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# How many gallons of water must be mixed with 1 gallon of a

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Intern
Joined: 27 Feb 2012
Posts: 37
How many gallons of water must be mixed with 1 gallon of a  [#permalink]

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Updated on: 29 Mar 2012, 22:50
2
4
00:00

Difficulty:

(N/A)

Question Stats:

73% (01:25) correct 27% (01:36) wrong based on 110 sessions

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The below questions were taken from two paper tests, i know the answer however wanted to see if anyone could solve based on the attached "Mixture Problems Made Easy"

The attached works great for mixture problems

How many gallons of water must be mixed with 1 gallon of a 15% salt solution To obtain a 10% salt solution

A. 5
B. 67
C. 1.00
D. 1.50
E. 2.00

OA: A

One fourth of a solution that was 10% sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?

A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%

OA: A

for this problem based on the attached method, which this problem and the one below appear,

i understand how to get (x-16):6
but how do i get to 3:1 (since 1/4th was taken out) how is this calculated?
then solving for x give me 34 but how do i solve for x?

OPEN DISCUSSION OF THE FIRST QUESTION IS HERE: https://gmatclub.com/forum/how-many-gal ... 02888.html

OPEN DISCUSSION OF THE SECOND QUESTION IS HERE: https://gmatclub.com/forum/one-fourth-o ... 49134.html

Attachments

Mixture Problems Made Easy.pdf [53.94 KiB]

Originally posted by jsphcal on 23 Mar 2012, 16:04.
Last edited by jsphcal on 29 Mar 2012, 22:50, edited 3 times in total.
Intern
Joined: 27 Feb 2012
Posts: 37
Re: How many gallons of water must be mixed with 1 gallon of a  [#permalink]

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Updated on: 29 Mar 2012, 22:58
also if one could elaborate on both questions and answers based on attachments,
would be greatly appreciated since the attached doesnt provide an answer for the

15% salt added to 5 liters of solution 8% salt, resulting in 10% salt solution

Originally posted by jsphcal on 23 Mar 2012, 19:09.
Last edited by jsphcal on 29 Mar 2012, 22:58, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 52232
Re: How many gallons of water must be mixed with 1 gallon of a  [#permalink]

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24 Mar 2012, 01:42
How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution
A. 5
B. 67
C. 1.00
D. 1.50
E. 2.00

Since we are adding pure water then the amount of salt in both solutions will be the same, so 0.15*1=0.1*(1+x) --> x=0.5.

One fourth of a solution that was 10% sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?
A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%

This is a weighted average question.

Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.1+1/4*x=1*0.16 --> x=0.34. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.1+25*x=100*0.16 --> x=0.34.

P.S. Please post one question per topic.
_________________
Manager
Joined: 28 Jul 2011
Posts: 181
Re: How many gallons of water must be mixed with 1 gallon of a  [#permalink]

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25 Mar 2012, 10:39
Ans : A

Total Solution = x

Sugar contain = 10% (x)

1/4 (x) is replaced with new solution with y% sugar

y% [(1/4)(x)]

New Solution contain 16% sugar 16%(x)

Remaining solution + replaced solution = new sugar
[ 10/100[(3/4)(x)] ] + y% [(1/4)(x)] = [16/100](x)
3/40(x) + xy/400 = 16x/100
xy/400 = 16x/100 -3x/40
xy/400 = 340x/4000
y = 34%
Intern
Joined: 27 Feb 2012
Posts: 37
Re: How many gallons of water must be mixed with 1 gallon of a  [#permalink]

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26 Mar 2012, 07:40
Bunuel wrote:
How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution
A. 5
B. 67
C. 1.00
D. 1.50
E. 2.00

Since we are adding pure water then the amount of salt in both solutions will be the same, so 0.15*1=0.1*(1+x) --> x=0.5.

One fourth of a solution that was 10% sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?
A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%

This is a weighted average question.

Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.1+1/4*x=1*0.16 --> x=0.34. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.1+25*x=100*0.16 --> x=0.34.

P.S. Please post one question per topic.

Bunuel,

and in the future i will only post one question at a time, thank you.
Intern
Joined: 12 Mar 2012
Posts: 10
Re: How many gallons of water must be mixed with 1 gallon of a  [#permalink]

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05 Apr 2012, 06:07
Bunuel wrote:
How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution
A. 5
B. 67
C. 1.00
D. 1.50
E. 2.00

Since we are adding pure water then the amount of salt in both solutions will be the same, so 0.15*1=0.1*(1+x) --> x=0.5.

One fourth of a solution that was 10% sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?
A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%

This is a weighted average question.

Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.1+1/4*x=1*0.16 --> x=0.34. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.1+25*x=100*0.16 --> x=0.34.

P.S. Please post one question per topic.

Dear Bunnel,

Is my approach right to solve such problems??

I use weighted average formula-

V1/V2= (C2-C3)/( C3-C1)

1/X= (0-10)/(10-15)

1/x=2
X=0.5

Math Expert
Joined: 02 Sep 2009
Posts: 52232
Re: How many gallons of water must be mixed with 1 gallon of a  [#permalink]

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08 Jan 2018, 22:16
OPEN DISCUSSION OF THE FIRST QUESTION IS HERE: https://gmatclub.com/forum/how-many-gal ... 02888.html

OPEN DISCUSSION OF THE SECOND QUESTION IS HERE: https://gmatclub.com/forum/one-fourth-o ... 49134.html

_________________
Re: How many gallons of water must be mixed with 1 gallon of a &nbs [#permalink] 08 Jan 2018, 22:16
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