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Zarrolou
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sagarswamy
Zarrolou- Thanks for the approachThree grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?

A. y + 3z
B. (y +z) / 4
C. 2y + 3z
D. 3y + z
E. 3y + 4.5z

Can you please let me know how I could solve this question with the help of your table.
Basically I need the table for more than 2 unknown mixtures.

You can check various methods to solve this question here: three-grades-of-milk-are-1-percent-2-percent-and-3-percent-fat-126122.html

Hope it helps.
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Wow, this makes mixture problems so much easier. That's one of the sections i've been having problems understanding the logic behind them.
First i think i need to look at these graphs to get used to using this method, but after a while i think it will just pop from the back of my head.
THAnK YOU!
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In first example, how did you get the answer as 33℅ after getting x/y=1/2?

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In first example, how did you get the answer as 33℅ after getting x/y=1/2?

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x/y = 1/2;

x/(x + y) = 1/(1 + 2) = 1/3 = 0.333....

You can find detailed discussion of that question here: https://gmatclub.com/forum/seed-mixture ... 60580.html
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but many mixture problems are not solvable with this approach. E.g, this one:

There are 2 bars of gold-silver alloy; one piece has 2 parts of gold to 3 parts of silver and another has 3 parts of gold to 7 parts of silver. If both bars are melted into 8 kg bar with the final gold to silver ratio of 5:11. What was the weight of the first bar?
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Zarrolou
Hi guys!

This is my second post of Tips and Tricks, if you have missed the first one be sure to check it out :arrow: Inequalities

In this one I will show you a method (disclamer: I did not invente it :roll: ) to solve easly any mixture problem: it's called Alligation.

It uses a simple table to solve any mixture problem, every answer to such problems can be obtain by looking at this table .

Attachment:
alli.png
Please note: the X concentration is the highest, the Y is the lowest

The results that you get by subtracting, as I show you in the table, are the ratios of the substances in the desired mixture.
\(RATIO\frac{X}{Y}=\frac{Desired-Y}{X-Desired}\)

An exmple will explain better than any of my words because this method is really simple to use. I took the following questions from here if you want to get some practice you can try some of those.

1)Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue.
If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of this mixture is X ?
(A) 10%
(B) 33.33 %
(C) 40%
(D) 50%
(E) 66.66 %

The question asks for the ryegrass so your table should look like this:
Attachment:
all1.png
Solution: The final raio is\(\frac{X}{Y}=\frac{5}{10}\) (or \(\frac{1}{2}\)) so for every 1 part of X 2 parts of Y will be in the final mixture
So for a 3 kg mixture (for example)=> 1X and 2Y => \(X=33%\) of the total B

This table can be used in other ways also, and this question is an example:
2)How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?
(A) 7/2
(B) 5
(C) 20/3
(D) 8
(E) 39/4

Your table:
Attachment:
all2.png
Final ratio: \(\frac{X}{Y} = \frac{5}{75}\)
We know that Y is 100 liter so \(\frac{X}{100}=\frac{5}{75}\) \(X=\frac{20}{3}\) C
Easy!

As you see mixture problems start to look very easy if you consider this method, and for sure all this will save you valuable time 8-)
Hope you guys like it

Cheers

I appreciate this as I've been searching for a breakdown on alligations. What I don't understand is the second half, for example with the 20/3 answer. Can you further break down your work so that it's clear how to use what you've found via the alligation in solving the problem?
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I think this might help:
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Divad
but many mixture problems are not solvable with this approach. E.g, this one:

There are 2 bars of gold-silver alloy; one piece has 2 parts of gold to 3 parts of silver and another has 3 parts of gold to 7 parts of silver. If both bars are melted into 8 kg bar with the final gold to silver ratio of 5:11. What was the weight of the first bar?
I don't think this question makes sense...

What is the "first bar"? The weight of the 2:3 bar? The weight of the 3:7 bar? They could be any weight at all, because only a portion of them was used to mix into the final 8kg bar.

The question also doesn't tell us the ratio between the 2:3 bar and the 3:7 bar.

If this was a DS question, I have a feeling it would be Insufficient data... So yeah, alligation won't help with this question, because the question is impossible.

If someone is able to solve it, I would be very happy to see an explanation!
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Divad
but many mixture problems are not solvable with this approach. E.g, this one:

There are 2 bars of gold-silver alloy; one piece has 2 parts of gold to 3 parts of silver and another has 3 parts of gold to 7 parts of silver. If both bars are melted into 8 kg bar with the final gold to silver ratio of 5:11. What was the weight of the first bar?
I don't think this question makes sense...

What is the "first bar"? The weight of the 2:3 bar? The weight of the 3:7 bar? They could be any weight at all, because only a portion of them was used to mix into the final 8kg bar.

The question also doesn't tell us the ratio between the 2:3 bar and the 3:7 bar.

If this was a DS question, I have a feeling it would be Insufficient data... So yeah, alligation won't help with this question, because the question is impossible.

If someone is able to solve it, I would be very happy to see an explanation!


Let us assume that the weight of gold and silver in first bar be 2x and 3x
Weight of gold and silver in 2nd bar be 3y and 7 y
On melting both bar, we get ratio of 5 : 11
Weight of gold will be 8 * 5/16 = 2.5
Weight of silver will be 8 *11/16 = 5.5

We can also write 2x+3y = 2.5
3x+7y= 5.5
On solving we get x = 0.2 and y = 0.7

Weight of first bar = 2x+3x = 5x = 1 kg
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Vubar
Divad
but many mixture problems are not solvable with this approach. E.g, this one:

There are 2 bars of gold-silver alloy; one piece has 2 parts of gold to 3 parts of silver and another has 3 parts of gold to 7 parts of silver. If both bars are melted into 8 kg bar with the final gold to silver ratio of 5:11. What was the weight of the first bar?
I don't think this question makes sense...

What is the "first bar"? The weight of the 2:3 bar? The weight of the 3:7 bar? They could be any weight at all, because only a portion of them was used to mix into the final 8kg bar.

The question also doesn't tell us the ratio between the 2:3 bar and the 3:7 bar.

If this was a DS question, I have a feeling it would be Insufficient data... So yeah, alligation won't help with this question, because the question is impossible.

If someone is able to solve it, I would be very happy to see an explanation!


Let us assume that the weight of gold and silver in first bar be 2x and 3x
Weight of gold and silver in 2nd bar be 3y and 7 y
On melting both bar, we get ratio of 5 : 11
Weight of gold will be 8 * 5/16 = 2.5
Weight of silver will be 8 *11/16 = 5.5

We can also write 2x+3y = 2.5
3x+7y= 5.5
On solving we get x = 0.2 and y = 0.7

Weight of first bar = 2x+3x = 5x = 1 kg
Ah I see, thanks! They were asking how much of the 8kg came from the first bar. That's not what they wrote though. The question they wrote is impossible to answer.

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