Official Solution:

By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 300 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution?

A. 1.5%
B. 1.9%
C. 10%
D. 15%
E. 19%


Algebraic solution:

Liquid X makes up 0.8 percent of the weight of solution A and 1,8 percent of the weight of solution B. Therefore, 300 grams of solution A contain \(\frac{0.8}{100}*300 = 2.4\) grams of liquid X, and 700 grams of solution B contain \(\frac{1.8}{100}*700 = 12.6\) grams of liquid X. When the two solutions are mixed, the resulting solution weighs 1000 grams and contains \(2.4 + 12.6 = 15\) grams of liquid X. This means that liquid X makes up \({15}{1000}*100 = 1.5%\) of the weight of the resulting solution.

Shortcut solution:

Liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. The percent of liquid X in the resulting solution (A + B) must be between 0.8 percent and 1.8 percent. Only A fits.


Answer: A
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I think the answer choices tend too high to make this 700 level question. It is too easy to guess .... we have 300g of 0.8% and 700g - more than double the amount - of 1.8% so we immediately know two things without any calculation

1) new % will be between 0.8 and 1.8
2) new % will be closer to 1.8 than 0.8 as we have more of that solution - more than double in fact (weighted averages)

This means we can immediately bin answers B, C, D and E as they're all too high

I think an actual GMAT question would include some answer options lower than option A. Usually you can't eliminate 4 options so rapidly. GMAT answer selection usually includes some too high, some too low and one or two "trip up" answers