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The 20% acid liquid solution is produced by adding a gallons of 10% ac
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MathRevolution
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The 20% acid liquid solution is produced by adding a gallons of 10% ac [#permalink] New post  26 Feb 2018, 01:36
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[GMAT math practice question]

The 20% acid liquid solution is produced by adding a gallons of 10% acid liquid solution to b gallons of 50% acid liquid solution. To get 10 gallons of 20% acid liquid solution, how many gallons of 50% acid liquid solution are needed?

A. 1
B. 1.5
C. 2
D. 2.5
E. 3
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Re: The 20% acid liquid solution is produced by adding a gallons of 10% ac [#permalink] New post  26 Feb 2018, 02:03
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For most weighted average questions, there are usually 3 key values: A, B & C

A = Highest Value
B = Desired Average
C = Lowest Value

we can use the following formula to get the ratio of "pull":

\(\frac{A - B}{B - C}\)

For the question,

A = 50
B = 20
C = 10

\(\frac{A - B}{B - C} = \frac{50-20}{20-10} = \frac{30}{10} = \frac{3}{1}\)

Since B is closer to C than A, the ratio of A:C is 1:3

Gallons of A required = \(\frac{10}{4}*1 = 2.5\)

Ans: D
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Re: The 20% acid liquid solution is produced by adding a gallons of 10% ac [#permalink] New post  26 Feb 2018, 08:55
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MathRevolution wrote:
[GMAT math practice question]

The 20% acid liquid solution is produced by adding a gallons of 10% acid liquid solution to b gallons of 50% acid liquid solution. To get 10 gallons of 20% acid liquid solution, how many gallons of 50% acid liquid solution are needed?

A. 1
B. 1.5
C. 2
D. 2.5
E. 3


Given \(0.1a+0.5b=0.2(a+b)\). Resulting mixture's volume will be summation of volumes of individual contents

\(=>3b=a => a:b=3:1\)

New mixture has volume of 10 gallons, Hence \(b= \frac{1}{(1+3)}*10=2.5\)

Option D
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Re: The 20% acid liquid solution is produced by adding a gallons of 10% ac [#permalink] New post  26 Feb 2018, 17:08
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MathRevolution wrote:
[GMAT math practice question]

The 20% acid liquid solution is produced by adding a gallons of 10% acid liquid solution to b gallons of 50% acid liquid solution. To get 10 gallons of 20% acid liquid solution, how many gallons of 50% acid liquid solution are needed?

A. 1
B. 1.5
C. 2
D. 2.5
E. 3


.1(10-b)+.5b=.2*10
b=2.5 gallons
D
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MathRevolution
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Re: The 20% acid liquid solution is produced by adding a gallons of 10% ac [#permalink] New post  28 Feb 2018, 00:29
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=>

We have \(a + b = 10.\)

\(\frac{(0.1a + 0.5b)}{10} = 0.2\)
\(⇔ 0.1a + 0.5b = 2\)
\(⇔ 0.1(10-b) + 0.5b = 2\)
\(⇔ 1 – 0.1b + 0.5b = 2\)
\(⇔ 0.4b = 1\)
\(⇔ b = 2.5\)

Therefore, D is the answer.

Answer: D
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The 20% acid liquid solution is produced by adding a gallons of 10% ac [#permalink] New post  28 Feb 2018, 09:59
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MathRevolution wrote:
[GMAT math practice question]

The 20% acid liquid solution is produced by adding a gallons of 10% acid liquid solution to b gallons of 50% acid liquid solution. To get 10 gallons of 20% acid liquid solution, how many gallons of 50% acid liquid solution are needed?

A. 1
B. 1.5
C. 2
D. 2.5
E. 3

To find the amount of one solution in a resultant mixture, I use this weighted average formula:
\((Concen_{A})(Vol_{A}) + (Concen_{B})(Vol_{B}) = (Concen_{A+B})(Vol_{A+B})\)

Let A = volume of the solution with 10% acid
Let B = volume of the solution with 50% acid

A + B = resultant mixture
A + B = 10 (gallons in volume)
A = (10 - B)
Desired concentration of resultant solution: 20%

1) the equation without substitution
\((.10)(A) + (.50)(B) = .20(A + B)\)

2) Substitute (10-B) for A, and 10 for (A+B):

\(.10(10-B) + .50B = .20(10)\)
\(1 - .10B + .50B = 2\)
\(.40B = 1\)
\(B =\frac{1}{.4}=\frac{10}{4}=2.5\)

Answer D
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