Problem Solving

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

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

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