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A feed store sells two varieties of birdseed: Brand A, which

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A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 17 Dec 2009, 15:48
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A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A?

A) 40%

B) 45%

C) 50 %

D) 60 %

E) 55 %
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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 02 Jun 2014, 20:47
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umaa wrote:
A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A?

A) 40%

B) 45%

C) 50 %

D) 60 %

E) 55 %


Use the scale method:
40% millet and 65% millet are mixed together to get 50% millet.

w1/w2 = (65 - 50)/(50 - 40) = 15/10 = 3/2
So brand A is 3/5 i.e. 60% of the mix.
Answer (D)

For more on this method, check: http://www.veritasprep.com/blog/2011/03 ... -averages/
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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 19 May 2014, 22:17
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Another method to solve this question using equations:

1 kg of Brand A will have 400g millet and 600g sunflower.
1 kg of Brand B will gave 650g millet and 350g sunflower.

Suppose,x kg of Brand A and y kg of Brand B are in the mixture.
Then total weight of millet = 400x+650y g
Total weight of mixture = 1000x + 1000y g
Given that millet is 500% hence
(400x+650y)/(1000x + 1000y) = 1/2
or, 800x + 1300y = 1000x+1000y
or 300y=200x
or, x/y = 3/2
% of Brand A = (3/(3+2))*100 =60%
Hence answer is D
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Re: Percent Mix Problem  [#permalink]

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New post 17 Dec 2009, 16:21
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Another alligation method:

Set up a table:
Millet Sunflower
Brand A 40% 60%
Brand B 65% 35%

B--------Average--------A
(from mean) (from mean)
15 50 10

So A/A+B = 15/25 = 60%
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Re: Percent Mix Problem  [#permalink]

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New post 17 Dec 2009, 20:58
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this can be done easily with the tricks of mix and alligation

ans is 60%

40________________________65
____________50____________
65-50=15______:_______ 50-40=10


so ratio is 15:10
% is 15/25 *100=60
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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 02 Jun 2014, 18:43
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Took me 1min.

Only take the Millet percentages since that's the goal mix you´re trying to find.

0.40x + 0.65(1-x) = 0.50
0.40x+ 0.65 - 0.65x = 0.50
0.25x = 0.15
x = 0.60

Hope it helps!
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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 01 Jul 2014, 08:55
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why r we taking 15/10 and not 10/15 when 10 denotes brand A part .?
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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 02 Jul 2014, 22:31
kunaljain1701 wrote:
why r we taking 15/10 and not 10/15 when 10 denotes brand A part .?


It's actually 15 parts of brand A and 10 parts of brand B. So fraction of brand A is 15/25. The w1 and w2 in the formula are the weights of brand A and brand B. They do not represent the fraction of total but only the parts of brand A and brand B. Check out the link I have given above. It discusses weights in more detail.
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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 23 Oct 2014, 04:55
Bumping up and asking for a different explanation. So, according to MGMAT's explanation, they used a table method to solve this question - which is not very helpful. Could someone explain in a simpler way to solve this using the table method? Also, isn't there "one ring to rule them all" for this type of questions?

p.s.: Sadly,I can't attach a screen grab of their explanation to this reply
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A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 23 Oct 2014, 06:52
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Blackbox wrote:
Bumping up and asking for a different explanation. So, according to MGMAT's explanation, they used a table method to solve this question - which is not very helpful. Could someone explain in a simpler way to solve this using the table method? Also, isn't there "one ring to rule them all" for this type of questions?

p.s.: Sadly,I can't attach a screen grab of their explanation to this reply


A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A?

A) 40%

B) 45%

C) 50 %

D) 60 %

E) 55 %


Yes there is a simple method :

Consider the following method

Brand A : 40% millet and 60% sunflower
Brand B : 65% millet and 35% safflower

Mix : 50% millet


Here the weighted average is 50%,

Now Brand A has 40% millet, which is 10% less than the weighted average of mix = - 0.10 A --------------- I
Similarly, Brand B has 65 % millet, which is 15 % more than the weighted average of mix = + 0.15 B ------------ II

Now, both Brand A and Brand B are combined to give a 50% mix containing millet, so equate I and II

implies, 0.10 A = 0.15 B

Therefore A/B = 0.15/0.10 = 3/2

A : B : (A + B) = 3 : 2 : (3+2) = 3 : 2 : 5

We have to find, percent of the mix is Brand A i.e. A : (A + B) = 3 : 5 = (3 / 5) * 100 = 60 %



Here is a pictorial representation :



Brand A= 40%------------------------10% or 0.10 below average, A times-----------------Total below = - 0.10 A

---------------------------------------------------------------------------------------- Average = 50% or 0.50

Brand B = 65 %--------------------------15% or 0.15 above average, B times-----------------Total above = + 0.15 B

Since the amount below the average has to equal the average above the average; therefore,
0.10 A = 0.15 B

A/B = 3/2

A:B: Total = 3:2:5


Therefore
A/Total = 3:5 = 60 %
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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 23 Oct 2014, 10:26
Thanks for the explanation, Ashish.

1. Does this approach work with all sorts of problems with percents?
2. How did you come up with 50% as a weighted average? Is it because it is given "If a customer purchases a mix of the two types of birdseed that is 50% millet"?
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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 23 Oct 2014, 21:08
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Blackbox wrote:
Thanks for the explanation, Ashish.

1. Does this approach work with all sorts of problems with percents?
2. How did you come up with 50% as a weighted average? Is it because it is given "If a customer purchases a mix of the two types of birdseed that is 50% millet"?




This approach works for mixture problems.

Its better to convert the information into ratios. It causes less confusion. This is a weighted avg problem of sorts, because you got 2 Brands and the final mix contains some part of Brand and some part of Brand B. This is evident from the fact that

Brand A has 40 % millet, Brand B has 65 % millet and Mix has 50 % millet

40% Millet in Brand A------------ 50% Millet in Mix ------------ 65% Millet in Brand B.

As you see, Brand A and Brand B combine to form the Mix. Had the Quantity of Brand A and Quantity of Brand B been Equal then the Mix would have had 52.5% Millet. But this is not the case here. We are given that the Mix has 50% millet i.e. the Quantity of Brand A in mix is greater than Quantity of Brand B in mix since 50% is closer to 40% than it is to 65%. So, this situation can only arise if and only if this was a weighted average problem.

In case you need the Weighted Avg formula,

Weighted Avg = [(Quantity of A*Quality of A) + (Quantity of B*Quality of B)] / ( Quantity of A + Quantity of B )
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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 23 Oct 2014, 21:11
Ashishmathew01081987 wrote:
Blackbox wrote:
Thanks for the explanation, Ashish.

1. Does this approach work with all sorts of problems with percents?
2. How did you come up with 50% as a weighted average? Is it because it is given "If a customer purchases a mix of the two types of birdseed that is 50% millet"?




This approach works for mixture problems.

Its better to convert the information into ratios. It causes less confusion. This is a weighted avg problem of sorts, because you got 2 Brands and the final mix contains some part of Brand and some part of Brand B. This is evident from the fact that

Brand A has 40 % millet, Brand B has 65 % millet and Mix has 50 % millet

40% Millet in Brand A------------ 50% Millet in Mix ------------ 65% Millet in Brand B.

As you see, Brand A and Brand B combine to form the Mix. Had the Quantity of Brand A and Quantity of Brand B been Equal then the Mix would have had 52.5% Millet. But this is not the case here. We are given that the Mix has 50% millet i.e. the Quantity of Brand A in mix is greater than Quantity of Brand B in mix since 50% is closer to 40% than it is to 65%. So, this situation can only arise if and only if this was a weighted average problem.

In case you need the Weighted Avg formula,

Weighted Avg = [(Quantity of A*Quality of A) + (Quantity of B*Quality of B)] / ( Quantity of A + Quantity of B )



Also, keep an eye on the value that is changing. Here, the value is that of the proportion of Millet. Sunflower and safflower values are of no use.
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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 25 Oct 2014, 00:24
hey guys , m satisified with the above explanations but let me give u an easy one which is undersble by a newbie.


this is very a simple approach u can also find same question in og13(i guess in the last questions)

consider brand A-40(millet) and 60(other one)

n brand B -0.65x(millet) and 0.35x(other one)

acc to question the eq is

40+ 0.65x=0.5(x+100)

u get x=200/3

now percentage =brand A/mixture

100/(200/3) +100 =3/5 which is 60%

simple D :)

-h
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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 26 Oct 2014, 06:39
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hsbinfy wrote:
hey guys , m satisified with the above explanations but let me give u an easy one which is undersble by a newbie.


this is very a simple approach u can also find same question in og13(i guess in the last questions)

consider brand A-40(millet) and 60(other one)

n brand B -0.65x(millet) and 0.35x(other one)

acc to question the eq is

40+ 0.65x=0.5(x+100)

u get x=200/3

now percentage =brand A/mixture

100/(200/3) +100 =3/5 which is 60%

simple D :)

-h


Yup. That's one other explanation I read on MGMAT. Thanks for bringing it up, HSBINFY.
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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 20 Apr 2015, 11:14
Could anyone explain why this solution is incorrect;

0.4x+0.65y=0.5(x+y)
0.15y=0.1x -> Total weight is 0.25
x= 40% of total.


For reference in this problem this approach works.

Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 % fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X?

A. 10%
B. 33 1/3%
C. 40%
D. 50%
E. 66 2/3%

0.4x+0.25y = 0.3(x+y)
0.4x-0.3x = 0.3y - 0.25y
0.1x=0.05y
or
2x=y So Y=33 1/3 %
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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 20 Apr 2015, 18:58
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Hi JeroenReunis,

Your calculations are correct; you make a mistake in your end deduction though.

When you get to this calculation....

.15Y = .1X

You have a RATIO of X to Y. Here's what you need to do with this ratio to get to the correct answer:

Let's multiply both sides by 100 to get rid of the decimal....

15Y = 10X

From here, you can do work in a couple of different ways. I'm going to continue to do "ratio math"....

15Y = 10X

15/10 = X/Y

3/2 = X/Y

This means that for every 3 "units" of X, we have 2 "units" of Y. So, for every 5 total units, 3/5 are X and 2/5 are Y. The question asks for the percent of the mixture that is X...

3/5 = 60%

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A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 21 Apr 2015, 02:43
EMPOWERgmatRichC wrote:
Hi JeroenReunis,

Your calculations are correct; you make a mistake in your end deduction though.

When you get to this calculation....

.15Y = .1X

You have a RATIO of X to Y. Here's what you need to do with this ratio to get to the correct answer:

Let's multiply both sides by 100 to get rid of the decimal....

15Y = 10X

From here, you can do work in a couple of different ways. I'm going to continue to do "ratio math"....

15Y = 10X

15/10 = X/Y

3/2 = X/Y

This means that for every 3 "units" of X, we have 2 "units" of Y. So, for every 5 total units, 3/5 are X and 2/5 are Y. The question asks for the percent of the mixture that is X...

3/5 = 60%

Final Answer:

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Rich



Hello Rich,


First of all many thanks for your reply, this question can't get out of my mind.
However I still do not get it.

Since 10x = 15y

I would assume that for every 1X there are 1.5Y.
So for every 2X there are 3Y. (Ratio is 2:3)
So in total there are 5 units, X= 2/5 of Total which is 40%.

Even after I put down 10 paperclips (=X) and 15 coins(=Y) on my desk, i still see it as there are 1.5Y for every 1X.

Another example if the ratio of cows to pigs is 2 to 4 than 1C=2P right? How is this any different?


Could you please try to explain to me where my thinking goes wrong? Just don't get it :(
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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 21 Apr 2015, 03:29
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umaa wrote:
A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A?

A) 40%

B) 45%

C) 50 %

D) 60 %

E) 55 %

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Re: A feed store sells two varieties of birdseed: Brand A, which  [#permalink]

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New post 21 Apr 2015, 18:48
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Hi JeroenReunis,

The given equation can be re-written as a ratio, but your interpretation of it is not correct....

10X = 15Y

means "10 times X" equals "15 times Y"

This does NOT mean "for every 10X there are 15Y"

You can prove this by TESTing VALUES.

10X = 15Y

IF....
X = 3 then Y = 2

THIS is the ratio that actually exists: X:Y = 3 to 2

Any additional sets of values that you plug in for X and Y will confirm this ratio.

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Re: A feed store sells two varieties of birdseed: Brand A, which &nbs [#permalink] 21 Apr 2015, 18:48

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