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A scientist has 400 units of a 6% phosphoric acid solution,

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A scientist has 400 units of a 6% phosphoric acid solution,

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A scientist has 400 units of a 6% phosphoric acid solution, and an unlimited supply of 12% phosphoric acid solution. How many units of the latter must she add to the former to produce a 10% phosphoric acid solution?

A. 200
B. 400
C. 500
D. 600
E. 800

The OA is E

Source: Magoosh

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Hi All,

While an Algebra approach (using the "weighted average" formula) would work nicely on this prompt, you can also answer it rather quickly by TESTing THE ANSWERS and using a bit of logic. Here, we're going to mix 400 ounces of a 6% acid solution with X ounces of a 12% acid solution to form a 10% acid solution. We're asked for the value of X. The answers are all nice, round numbers, so we can take advantage of them....

Let's start with Answer B....

IF.....
X = 400 ounces
Then we'd have the same amount of each solution: 400 ounces of 6% and 400 ounces of 12% -->
this would produce a (6%+12%)/2 = 9% mixture
This is TOO SMALL. X must be BIGGER. Eliminate Answers A and B.

Now, let's TEST Answer D...

IF....
X = 600 ounces
Then with 400 ounces of 6% and 600 ounces of 12%, we'd have...

[(400)(.06) + (600)(.12)]/(400 + 600) =

(24 + 72)/1000 =
96/1000 = 9.6%,
This is also TOO SMALL. X must be BIGGER. Eliminate C and D.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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swerve wrote:
A scientist has 400 units of a 6% phosphoric acid solution, and an unlimited supply of 12% phosphoric acid solution. How many units of the latter must she add to the former to produce a 10% phosphoric acid solution?

A. 200
B. 400
C. 500
D. 600
E. 800

The OA is E

Source: Magoosh
We will add 400 units of 6% solution to x units of 12% solution to obtain a total of (400 + x) units of 10% solution. We can create the following equation:

0.06(400) + 0.12x = 0.1(400 + x)

24 + 0.12x = 40 + 0.1x

0.02x = 16

x = 16/0.02 = 800

Answer: E

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Scott Woodbury-Stewart Founder and CEO

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swerve wrote:
A scientist has 400 units of a 6% phosphoric acid solution, and an unlimited supply of 12% phosphoric acid solution. How many units of the latter must she add to the former to produce a 10% phosphoric acid solution?

A. 200
B. 400
C. 500
D. 600
E. 800

The OA is E

Source: Magoosh
We can solve this question with the weighted averages formula:

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Let x = the number of units of 12% phosphoric acid solution needed
Since we're adding x units to 400 units, the volume of the RESULTING mixture = 400 + X

A scientist has 400 units of a 6% phosphoric acid solution. . .
So, the PROPORTION of 6% solution in the RESULTING mixture = 400/(400 + x)

. . . and an unlimited supply of 12% phosphoric acid solution
We are adding x units of 12% solution
So, the PROPORTION of 12% solution in the RESULTING mixture = x/(400 + x)

How many units of the latter must she add to the former to produce a 10% phosphoric acid solution?
We want the resulting mixture to contain 10% phosphoric acid

Applying the formula, we can write: 10 = [400/(400 + x)][6] + [x/(400 + x)][12]
Multiply both sides by (400 + x) to get: 10(400 + x) = 2400 + 12x
Expand left side to get: 4000 + 10x = 2400 + 12x
Solve: x = 800

Answer: E

Cheers,
Brent

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Brent Hanneson – Creator of GMATPrepNow.com
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