003, 12:05
HereтАЩs my solution:

Original quantity = A
Substituted quantity = B

Then:

(A*0.4 + 0.25*B тАУ 0.4*B ) / A = 0.35

0.4 + (B/A)*(-0.15)=0.35

B/A=-0.05/-0.15=1/3
Senior Manager
Joined: 11 Nov 2003
Posts: 346
Location: Illinois

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31 Dec 2003, 08:21
3
1
In this kinds of problems, we should always try to apply the concept of weighted average.

(strength of one solution) (quantity of that solution) + (strength of another solution) (quantity of that solution) = (strength of resultant solution) (quantity of the resultant solution)

(0.40) (1-q) + (0.25)q = (0.35) (1)

Solving for q = 1/3
SVP
Joined: 30 Oct 2003
Posts: 1731
Location: NewJersey USA

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10 Jan 2004, 17:53
This is how I did it. But it took some time for me to come up with a solution.

I like beer so I will go with this example.
The beer contained 40% alcohol 60% water. from this x amount was taken out. This x amount will carry same amount of alcohol with it so we have

0.4a + 0.6w - ( 0.4ax + 0.6wx )

then we add same x with 25% alcohol
so we have

0.4a+0.6w - ( 0.4ax + 0.6wx ) + ( 0.25ax + 0.75 wx )
= 0.4a+0.6w-(0.15ax - 0.15wx )
this equals beer with 35% alcohol

0.4a+0.6w-(0.15ax-0.15wx) = 0.35a+0.65w

0.15ax-0.15wx = 0.05a-0.05w
so
x = 0.05(a-w) / 0.15(a-w) = 5/15 = 1/3
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Re: Mixture problem  [#permalink]

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08 May 2009, 10:41
2
gmatprep09 wrote:
A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?

(A) 1/4

(B) 1/3

(C) 1/2

(D) 2/3

(E) 3/4

oringal quantity of solution=1
solution replaced = x

0.4 *(1-x)+0.25x= 0.35 *1

0.05= 0.15 x--> x= 1/3
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Re: Mixture problem  [#permalink]

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10 May 2009, 03:29
Can u please the below eqn ?

i belive here 1-x is the remaining soln. Now can you why are we taking 40 % of 1-x. I do not get it. Appreciate ur help.

0.4 *(1-x)+0.25x= 0.35 *1
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Joined: 06 Apr 2009
Posts: 2
Re: Mixture problem  [#permalink]

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19 May 2009, 23:23
I back solved it:
Since it deals with percent, lets take 100 as the base.

When 1/4 - total mixrure is 40 + 25*4 / 500 = 140/500 ; this is not eq 35.
When 1/3 - total mixture is 40 + 25*3/ 400 = 115/400 = 35% - this is the ans.
When 1/2 - total mixture is 40 + 20*2/ 300 = 80/300 ; not eq 35%
Similarly for D & E.

Thus B is correct. IMO
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Re: Mixture problem  [#permalink]

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20 May 2009, 02:13
tkarthi4u wrote:
Can u please the below eqn ?

i belive here 1-x is the remaining soln. Now can you why are we taking 40 % of 1-x. I do not get it. Appreciate ur help.

0.4 *(1-x)+0.25x= 0.35 *1

Let me try out, the logic here is

You removed x quantity of 40% concentration solution from 1 and added same x quantity of 25% concentration solution, which total to original quantity 1 of solution with 35% concentration. Hence

Remaining quantity of 40% solution + added quantity of 25% solution = Total solution with 35% concentration.
0.4(1-x) + 0.25x = .35
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Joined: 20 Dec 2010
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Re: Mixture problem  [#permalink]

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21 Jul 2011, 20:09
2
gmatprep09 wrote:
A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?

(A) 1/4

(B) 1/3

(C) 1/2

(D) 2/3

(E) 3/4

Let actual solution be "T"
Replaced solution be "R"

(T-R)-> 40%
R->25%
Average->35%

(T-R)0.4+R*0.25=0.35T
0.4T-0.4R+0.25R=0.35T
0.05T=0.15R
R/T=0.05/0.15=1/3

Ans: "B"

OR using other form of Weighted Average:

$$\frac{T-R}{R}=\frac{35-25}{40-35}$$

$$\frac{T-R}{R}=\frac{10}{5}=2$$

$$\frac{T}{R}-1=\frac{10}{5}=2$$

$$\frac{T}{R}=3$$

Invertendo:
$$\frac{R}{T}=\frac{1}{3}$$
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Re: A certain quantity of 40% solution is replaced with 25% solu  [#permalink]

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20 Jul 2015, 20:52
3
VeritasPrepKarishma wrote:
gmatprep09 wrote:
A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?

(A) 1/4

(B) 1/3

(C) 1/2

(D) 2/3

(E) 3/4

Or use our standard mixtures formula for replacements too. In a certain quantity of 40% solution, 25% solution is added to give 35% solution.
w1/w2 = (A2 - Aavg)/(Aavg - A1) = (40 - 35)/(35 - 25) = 1/2
So quantity of 40% sol:25% solution = 2:1
This means the initial total solution was 3 and the fraction of 25% now in the mixture is 1. Therefore, 1/3 of the 40% solution was removed and replaced with 25% solution.

For explanation of the formula, see:
http://www.veritasprep.com/blog/2011/03 ... -averages/

Responding to a pm:

Quote:
However I do not really understand the last part where you say that 1/3 of the original solution was replaced. Do you get to 3 by adding 2 and 1?

And why is 40% 1/3 of the original solution?

I also tried to solve it using smart numbers but did not work...

From your calculations, you get that when you mix 2 parts of 40% solution with 1 part of 25% solution, you get resultant 35% solution.

Initially, you had only 40% solution. You removed say x of it and put x of 25% solution in its place. This x was 1 part and you had 2 parts of 40% solution left. So initially, you must have had 3 parts of 40% solution. You then must have removed 1 part and replaced it with 25% solution. That is how you would have ended up mixing 2 parts of 40% with 1 part of 25% to get 35% solution.

So we must have replaced 1 part out of 3 (i.e. 1/3) of the original 40% solution.
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A certain quantity of 40% solution is replaced with 25% solu  [#permalink]

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06 Sep 2015, 16:22
1
let x=fraction of solution replaced
.4-.4x+.25x=.35
x=1/3
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Posts: 7
Re: A certain quantity of 40% solution is replaced with 25% solu  [#permalink]

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17 Nov 2015, 09:59
Geethu wrote:
I find it difficult to explain it in words. So, I am pasting the way i did it.

Geethu - how did u convert ratio 2:1 to 1/3..?
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Re: A certain quantity of 40% solution is replaced with 25% solu  [#permalink]

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19 Nov 2015, 13:54
I did it like this:

40-----35-----25
----5------10-----

5+10=15

10/15 was taken out.
5/15 = 1/3 was replaced. Answer B
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Re: A certain quantity of 40% solution is replaced with 25% solu  [#permalink]

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10 Jun 2017, 01:12
shubhangi wrote:
A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?

(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4

1. (Quantity of 40%solution- quantity removed) *(concentration of the solution) + (Quantity of 25% solution added) *(concentration of the solution)/ (Initial Quantity) = 35/100
2. Let x be the initial quantity of 40% solution. Let y of it be removed and y of 25% solution added.
3. (x -y)*0.4 + y*0.25/x = 0.35
4. y/x=1/3 or in other words 1/3 of the solution was replaced.
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Re: A certain quantity of 40% solution is replaced with 25% solu  [#permalink]

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15 Apr 2018, 10:55
+1 for option B. Use the concept of weighted averages.
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Re: A certain quantity of 40% solution is replaced with 25% solu   [#permalink] 15 Apr 2018, 10:55
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