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# Four-ninths of a drink mix is dye and the rest is sugar. Whe

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Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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25 Dec 2010, 06:26
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Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 7.5% sugar. What percentage of the gallon is dye?

(A) 6
(B) 6.5
(C) 7.5
(D) 8
(E) 24
[Reveal] Spoiler: OA

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25 Dec 2010, 07:47
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The proportion of Dye and sugar will remain constant.

Dye/Sugar = (4/9)/(5/9) = x/7.5
=> 4/5 = x/7.5 => x = 4*7.5/5 = 6.

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25 Dec 2010, 07:49
I use a very simple way with fractions to find the calue of x:

$$\frac{4}{9}/\frac{x}{100} = \frac{5}{9}/\frac{7,5}{100}$$

When you solve it you will find that x=6
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25 Dec 2010, 08:41
Can some one explain when to use traditional mixture solutions using grid and when to use simple proportionality equations?
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25 Dec 2010, 17:20
rg1 wrote:
Can some one explain when to use traditional mixture solutions using grid and when to use simple proportionality equations?

Here you are adding the whole mixture to water, also the ratio water to sugar remains unchanged.

Also you only have to make simple comptutation: 7,5/5*4=6
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30 Oct 2013, 07:52
Hello from the GMAT Club BumpBot!

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Re: Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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16 Dec 2013, 05:42
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rxs0005 wrote:
Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 7.5% sugar. What percentage of the gallon is dye?

(A) 6
(B) 6.5
(C) 7.5
(D) 8
(E) 24

Here, let's say that the gallon is 100 litres.
Then sugar in the gallon will be 7.5 litres
Now 5/9x=7.5
'x' is the amoung of the mix poured into gallon
x = (9)(1.5)

Now dye will be 9(1.5)*(4/9)=1.5*4=6

Hence A

Even if you don't find the way to solve it you can straight eliminate answers C,D,E cause the amount of dye is always going to be less given the
4:5 ratio

Hope it helps
Cheers!
J
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Re: Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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14 Jan 2015, 07:51
Hello from the GMAT Club BumpBot!

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Re: Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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14 Jan 2015, 20:57
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In the drink mix, if $$\frac{4}{9} =$$ dye, then

sugar $$= 1 - \frac{4}{9} = \frac{5}{9}$$

If sugar constitutes $$\frac{7.5}{100}$$, then dye percentage $$= \frac{7.5}{100} * \frac{4}{9} * \frac{9}{5} = \frac{6}{100} = 6%$$

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Re: Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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17 May 2016, 12:22
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Four-ninths of a drink mix is dye and the rest is sugar. Whe   [#permalink] 17 May 2016, 12:22
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