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Cereal A is 10% sugar by weight, whereas healthier but less delicious

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Cereal A is 10% sugar by weight, whereas healthier but less delicious [#permalink]

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Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?

(A) 2:9
(B) 2:7
(C) 1:6
(D) 1:4
(E) 1:3


I took this question from MGMAT. However, I'm not satisfied with the approach and explanation and wish there was an easy way to solve this. Can someone please help explain?

Thanks!
[Reveal] Spoiler: OA

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Re: Cereal A is 10% sugar by weight, whereas healthier but less delicious [#permalink]

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New post 18 Apr 2011, 12:51
mniyer wrote:
Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?

(A) 2:9
(B) 2:7
(C) 1:6
(D) 1:4
(E) 1:3


I took this question from MGMAT. However, I'm not satisfied with the approach and explanation and wish there was an easy way to solve this. Can someone please help explain?

Thanks!



The proportion needed of each starting percentage is the positive difference between the other two percentages.

Wt (10%) = 4-2 = 2

Wt( 2%) = 10-4= 6
cereal A to B = 2/6 = 1/3
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Re: Cereal A is 10% sugar by weight, whereas healthier but less delicious [#permalink]

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New post 18 Apr 2011, 13:30
mniyer wrote:
Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?

(A) 2:9
(B) 2:7
(C) 1:6
(D) 1:4
(E) 1:3


I took this question from MGMAT. However, I'm not satisfied with the approach and explanation and wish there was an easy way to solve this. Can someone please help explain?

Thanks!


Please read this:
http://www.veritasprep.com/blog/2011/03 ... -averages/
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Re: Cereal A is 10% sugar by weight, whereas healthier but less delicious [#permalink]

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New post 18 Apr 2011, 17:50
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(10/100)A+(2/100)B = (4/100)(A+B)
6A =2B
=> A/B = 1/3

Answer is E.

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Re: Cereal A is 10% sugar by weight, whereas healthier but less delicious [#permalink]

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Using Alligation :

Ratio of A / Ratio of B = (Avergate Wt of Mixture - Wt of B)/(Wt of A - Avergate Wt of Mixture)

=> Ratio of A / Ratio of B = (4 - 2)/(10 - 4) = 2/6 = 1/3

So they should be mixed in the ratio 1:3

Answer - E
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Re: Cereal A is 10% sugar by weight, whereas healthier but less delicious [#permalink]

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New post 18 Apr 2011, 18:53
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fluke wrote:
mniyer wrote:
Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?

(A) 2:9
(B) 2:7
(C) 1:6
(D) 1:4
(E) 1:3


I took this question from MGMAT. However, I'm not satisfied with the approach and explanation and wish there was an easy way to solve this. Can someone please help explain?

Thanks!


Please read this:
http://www.veritasprep.com/blog/2011/03 ... -averages/


Excellent. Thank you mate. I liked the scale method lot better :)

10%------------|--------4%------2%

Distance between 10 and 4 is 6
Distance between 4 and 2 is 2.

Flip the numbers while forming the ratio. So 2:6 which is 1:3. Phew!

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Re: Cereal A is 10% sugar by weight, whereas healthier but less delicious [#permalink]

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New post 24 Feb 2015, 11:45
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for such questions , just write down figures in following way on paper
10 2
4
2 6 which is 1:3

What i did here is 10-4= 6 and 4-2 = 2
line number 3 is your answer.
Hope this helps !!!

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Re: Cereal A is 10% sugar by weight, whereas healthier but less delicious [#permalink]

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Hi All,

This is an example of a "Weighted Average" question. These types of prompts can be solved in a variety of ways - here's how you can use the Weighted Average Formula to answer the question:

We're told that two types of cereal....
1) A certain amount of Cereal A, which is 10% sugar by weight
2) A certain amount of Cereal B, which is 2% sugar by weight

....are mixed together to form a Cereal that is 4% sugar by weight.

We're asked for the ratio of Cereal A to Cereal B in the new cereal.

A = # of ounces of Cereal A
B = # of ounces of Cereal B

[.10(A) + .02(B)]/(A+B) = .04

.1A + .02B = .04A + .04B
.06A = .02B

6A = 2B

Since the question asks for A/B, we just have to do a little more math....

A/B = 2/6 = 1/3

Final Answer:
[Reveal] Spoiler:
E


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Re: Cereal A is 10% sugar by weight, whereas healthier but less delicious [#permalink]

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New post 18 Aug 2016, 04:41
Hey @cheetan2u
i did it exactly as EMPOWERgmatRichC quoted.
Each and every step.
And got the answer too.
Any quicker ways?
Can we solve it any other way as the people above are quoting=> "Weighted average"
I can you explain this terminology.

Any theory would be helpful.
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Re: Cereal A is 10% sugar by weight, whereas healthier but less delicious [#permalink]

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New post 18 Aug 2016, 05:50
Simply set up an equation and solve for the answer.

Weights:
x+y=1
y=1-x
1=(1-x)+x

Solution equation with weights(note that x = part of cereal A/whole solution):
4=10x+2(1-x)
2=8x
1/4=x

As 1/4 of the solution is cereal A, the rest (3/4) must be cereal B.

1:3 is thus the answer.
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Re: Cereal A is 10% sugar by weight, whereas healthier but less delicious [#permalink]

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Re: Cereal A is 10% sugar by weight, whereas healthier but less delicious   [#permalink] 11 Oct 2017, 06:36
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