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There is a% of saline solution of 500g. Alice wants to have

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by Max@Math Revolution » Wed Sep 18, 2019 11:55 pm

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[GMAT math practice question]

There is a% of saline solution of 500g. Alice wants to have b% of saline solution by boiling saline solution where b > a. What is the lost weight of the saline solution by boiling?

1) a = 20
2) a/b = 2/5
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Sep 22, 2019 5:37 pm
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Let x be the lost weight of b% saline solution by boiling.
The question asks the value of x such that (a/100)500 = (b/100)(500-x).
(a/100)500 = (b/100)(500-x)
=> 500a = b(500-x)
=> 500a = 500b - bx
=> bx = 500(b-a)
=> x = 500(b-a)/b
=> x = (500)(1-a/b)
Thus, condition 2) is sufficient.

When a question asks for a ratio, if one condition includes a ratio and the other condition just gives a number, the condition including the ratio is most likely to be sufficient. This tells us that B is most likely to be the answer to this question.

Condition 1) is not sufficient obviously, since we don't have any information about the variable a.

Therefore, B is the answer.
Answer: B
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