GMATantidote wrote:

An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2:7. These two alloys are mixed in such a way that in the overall alloy, there is more aluminum than Zinc, and copper constitutes x% of this alloy. What is the range of values x can take?

A) 30% ≤ x ≤ 40%

B) 32.5% ≤ x ≤ 40%

C) 32.5% ≤ x ≤ 42%

D) 33.33% ≤ x ≤ 40%

E) 33.33 % ≤ x ≤ 42%

What is the source of this problem? It is certainly not GMAT specific because the numbers given are hard to work with. Also, the options are not accurate. "Range" means that we need to give the values that x does take. Option (A) covers extra values (like codomain) while option (B) doesn't cover all values. In a question like this, you cannot have an "approximate value" of x.

Given: "in the overall alloy, there is more aluminum than Zinc,"

The maximum aluminium you can have is when you mix copper and aluminium alloy (say alloy A) with infinitesimally small amount of copper and zinc alloy (alloy B). In that case, you will have almost 40% of copper in the mix (because alloy A has 40% of copper). So x% < 40%.

Minimum case:

60% of alloy A > (7/9) of alloy B

A/B > 35/27

If the two alloys are mixed in this ratio, the copper concentration will be:

Using weighted average:

Cavg = (2/5 * 35 + 2/9 * 27)/(35 + 27)

Cavg = (14 + 6)/62= 20/62 = 32.26% (rounded to 2 decimal places)

So x% > 32.26%

Answer: 32.26 < x < 40

Thanks for the answer, I went through your posts on weighted average and scale on

and really liked the approach.

Can you pls explain - In this particular question, while calculating the maximum for Aluminum how are we using the statement that Aluminum can be no more than Zinc?

Also would be interested in getting answer to this question, since I learned Weighted average from your posts - so thought it will be good to understand your POV.