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KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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23 Jun 2010, 17:34
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82% (01:12) correct 18% (01:29) wrong based on 179 sessions
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KrisP cereal is 10% sugar by weight, whereas healthier but less delicious Bran0 cereal is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of KrisP cereal to Bran0 cereal, by weight? A. 1:3 B. 2:7 C. 2:3 D. 4:5 E. 1:9 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: KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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26 Jun 2010, 16:47
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.
____________
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 AxTotal averageyAverage 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: KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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27 Jun 2010, 19:21
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 [ 3.37 KiB  Viewed 8807 times ]
Hence the ratio of quantities is 2:6=1/3



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Re: KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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23 Jun 2010, 18:29
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
(104) x = (42) y
This implies that:
\(\frac {x}{y}\) = \(\frac {42}{104}\) = \(\frac {2}{6}\)= \(\frac {1}{3}\)
Hope this helps.



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An easy way to find ratios in weighted averages problems
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01 Apr 2015, 06:59
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 BranO 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 BranO 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 BranO, with its 2% is 2 "too little", which means we need to remove 6 from KrisP and add 2 from BranO
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 BranO is 2:6  or 1:3
Hope this helps



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Re: KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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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
(104) x = (42) y
This implies that:
\(\frac {x}{y}\) = \(\frac {42}{104}\) = \(\frac {2}{6}\)= \(\frac {1}{3}\)
Hope this helps. it should be (10y + 2x) (x + y)= 4 (xy)



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Re: KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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24 Jun 2010, 16:25
Can you explain the logic behind that?



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Re: KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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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



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Re: KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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08 Apr 2016, 23:42
Jinglander wrote: 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. Say, w1 is the weight krisp, w2 is the weight of Brano using weihted average formula w1/w2 = (c2  avg) / (Avgc1) w1/w2 = 42 / 106 = 2/3 So Krisp and brano should be mixed in the ratio of 1/3.
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Re: KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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30 Jul 2016, 19:58
.10k+.02b=.04(k+b) k/b=1/3



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Re: KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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13 Oct 2017, 03:55
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



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Re: KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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28 Dec 2018, 21:27
10% sugar in Krisp (x) = 0.1x 2% sugar in Bran0 (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



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Re: KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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28 Dec 2018, 21:45
CLIMBTHELADDER wrote: KrisP cereal is 10% sugar by weight, whereas healthier but less delicious Bran0 cereal is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of KrisP cereal to Bran0 cereal, by weight?
A) 1:3 B) 2:7 C) 2:3 D) 4:5 E) 1:9 Use weighted average method.. ....B0..A.......KP So 2...4........10 Ratio of KP to B0.....\(\frac{AverageB0}{KPaverage}\)=\(\frac{42}{104}\)=2/6=1/3.. A
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Re: KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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28 Jan 2019, 03:33
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?



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KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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04 Aug 2019, 15:09
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(100x) = 4 0.10x + 2  0.02x = 4 0.08x = 2 8x=200 x= 25 Plug back in to find weight of healthy 10025 = 75 Thus ratio is 25:75 or 1:3
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KrisP cereal is 10% sugar by weight, whereas healthier but less delic
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