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Source: Official Guide Revised GRE 1st Ed. Part 6; Set 2; #9


By weight, liquid A makes up 8 percent

By weight, liquid A makes up 8 percent of solution R and 18 percent of solution S. If 3 grams of solution R are mixed with 7 grams of solution S, then liquid A accounts for what percent of the weight of the resulting solution? 10%, 13%, 15%, 19%, 26%

3 Explanations


Ramlah Merchant

I didn't quite understand why we did 8% of 3g and 18% of 7g/3+7 here. Could you please explain how you got this formula?

Apr 26, 2017 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Ramlah,

Happy to help :)

The formula is for weighted averages, which we can use to find out the percent of liquid A in the solution. In this question, we're told that Liquid A is 8% R and 18% S (by weight). Then, we're asked to consider a mixture of R and S: 3g R + 7g S.

As I mentioned above, we need to find out how much Liquid A is in this mixture of 3g R and 7g S. First, let's find the amount of liquid A in each of the two solutions:

Solution R: 0.08*3g = 0.24g
Solution S: 0.18*7g = 1.26g

So the total weight of A in the mixture is
0.24 + 1.26 = 1.5g

And the total weight of the entire mixture is
3g R + 7g S = 10g

Therefore the % weight of A in the mixture is

1.5g/10g * 100% = 15%

The formula combines the two steps above into one formula, leading to the same result :)

Hope this helps!

Apr 28, 2017 • Reply

Hi, I also can't understand neither. I know what you mean overall. but at first, to be an your answer,
question should ask
"liquid A was consisted of 8 percent of solution R and 18 percent of solution S"
not "liquid A makes up 8 percent of solution R and 18 percent of solution S"
isn't it?

if they asked to me with first question, I can understand clearly. but if they ask with second question, I just understand like "if A is 100L liquid, 8L of solution R and 18L of solution S is consisted of liquid A"

am I wrong or right?

May 25, 2018 • Reply

David Recine

Actually, if you're going to use any form of the word consists, the proper grammar would be "8 percent of solution R consists of liquid A and 18 percent of solution S consists of liquid A."

"Was consisted" (or "is consisted") is a passive voice form, and as such your re-wording suggests that liquid A used to consist or currently consists of a combination of solution R and solution S.

In short, the original wording, "liquid A makes up..." is the simplest and most straightforward wording. Or at least, it's the simplest and most straightforward he perspective of a native English speaker. You alternative suggested phrases are harder to follow and seem to change the meaning of the original. Careful study of the questions original wording could be helpful here, as similar wording will appear on other mixture problems found on the test.

May 25, 2018 • Reply

8% of 3g 18% of 7g = 0.24+1.26=1.5

Jul 14, 2019 • Reply


That's just about right! We end up with 1.5 grams of liquid A. Since we have 10 grams of total solution, the percentage of liquid A is 1.5/10 = 0.15 = 15%.

Jul 21, 2019 • Reply


Bilal Farooq

What topic would this be categorized as?

Sep 10, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Bilal! This is a percent/fractions/ratio question from the Quant Section :)

Sep 11, 2016 • Reply


Chris Lele

Oct 7, 2012 • Comment

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