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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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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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Re: Mixture problem [#permalink]

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New post 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.

Answer is A.

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Re: Mixture problem [#permalink]

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New post 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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Re: Mixture problem [#permalink]

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New post 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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Re: Mixture problem [#permalink]

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New post 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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Re: Mixture problem [#permalink]

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New post 30 Oct 2013, 07:52
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Re: Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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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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New post 14 Jan 2015, 07:51
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Re: Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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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 \(= \frac{7.5}{100} * \frac{4}{9} * \frac{9}{5} = \frac{6}{100} = 6%\)

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

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

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

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Bunuel 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


ratio of sugar in mix to sugar in gallon=(5/9)/.075
ratio of dye in mix to dye in gallon=(4/9)/x
(5/9)/(.075)=(4/9)/x
x=6/100=6%
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Re: Four-ninths of a drink mix is dye and the rest is sugar. When the mix [#permalink]

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New post 29 Jan 2017, 02:38
Bunuel 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


suppose it is a litre instead of gallon (As 1 litre =1000 ml)

7.5 % of a litre of solution is sugar
75ml is sugar
Now 75 ml sugar constitutes 5/9 of initial mixture
means 55.55% of initial mixture
means initial mixture is 134 ml thus dye is ~45%(ie 4/9) of 134 ml
thus 60 ml
so 60ml is 6% of 1000ml ie 1Litre

Ans A

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

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New post 29 Jan 2017, 09:38
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Is answer A ? Let x be volume of dye. sugar is 5/9x.
5/9x = 7.5/100.

x= 27/200.
dye % = 4/9 * 27/200 *100 = 6%

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

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New post 29 Jan 2017, 11:47
Bunuel 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


A is the answer.

4/9 is dye , 5/9 sugar

5/9 represent 7.5 %
4/9 represent X

(4/9*7.5)/5/9
6 we will get....

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

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Let initial amount be 9.
so dye equals 4 parts and sugar equals 5 parts.

now, 5 parts is 7.5% of the total. let total amount now be = a.
thus 7.5/100 a = 5.
a = 500/7.5

we need sugar / total
sugar hasn't changed so : 4/a = 4/ (500/7.5) = 0.06.
thus 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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New post 20 Aug 2017, 23:08
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] 20 Aug 2017, 23:08
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