M31-02

Question

Substance X constitutes 0.8 percent of the weight of Solution A and 1.8 percent of the weight of Solution B. When 300 grams of Solution A are combined with 700 grams of Solution B, what percentage of the weight does Substance X represent in the resulting mixture?

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

Show Answer

Official Answer

A

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

Bunuel · Answer

Official Solution:

Substance X constitutes 0.8 percent of the weight of Solution A and 1.8 percent of the weight of Solution B. When 300 grams of Solution A are combined with 700 grams of Solution B, what percentage of the weight does Substance X represent in the resulting mixture?

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

Show Answer

Official Answer

A

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

Algebraic solution: 
 
Substance X constitutes 0.8 percent of the weight of Solution A and 1.8 percent of the weight of Solution B. Thus, 300 grams of Solution A contains 0.8% of 300 grams (0.008*300 = 2.4 grams) of Substance X, while 700 grams of Solution B contains 1.8% of 700 grams (0.018*700 = 12.6 grams) of Substance X. When the two solutions are combined, the resulting mixture weighs 1000 grams and contains 2.4 + 12.6 = 15 grams of Substance X. This means that Substance X represents 1.5% of the weight of the resulting solution (15/1000*100 = 1.5%).
 
 Shortcut solution: 
 
Substance X constitutes 0.8 percent of the weight of Solution A and 1.8 percent of the weight of Solution B. The percentage of Substance X in the resulting mixture (Solution A + Solution B) must lie between 0.8 percent and 1.8 percent. Only 1.5% fits within this range.

Answer: A

vishwaprakash · Answer

Total volume of new solution = 300 + 700 = 1000 gms.

Liquid X in new solution = Liquid X from solution A + Liquid X from solution B
 = 0.8 % 300 + 1.8 % 700 = 2.4 + 12.6 = 15 gms

percent of the weight of the resulting solution = 15 gms / 1000 = 1.5%

Option A

Note : Usually we commit mistake while considering the total volume, Here total volume is 1000 gms since it is addition of solution A (300 gms) and solution B ( 700 gms)

tinyinthedesert · Answer

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

PrayasT · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

M31-02

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards