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.

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)

Can you explain the logic behind that?

An Easier approach:



Hence the ratio of quantities is 2:6=1/3

K -->10
B ---> 2
So 10K+2B = (K+B)4 --> 10K+2B = 4K+4B --> 6K = 2B --> K/B = 2/6 = 1/3

This is a theory I learned through Manhattans Strategy Guides, however, for some reason, they don't always use it in their own problems.

But here goes a quick way to find a ratio. See the following question (taken from Manhattans FDP guide)

"Kris P cereal is 10% sugar by weight, whereas healthier but less delicious Bran-O cereal is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Kris P cereal to Bran-O cereal,by weight?

Instead of setting up a grid, think like this: Kris P is 10%, and 4% is our goal, that means that Kris P is 6 "too much", whereas Bran-O, with its 2% is 2 "too little", which means we need to remove 6 from Kris-P and add 2 from Bran-O

So, x(-6) + y(+2) = 0. In order for this to be 0. X needs to be 2, and Y needs to be 6. Hence, the ratio for Kris P to Bran-O is 2:6 - or 1:3


Hope this helps

Say, w1 is the weight krisp, w2 is the weight of Brano

using weihted average formula w1/w2 = (c2 - avg) / (Avg-c1)

w1/w2 = 4-2 / 10-6 = 2/3

So Krisp and brano should be mixed in the ratio of 1/3.
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.10k+.02b=.04(k+b)
k/b=1/3

I approached this algebraically:
X= total weight of Krisp
Y= total weight of Bruno

10x/100 + 2y/100=4(x+y)/100
10x/100 + 2y/100=4x/100 + 4y/100
6x/100=2y/100
6x=2y
x=1/3(y)
x/y=1/3

10% sugar in Kris-p (x) = 0.1x
2% sugar in Bran-0 (y) = 0.02y
Mixture contains 4% sugar = 0.04(x+y)

0.1x + 0.02y = 0.04(x+y)
0.06x = 0.02y
x/y = 2/6
x/y = 1/3

Use weighted average method..
....B0..A.......KP
So 2...4........10
Ratio of KP to B0.....\(\frac{Average-B0}{KP-average}\)=\(\frac{4-2}{10-4}\)=2/6=1/3..

A
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What is this "Easier approach" with no explanation posted by achiever01?
Does it have a name? Are there mixture questions where it does not work?

Here is a simple approach: test total weight equals 100 as the weight [b][color=#0000ff]


Thus from the captured table.
0.10x + 0.02(100-x) = 4
0.10x + 2 - 0.02x = 4
0.08x = 2
8x=200
x= 25

Plug back in to find weight of healthy
100-25 = 75
Thus ratio is 25:75 or 1:3

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