IR Two Part Question Bank # 10

[sophia.lin12345]

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.

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

I apologize for the format being off from the original; at the moment, I'm still unfamiliar with the coding. To clarify, we're trying to figure out which of the 5 percentages shown - 25%, 35%, 50%, 60%, 65% or 75% - would apply for "Alloy X (% of Alloy Z)" and "Copper (% of Alloy Z)."


Solution:
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%).

Even though I read the solution (above), I'm still not sure what the problem is asking for. What does it mean that the percents must be consistent with each other and the original percentages?

[tim]

Can you post the entire text of the problem so our discussion will benefit other students as well?

[sophia.lin12345]

Just edited the original post to include the problem and solution. Also, reading through the forums, it sounds like I'm prohibited from referencing the question # from the OG even if I don't post the actual problem word for word. Is that correct?

[tim]

"consistent" in this context just means the numbers have to fit together. For instance, consider this simpler problem that is very much the same style:

XY-Y = 20. Choose a value for X and a value for Y consistent with the information given.

X Y
0
2
3
4
6

As you can see, there is only one choice for X and Y consistent with the equation XY-Y = 20, and that is X=6 Y=4.

Regarding your question about the OG, there is nothing wrong with saying "hey look at problem 8!", but don't expect us to comment on it, because we tend to reserve our comments for threads where the entire question is written out for the benefit of the other students - but of course this is impossible with the copyrighted questions from the OG unless they appear in a free resource like GMAT Prep.

[sophia.lin12345]

Just to clarify, using the information we already have, we're trying to find out the percent of Alloy Z that is comprised of Alloy X, so that it will yield a solution with one of the following: 25%, 35%, 50%, 60%, 65% or 75% copper?

[tim]

That looks right to me!