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

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%

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

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

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.

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 %

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 )

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 %

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:

GMAT assassins aren't born, they're made,
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

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.

GMAT assassins aren't born, they're made,
Rich

We can let x = the amount of millet in Brand A and y = the amount of millet in Brand B: We can create the equation:

0.4x + 0.65y = 0.5(x + y)

40x + 65y = 50x + 50y

15y = 10x

3y = 2x

We see that we can let x = 3 and y = 2 (so that 3y = 2x). Thus, the percent of the mix that is Brand A is 3/(3 + 2) = 3/5 = 60%.

Answer: D

I always do these type of questions in the following way -

Since we are given the Millet % in the final mixture, lets form the overall equation -

x-> Amount of Brand A used.
y -> Amount of Brand B used.

Therefore,

x*40% + y*60% = 65%(x+y)
--> x*0.4 + y*0.6 = 0.65*(x+y)
--> x/y = 3/2.

We are asked what % of Brand A in the final mixture. Which is nothing but -
x/(x+y)= 3/(3+2) = 3/5 = 60%.

Answer: D

0.4a + 0.65b = 0.5*(a+b)
0.15b = 0.1a
a:b = 3:2

So, a is 60% of the mixture

Let's use a weighted average approach to solve this problem.

Let x be the proportion (as a decimal) of Brand A in the mix. Then, the proportion of Brand B in the mix is 1 - x.

Now, we can set up an equation based on the millet content:

0.40x (millets in Brand A) + 0.65(1 - x) (millets in Brand B) = 0.50 (desired millet content in the mix)

Now, let's solve for x:

0.40x + 0.65 - 0.65x = 0.50

0.40x - 0.65x + 0.65 = 0.50

-0.25x = -0.15

x = -0.15 / -0.25

x = 0.6

So, 60% of the mix is Brand A.

The correct answer is (D) 60%.