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# M31-02

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Math Expert
Joined: 02 Sep 2009
Posts: 49490

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07 Jun 2015, 08:29
00:00

Difficulty:

35% (medium)

Question Stats:

78% (01:10) correct 23% (01:39) wrong based on 40 sessions

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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%

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Math Expert
Joined: 02 Sep 2009
Posts: 49490

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07 Jun 2015, 08:29
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.

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08 Jun 2015, 00:22
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)
Manager
Joined: 26 Feb 2018
Posts: 79
Location: United Arab Emirates
GMAT 1: 710 Q47 V41
GMAT 2: 770 Q49 V47

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10 Mar 2018, 14:49
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
Manager
Joined: 26 Feb 2018
Posts: 53
Location: India
GMAT 1: 560 Q41 V27
WE: Web Development (Computer Software)

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19 Jun 2018, 14:36
I think this is a high-quality question and I agree with explanation.
Re M31-02 &nbs [#permalink] 19 Jun 2018, 14:36
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# M31-02

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