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Mixtures

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Mixtures [#permalink] New post 23 Jun 2010, 17:34
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Can someone walk me through this please

Krisp cereal is 10% sugar by weight. Brano cereal is 2% sugar by weight. If you wanted to make the mixture 4% sugar by weight what should the ratio of krisp to brano.
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Re: Mixtures [#permalink] New post 23 Jun 2010, 18:29
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A similar logic to what I said in the previous question can be used here.

Let us assume he takes x grams of Krisp and y grams of Brano.

So the total weight of the new mixture is (x+y)

Now with respect to percentages, we have:

\frac {10}{100} x + \frac {2}{100} y = \frac {4}{100} (x+y)

So, canceling all the 100s from the denominators, we get

10x + 2y = 4(x+y)

Rearranging like terms, we get

(10-4) x = (4-2) y

This implies that:

\frac {x}{y} = \frac {4-2}{10-4} = \frac {2}{6}= \frac {1}{3}

Hope this helps.
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Re: Mixtures [#permalink] New post 24 Jun 2010, 16:13
whiplash2411 wrote:
A similar logic to what I said in the previous question can be used here.

Let us assume he takes x grams of Krisp and y grams of Brano.

So the total weight of the new mixture is (x+y)

Now with respect to percentages, we have:

\frac {10}{100} x + \frac {2}{100} y = \frac {4}{100} (x+y)

So, canceling all the 100s from the denominators, we get

10x + 2y = 4(x+y)

Rearranging like terms, we get


(10-4) x = (4-2) y

This implies that:

\frac {x}{y} = \frac {4-2}{10-4} = \frac {2}{6}= \frac {1}{3}

Hope this helps.


it should be

(10y + 2x) (x + y)= 4 (xy)
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Re: Mixtures [#permalink] New post 24 Jun 2010, 16:25
Can you explain the logic behind that?
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Re: Mixtures [#permalink] New post 26 Jun 2010, 16:47
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Krispo is 10%. Bruno is 2%.

Question. Suppose we wanted the final solution to be 6% (not 4%). Because 6 is the midpoint between 10 and 2, wouldn't it then be clear that we would need the final solution to be half of each, and that ratio would be 1:1? It is helpful to visualize this on the number line:

2...6...10

Here we want the final solution to be 4%. So it looks like this:

2.4.....10

Because the grand average is skewed towards Bruno, in order to make the final solution 4%, clearly we need more Bruno than Krisp. In fact, because 4 is only 2 units away from 2 but 6 units away from 10, we need 6:2 or 3:1 as much Bruno as Krisp or 1:3 Krisp to Bruno.

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TAKEAWAY: The amount of skew is inversely proportional to the relative quantities of each item. If we have two groups, A, and B, then we have ("x" and "y" represent distance from the total average):

Average of A-------x-------Total average------y--------Average of B

(# in A)/(# in B) = y/x

This concept recurs fairly frequenly on the GMAT, especially in Data Sufficiency questions. If x and y are integers, then using this approach is quick and effective.
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Re: Mixtures [#permalink] New post 27 Jun 2010, 19:21
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Jinglander wrote:
Can someone walk me through this please

Krisp cereal is 10% sugar by weight. Brano cereal is 2% sugar by weight. If you wanted to make the mixture 4% sugar by weight what should the ratio of krisp to brano.


An Easier approach:


Attachment:
pic.JPG
pic.JPG [ 3.37 KiB | Viewed 1753 times ]

Hence the ratio of quantities is 2:6=1/3
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Re: Mixtures [#permalink] New post 28 Jun 2010, 04:23
K -->10
B ---> 2
So 10K+2B = (K+B)4 --> 10K+2B = 4K+4B --> 6K = 2B --> K/B = 2/6 = 1/3
Re: Mixtures   [#permalink] 28 Jun 2010, 04:23
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