Can someone help?
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.
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.
Alloy X (% of Alloy Z) Copper (% of Alloy Z) Percent
25%
35%
50%
60%
65%
75%
MGMAT 5th Edition  2 part question
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The percentages have come under the wrong column. Basically, there are 3 columns ' Alloy X (% of Alloy Z)', 'Copper (% of Alloy Z)' and 'Percent' and the percentages are under the 'Percent' column. We need to choose the correct percentage from the given options.
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 ceilidh.erickson
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Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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 ceilidh.erickson
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This is a weighted average question. We're being asked: which is a possible combination of answer choices for the percentage of alloy X within alloy Z, and of copper within alloy Z?
Students often get these questions mixed up, because we have two different kinds of percentages to deal with.
 if the overall mixture were made up of 100% of alloy X, it would have 25% copper
 if the overall mixture were 0% alloy X (100% alloy Y), it would have 65% copper
We can represent this kind of weighted average with a scale (or seesaw):
Based on the above, it would be impossible for the amount of copper in alloy Z to be 25% unless the amount of alloy X was 100% (not an option), or to be 65% unless the amount of X was 0% (also not an option).
Now, test some of the other answer choices:
 what if we has 50% of alloy X, 50% of alloy Y? Then we'd be exactly halfway between 25 and 65% copper: 45%. Since that's not an answer option, we can't have 50% of X.
 If we had 25% of X and 75% of Y, we'd have 0.25(25) + 0.75(65) = 55% copper. Not an answer option.
 If we had 35% of X and 65% of Y, we'd have 0.35(25) + 0.65(65) = 51%  not an option
 If we had 60% of X and 40% of Y, we'd have 0.6(25) + 0.4(65) = 41%  not an option
 If we had 65% of X and 35% of Y, we'd have 0.65(25) + 0.35(65) = 39%  not an option
 If we had 75% of X and 25% of Y, we'd have 0.75(25) + 0.25(65) = 35%  BINGO!
Students often get these questions mixed up, because we have two different kinds of percentages to deal with.
 if the overall mixture were made up of 100% of alloy X, it would have 25% copper
 if the overall mixture were 0% alloy X (100% alloy Y), it would have 65% copper
We can represent this kind of weighted average with a scale (or seesaw):
Based on the above, it would be impossible for the amount of copper in alloy Z to be 25% unless the amount of alloy X was 100% (not an option), or to be 65% unless the amount of X was 0% (also not an option).
Now, test some of the other answer choices:
 what if we has 50% of alloy X, 50% of alloy Y? Then we'd be exactly halfway between 25 and 65% copper: 45%. Since that's not an answer option, we can't have 50% of X.
 If we had 25% of X and 75% of Y, we'd have 0.25(25) + 0.75(65) = 55% copper. Not an answer option.
 If we had 35% of X and 65% of Y, we'd have 0.35(25) + 0.65(65) = 51%  not an option
 If we had 60% of X and 40% of Y, we'd have 0.6(25) + 0.4(65) = 41%  not an option
 If we had 65% of X and 35% of Y, we'd have 0.65(25) + 0.35(65) = 39%  not an option
 If we had 75% of X and 25% of Y, we'd have 0.75(25) + 0.25(65) = 35%  BINGO!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
GMAT/MBA Expert
 ceilidh.erickson
 GMAT Instructor
 Posts: 2094
 Joined: 04 Dec 2012
 Thanked: 1443 times
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One shortcut would be to recognize that weighted averages are PROPORTIONAL.
For example, if you had 5 grams of mixture A that was 20% alcohol, and 10 grams of mixture B that was 50% alcohol, you would have a 1:2 ratio of A:B. The distance between your extreme points (20% and 50%) and the actual amount will be in the same ratio 1:2. Since the total range of possible alcohol percentages is 30 (50  20), then the percentage of the total mixture must be 40% (20 away from A's amount, 10 away from B's amount).
In the problem above, you might recognize that the total range is 40 (65%  25%). Therefore, you might want to start with 25% and 75% for the percentage of alloy X, as that would correspond nicely to a 1:3 or 3:1 ratio out of a total of 4.
For more on weighted averages, see:
https://www.manhattanprep.com/gmat/blog ... pendown/
https://www.manhattanprep.com/gmat/blog ... problems/
https://www.manhattanprep.com/gmat/blog ... lemseasy/
https://www.manhattanprep.com/gmat/blog ... thegmat/
For example, if you had 5 grams of mixture A that was 20% alcohol, and 10 grams of mixture B that was 50% alcohol, you would have a 1:2 ratio of A:B. The distance between your extreme points (20% and 50%) and the actual amount will be in the same ratio 1:2. Since the total range of possible alcohol percentages is 30 (50  20), then the percentage of the total mixture must be 40% (20 away from A's amount, 10 away from B's amount).
In the problem above, you might recognize that the total range is 40 (65%  25%). Therefore, you might want to start with 25% and 75% for the percentage of alloy X, as that would correspond nicely to a 1:3 or 3:1 ratio out of a total of 4.
For more on weighted averages, see:
https://www.manhattanprep.com/gmat/blog ... pendown/
https://www.manhattanprep.com/gmat/blog ... problems/
https://www.manhattanprep.com/gmat/blog ... lemseasy/
https://www.manhattanprep.com/gmat/blog ... thegmat/
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education