A metal works company is creating alloy Z by combining alloy X and all

Question

A metal works company is creating alloy Z by combining alloy X and alloy Y in a specific ratio. Alloy X is 25% copper by weight and alloy Y is 65% copper by weight. 
 
In the columns below, identify the percent of alloy Z that is composed of alloy X and the percent of alloy Z that is copper by weight. These percents must be consistent with each other and with the conditions stated above. Make exactly one selection in each column

Bismuth83 · Accepted Answer

1. We are asked to  find the  percent of alloy X in alloy Z  and the  percent of Copper in alloy Z  .

2. Let's note that the fraction of copper in an alloy is  Copper(alloy)  and the amount of the alloy as  Amount(alloy) . It's given that Copper(X) = 0.25 and Copper(Y) = 0.65.

3. It's known that Amount(Z) = Amount(X) + Amount(Y) and Copper(Z)  *  Amount(Z) = Copper(X)  *  Amount(X) + Copper(Y)  *  Amount(Y) because  the mass of the alloy and copper stays the same .

4. Our question turns into finding  \frac{Amount(X)}{Amount(Z)}  and Copper(Z). From the equations above, we can derive Copper(Z) through  \frac{Amount(X)}{Amount(Z)} :

Copper(Z) = \frac{Copper(X) * Amount(X) + Copper(Y) * Amount(Y)}{Amount(Z)} = \frac{Amount(X)}{Amount(Z)} * Copper(X) + \frac{Amount(Y)}{Amount(Z)} * Copper(Y) = \frac{Amount(X)}{Amount(Z)} * 0.25 + (1 - \frac{Amount(X)}{Amount(Z)}) * 0.65 = 0.65 - 0.4\frac{Amount(X)}{Amount(Z)}

5. Our answer options are 0.25, 0.35, 0.5, 0.6, 0.65, and 0.75. The percent of  copper in alloy Z must be between 0.25 and 0.65, since it's a mixture . Now, we have three cases:

0.65 - 0.4\frac{Amount(X)}{Amount(Z)} = 0.35 . Then,  \frac{Amount(X)}{Amount(Z)} = 0.75 ,   which works  .

0.65 - 0.4\frac{Amount(X)}{Amount(Z)} = 0.5 . Then,  \frac{Amount(X)}{Amount(Z)} = 0.375 ,   which doesn't work  .

0.65 - 0.4\frac{Amount(X)}{Amount(Z)} = 0.6 . Then,  \frac{Amount(X)}{Amount(Z)} = 0.125 ,   which doesn't work  .

6. So, our answer is: Alloy X (% of Alloy Z) =   75%   and Copper (% of Alloy Z) =   35%  .

MalachiKeti · Answer

Here's how I did it

A metal works company is creating alloy Z by combining alloy X and alloy Y in a specific ratio. Alloy X is 25% copper by weight and alloy Y is 65% copper by weight.
  
So to find the copper % in the mixture it will be between 25 and 65

So 25, 65, 75 are out for column B

I randomly picked 35 for column b to start with

Y X
65 25
 \ /
 35
10 : 30

So component of First mixture is 30/40*100 = 75% and the Copper % in Alloy Z is 35% both are in options

kayarat600 · Answer

I don't think this is a gmat question tho it should be something doable for all of them.

pappal · Answer

let % of copper be in ratio x:y
then using assumed mean method
y/x=( %age of copper in z - 25)/(65 - %age of copper in z)
using componendo
(y/x)+1=(x+y)/x=(%of copper in z-25+65-%of copper in z)/(65-%of copper in z)
=40/(65-%of copper in z)
using invertendo
x/(x+y)*100={(65-%of copper in z)/40}*100
 here LHS is percentage of X in Z while in RHS 5age of copper in Z
placing the values of %ages provided in the stems we can very easily find out that
only 35% in RHS gives 75% to validate the equation

AnuK2222 · Answer

Official explanation from Manhattan GMAT 
The easiest way to work through this problem is to use weighted averages. If alloy Z were entirely composed of alloy X, it would be 25% copper by weight. Similarly, if alloy Z were composed entirely of alloy Y, it would be 65% copper by weight. As you shift the proportion of X to Y, you change the percent of the weight that is copper, but you know that the value will always be between 25% and 65%.

As X becomes a higher percentage of the weight, the average gets closer to 25. Similarly, as Y becomes a higher percentage of the weight, the average gets closer to 65. Imagine 25 and 65 as two endpoints of a line segment. If the X and Y alloys are each 50% of alloy Z, then the average ends up exactly halfway between 25% and 65%. In this case, copper would be 45% of alloy Z. However, we don’t have both 50% and 45% as answer choices.

Similarly, if X is 25% of Z, and Y is 75% of Z, we can think of the copper composition percent as being 75% of the distance from X to Y. 65 – 25 = 40, so the copper percent is 0.75 × 40 = 30 units closer to Y. That means that Alloy Z would be 55% copper. However, we don’t have both 25% and 55% as answer choices.

Keep trying! If X were 75% of the total weight, the average would be 75% of the distance from Y to X. In this case, the percent copper by weight would be 65 – 30 = 35. These numbers actually match options we have in the table. Alloy X is 75% of the weight of alloy Z, and copper is 35% of the final weight. No other possible pairs work in the table.

Column 1: The correct answer is F (75%).

Column 2: The correct answer is B (35%).

NEYR0N · Answer

it took me a while to even understand what each column represents, the left is the ratio Wx/Wz, the second is the weighted average of the mix Z

The weighted average of Z has to be between x = 25 and y = 65, so option a (of the right column) would render the formula :

Wx/Wy = (y-wavg)/(wavg-x) impossible (since 25-25 = 0 in denominator)

thankfully, b yields a 3:1 ratio so we can find Wx of Wz to be 3:4 = 75%.

My approach was quite random; honestly, I wasn't solving with conviction. --

Bunuel , Is there a way to speed up the process ? How would you solve in 2 minutes.

thanks in advance

cheshire · Answer

You could use the alligation method:

this is the process:
-Take each copper % candidate (from the right column)
-Treat it as the target average
-Use the alligation method to find the ratio X:Y that would achieve that average
-Convert that ratio to a % of alloy Z from X (i.e., left column)
-See if it matches any of the answer choices

How to use the alligation method:

Step 1: Set up the allegation grid
Alloy Y (higher %)=65%
Alloy Z (mean)=35%
Alloy X (lower %)=25%

Now subtract diagonally:
Y’s part=35−25=10
X’s part=65−35=30
So, the  mixing ratio (X:Y) = 30:10 = 3:1

So X is 3 parts out of 4 = 75% of Z
Now check:
 
 % of Z from X = 75% (Left column) 
 % copper in Z = 35% (Right column)

it matches so we have our answer. This probably won't be faster at first but will be if you get used to applying it.

svsivakrishna · Answer

Given: Alloy X is 25% copper by weight and alloy Y is 65% copper by weight. and combining x and Y in a ratio gives Z.
Question: Weightage % of X in alloy Z (Say X) and % of copper in alloy Z (Say C)

Since the percentage of copper is 65% and 25%, the difference is 40%.
Lets say C% is the percentage of copper in the mixture, i.e, alloy Z.

Weightage of X in Z will be X = (65-C)/40 * 100.

Now verifying from the options given using this for values of X and C

Considering C =35%, (65-C)/40 * 100 = (65-35)/40 * 100 = 75% matches the given options.

DishaAgarwal12 · Answer

It took me 4.5 mins to get through this question. I took all options in column one and tried to arrive at an answer. I assumed z to be 400 grams and then did the calculations but best would be to use values between 25-65% for the final % of copper in the mixture Z

A metal works company is creating alloy Z by combining alloy X and all

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Alloy X (% of Alloy Z)	Copper (% of Alloy Z)
		25%
		35%
		50%
		60%
		65%
		75%

GMAT Two-part Analysis (TPA) Questions

A metal works company is creating alloy Z by combining alloy X and all

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