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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82
There is a gram of sugared water with a% density. If x grams of water  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 40% (02:27) correct 60% (02:21) wrong based on 15 sessions

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[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. $$\frac{5}{a}$$

B. $$\frac{a+5}{a-5}$$

C. $$\frac{a+5}{5}$$

D. $$\frac{5a}{a-5}$$

E. $$\frac{a-5}{a}$$

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Intern  B
Joined: 31 Oct 2018
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Re: There is a gram of sugared water with a% density. If x grams of water  [#permalink]

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Can you please provide solution for this problem?
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: There is a gram of sugared water with a% density. If x grams of water  [#permalink]

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=>

The amount of sugar in a gram of $$a%$$ sugared water is $$(\frac{a}{100})*a$$ grams.

When we add $$x$$ gram of water, we have $$[(\frac{a}{100})*a]/(a + x) = \frac{(a - 5)}{100}$$ or $$\frac{a^2}{(a + x)} = a - 5.$$

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 $$x = \frac{(5a)}{(a - 5)}.$$

_________________ Re: There is a gram of sugared water with a% density. If x grams of water   [#permalink] 22 Nov 2019, 02:00
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