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There is a gram of sugared water with a% density. If x gram

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by Max@Math Revolution » Tue Nov 19, 2019 11:56 pm
[GMAT math practice question]

There is a gram of sugared water with a% density. If x grams of water is poured into the sugared water, then the density becomes ( a-5 ) % ( a > 5 ). What is the value of x?

A. 5/a
B.a+5/a-5
C. a+5/5
D.5a/a-5
E.a-5/a
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by Max@Math Revolution » Fri Nov 22, 2019 12:18 am
=>

The amount of sugar in a gram of a% sugared water is (a/100)*a grams.
When we add x gram of water, we have [(a/100)*a]/(a + x) = (a - 5)/100 or a^2/(a + x) = a - 5.
Then we have a^2 = (a - 5)(a + x) or a^2 = a^2 + ax - 5a - 5x.
This can be rearranged to get 5a = ax - 5x, or x(a-5) = 5a. So x = (5a)/(a - 5).

Therefore, D is the answer.
Answer: D
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