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Re: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent [#permalink]
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Expert Reply
Hi All,

This question has a built-in conceptual "shortcut" that can help you to answer it rather quickly....

Since liquid X makes up .8 percent of one solution and 1.8 percent of another solution, mixing the 2 solutions (regardless of how much of each you mix) will end with a total percent that is BETWEEN .8 percent and 1.8 percent. There's only one answer that fits that range....


Final Answer:

GMAT assassins aren't born, they're made,
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Re: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent [#permalink]
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Liquid X in 300 g solution: 0.8% * 300 = 2.4 g
Liquid X in 700 g solution: 1.8% * 700 = 12.6 g
Total Liquid X = 12.6 +2.4 = 15g
% of weight of liquid X in the resulting solution = \(\frac{(15)}{(300+700)}\) * 100 = 1.5%

Answer: A
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Re: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent [#permalink]
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Solution A (0.8 percent of solution A (300)).

0.8/100 *300 = 2.4.

Solution B (1.8 percent of solution B (700)).

1.8/100 * 700 = 12.6.

Liquid X = Solution A + Solution B = 2.4 + 12.6 =15.

Total weight of X = 300 + 700 = 1000.

Our question is liquid X accounts for what percent of the weight of the resulting solution ?

X /100 * 1000 = 15

X = 15/10 = 1.5

Hence A. 1.5% is the correct Answer
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Re: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent [#permalink]
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Bunuel wrote:
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%

Kudos for a correct solution.


Ans: A

Solution:
lests say
A=100gm then X in it = 0.8gm so when A=300gm, X in it = 2.4gm
B=100gm then X in it = 1.8gm so when B=700gm, X in it = 12.6gm

now total solution= (300+700=1000)gm
total liquid X in the solution is (2.4+12.6=15)gm
percentage= 1.5%
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Re: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent [#permalink]
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Bunuel wrote:
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%

Kudos for a correct solution.


OFFICIAL SOLUTION:

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 0.8/100*300 = 2.4 grams of liquid X, and 700 grams of solution B contain 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.

Answer: A.

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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Re: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent [#permalink]
Bunuel wrote:
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%

Kudos for a correct solution.

Can be done with weighted avg. formula
w1/w2=(a2-avg)/(avg-a1)
300/700=(1.8-x)/(x-0.8)
x=1.5
Ans A
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Re: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent [#permalink]
This is a weighted average problem.

liquid % in resulting solution is: \(\frac{(0.8 * 300) + (1.8 * 700)}{1000}\)

This works out to 1.5 %

A is the correct option.
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Re: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent [#permalink]
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Re: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent [#permalink]
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