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# Solution A is 20% salt and Solution B is 80% salt. If you

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Senior Manager
Joined: 11 May 2004
Posts: 420
Location: New York
Solution A is 20% salt and Solution B is 80% salt. If you  [#permalink]

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Updated on: 08 Sep 2013, 07:47
7
30
00:00

Difficulty:

35% (medium)

Question Stats:

74% (02:06) correct 26% (02:48) wrong based on 566 sessions

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Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?

A. 6:4
B. 6:14
C. 4:4
D. 4:6
E. 3:7

Originally posted by desiguy on 08 Nov 2005, 19:14.
Last edited by Bunuel on 08 Sep 2013, 07:47, edited 1 time in total.
Edited the question.
Veritas Prep GMAT Instructor
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05 Jul 2011, 09:47
7
6
prashantbacchewar wrote:
Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?
6:4
6:14
4:4
4:6
3:7

What is faster way to solve this

Forget the volumes for the time being.
You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use
w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 = (80 - 50)/(50 - 20) = 1/1
So the volume of the two solutions will be equal. Answer has to be 4:4.

For details of this formula, see
http://www.veritasprep.com/blog/2011/03 ... -averages/
http://www.veritasprep.com/blog/2011/04 ... ge-brutes/
http://www.veritasprep.com/blog/2011/04 ... -mixtures/
_________________
Karishma
Veritas Prep GMAT Instructor

Current Student
Joined: 26 May 2005
Posts: 487

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06 Jul 2011, 05:19
2
4
prashantbacchewar wrote:
Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?
6:4
6:14
4:4
4:6
3:7

What is faster way to solve this

Fastest way to solve this Alligations.
You can solve any Alligation using this method.
Use the diagram,
30:30 = 1:1
hence its C
Attachments

Allegations.jpg [ 17.06 KiB | Viewed 10171 times ]

##### General Discussion
SVP
Joined: 05 Apr 2005
Posts: 1551

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08 Nov 2005, 21:13
1
1
the ACs are quite strange.

weingt of a = x
xa+b(1-x) = 0.5(a+b)
xa - 0.5a = 0.5b - b(1-x)
a(x-0.5) = b (x-0.5)
a = b =25.

total = a+b = 25+25 = 50
salt = 50% 0f 50 = 25%
salt from a = 20% of 25 = 5
salt from b = 80% of 25 = 20
so total = 25 which is 50% of 50.

so it should be 4:4.
VP
Joined: 22 Aug 2005
Posts: 1032
Location: CA

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09 Nov 2005, 12:13
3
let:
x = ounces taken from solution A (20% salt)
y = ounces taken from solution B (80% salt)

to prepare 50 ounce 50% salt.

first equation is simple:
x + y = 50

to get another equation so as to be able to solve, compute salt contents.

20% of x + 80% of y = 50% of 50 or
x/5 + 4/5 * y = 25 or
x+4y = 125

solve two equations to get:
x = 25
y = 25

so solutions has to mix in
1:1 oops 4:4
Manager
Joined: 23 Jan 2011
Posts: 107

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05 Jul 2011, 07:00
prashantbacchewar wrote:
Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?
6:4
6:14
4:4
4:6
3:7

What is faster way to solve this

I am not good at PS but here is my take on this

6+4/5*y*60 = 1/2 (30 +y*60)
Solve:
12+96y=30+60y
36 y = 18
y = 1/2

So y of 60 = 30
Ratio is 1:1 which is 4:4.
C
Manager
Joined: 11 Apr 2011
Posts: 79

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05 Jul 2011, 08:12
2
1
let in the final solution : contribution of A = x. B's = 50 -x.
0.2x + 0.8(50-x) = 50*0.5
solving x =25 = A's, B's = 25.

hence, 4:4, C
Intern
Joined: 11 Jan 2013
Posts: 15
Location: United States
Re: Solution A is 20% salt and Solution B is 80% salt. If you  [#permalink]

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08 Sep 2013, 07:32
If you have to look for the weights of different ingredients to come up with a target mix, there is an easy formula that you can apply:

W = weight
C = concentration

Wa/Wb = (Cb - Cavg)/(Cavg - Ca)

=> Wa/Wb = (0.8-0.5)/(0.5-0.2) = 0.3/0.3 = 1/1

=> The only multiple of 1/1 in the answer choices is 4/4
SVP
Joined: 06 Sep 2013
Posts: 1651
Concentration: Finance
Re: Solution A is 20% salt and Solution B is 80% salt. If you  [#permalink]

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16 Dec 2013, 06:57
desiguy wrote:
Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?

A. 6:4
B. 6:14
C. 4:4
D. 4:6
E. 3:7

Applying differentials. Forget the volumes

-3x+3y=0
3x=3y
x=y

So they have to be the same weight both

So 1:1 = 4:4

Cheers!
J

Let the Kudos rain begin!!
Manager
Joined: 27 May 2014
Posts: 79
Re: Solution A is 20% salt and Solution B is 80% salt. If you  [#permalink]

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21 Dec 2014, 15:55
How come everyone is ignoring the announces. If I take 50% of the 30g and 50% of the 60g I only have 45 g not 50.
Director
Joined: 23 Jan 2013
Posts: 546
Schools: Cambridge'16
Re: Solution A is 20% salt and Solution B is 80% salt. If you  [#permalink]

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22 Dec 2014, 00:17
1
1
weighted average

20x+80y/x+y=50

20x+80y=50x+50y

30y=30x

y/x=1/1 or 4/4

C
Intern
Joined: 08 Dec 2013
Posts: 32
Re: Solution A is 20% salt and Solution B is 80% salt. If you  [#permalink]

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01 Mar 2015, 04:30
hi karishma
why have you considered "percentages" in the scale method...can`t we use the weights of the solutions in the formula as in
w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 = (60 - 50)/(50 - 30) = 1/2

thanks a lot.
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Solution A is 20% salt and Solution B is 80% salt. If you  [#permalink]

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09 Mar 2015, 16:30
VeritasPrepKarishma wrote:
prashantbacchewar wrote:
Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?
6:4
6:14
4:4
4:6
3:7

What is faster way to solve this

Forget the volumes for the time being.
You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use
w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 = (80 - 50)/(50 - 20) = 1/1
So the volume of the two solutions will be equal. Answer has to be 4:4.

For details of this formula, see
http://www.veritasprep.com/blog/2011/03 ... -averages/
http://www.veritasprep.com/blog/2011/04 ... ge-brutes/
http://www.veritasprep.com/blog/2011/04 ... -mixtures/

Hi Karishma,

My question is also why are we ignoring the quantities.

The way I started thinking about it was like this:

(0.20) * (30) * (x) + (0.80) * (60) * (y) = (0.50) * (50) * (x+y)

However, this ends up in y/x = 9/23.

I then noticed that we are ignoring the actual quantities. Why is this so? Are we ignoring them because they anyway have to do with salt?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9331
Location: Pune, India
Re: Solution A is 20% salt and Solution B is 80% salt. If you  [#permalink]

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21 Apr 2016, 01:21
1
VeritasPrepKarishma wrote:
prashantbacchewar wrote:
Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?
6:4
6:14
4:4
4:6
3:7

What is faster way to solve this

Forget the volumes for the time being.
You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use
w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 = (80 - 50)/(50 - 20) = 1/1
So the volume of the two solutions will be equal. Answer has to be 4:4.

For details of this formula, see
http://www.veritasprep.com/blog/2011/03 ... -averages/
http://www.veritasprep.com/blog/2011/04 ... ge-brutes/
http://www.veritasprep.com/blog/2011/04 ... -mixtures/

Responding to a pm:
Quote:
But as per question asked ,why we cannot take respective weights of salt( i.e if 30 ounces of sol.A has 20% salt) ,then take salt weight as 6 ounces(20% of 30ounces)
then isnt is our question becomes "how much 6 ounces and 8 ounces will be added to get 25 ounces of salt"???

w1/w2 = (25-6) / (48 - 25)

You are not required to mix 30 ounces of solution A with some amount of solution B. You are not given that you have to use the entire 30 ounces of solution A. In fact, the volumes of the solution are not required at all since the question asks for the ratio in which A and B should be mixed. We know the concentration of salt in A, concentration of salt in B and average required concentration. This will simply give us the ratio in which the two solutions should be mixed (using the formula).
We find that both solutions should be mixed in equal quantities (ratio of 1:1 or 2:2 or 3:3 or 4:4 etc) so to make 50 ounces of mix, we will put 25 ounces of each solution.
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Karishma
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Re: Solution A is 20% salt and Solution B is 80% salt. If you  [#permalink]

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23 Apr 2016, 03:25
10 sec solution:
always compare the simple average to the weighted average first. Here simple average is 20+80 divided by 2 = 50.
And thats our answer. we have taken 50% of A and 50% of be to create the new solution.
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Posts: 1196
Re: Solution A is 20% salt and Solution B is 80% salt. If you  [#permalink]

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11 Aug 2017, 15:34
desiguy wrote:
Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?

A. 6:4
B. 6:14
C. 4:4
D. 4:6
E. 3:7

.2A+.8B=.5(A+B)
A/B=1
4:4
C
Intern
Joined: 06 Jul 2017
Posts: 7
Re: Solution A is 20% salt and Solution B is 80% salt. If you  [#permalink]

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11 Aug 2017, 18:00
desiguy wrote:
Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?

A. 6:4
B. 6:14
C. 4:4
D. 4:6
E. 3:7
Take the middle 25 ounces each, luckily it has 50% salt, the average. then it should be k:k for any integer k.

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Re: Solution A is 20% salt and Solution B is 80% salt. If you  [#permalink]

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04 Feb 2019, 18:38
1
desiguy wrote:
Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?

A. 6:4
B. 6:14
C. 4:4
D. 4:6
E. 3:7

We see that we need 25 ounces of salt. We can go through the choices:

A) 6:4

6x + 4x = 50

10x = 50

x = 5

So we have 6(5) = 30 ounces of A and 4(5) = 20 ounces of B. Does this produce 25 ounces of salt?

30 x 0.2 + 20 x 0.8 = 6 + 16 = 22 → No

B) 6:14

6x + 14x = 50

20x = 50

x = 2.5

So we have 6(2.5) = 15 ounces of A and 14(2.5) = 35 ounces of B. Does this produce 25 ounces of salt?

15 x 0.2 + 35 x 0.8 = 3 + 28 = 31 → No

C) 4:4

This means we have 25 ounces of A and 25 ounces of B. Does this produce 25 ounces of salt?

25 x 0.2 + 25 x 0.8 = 5 + 20 = 25 → Yes!

Alternate Solution:

Let A be the amount of Solution A and B be the amount of Solution B that produces a 50% salt solution when mixed. Since we want 50 ounces of 50% salt solution, there must be 50 x 0.5 = 25 ounces of salt in our solution.

We have the following:

A + B = 50

0.2A + 0.8B = 25

Let’s rewrite these two equations:

2A + 2B = 100

2A + 8B = 250

Let’s subtract the first equation from the second:

6B = 150

B = 25

Since A + B = 50, A = 25 also. Since there are A = 25 ounces of solution A and B = 25 ounces of solution B in our mixture, we need to mix A and B in the ratio of 1:1; or equivalently, 4:4.

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Re: Solution A is 20% salt and Solution B is 80% salt. If you   [#permalink] 04 Feb 2019, 18:38
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