Official Solution:

A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is 2 mm thick and its diameter is 15 mm). If the weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver, what will be the weight of a coin measuring 1 x 30 mm made of pure aluminum if silver is twice as heavy as aluminum?

A. 36 grams
B. 40 grams
C. 42 grams
D. 48 grams
E. 50 grams


Denote \(S\) as the weight of silver and \(A\) the weight of aluminum in the first coin. Compose the following equation: \(S + A = 30\) or \(2A + A = 30\). Thus, the aluminum half of the coin weighs 10 grams. If the coin were made of pure aluminum, the second half of the coin would also weigh 10 grams and the whole coin would weigh 20 grams.

If we look at the proportions of the second coin, we will see that it is twice as large as the first coin (volume2 = \((\frac{30}{2})^2*\pi\); volume1 = \(2*(\frac{15}{2})^2*\pi\)). A second coin made of pure aluminum would be twice as heavy as the first coin made of pure aluminum. The answer to the question is therefore \(20*2 = 40\) grams.


Answer: B
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Dear Bunuel,

Please explain sentence "second coin made of pure aluminum would be twice as heavy as the first coin made of pure aluminum"? Unfortunately, I don't understand your logic on deriving 20gram (second coin is composed of A only and we dont know how many A in there) and then multiplying it by 2.

Many thanks again.

Liza

Please check here: a-coin-made-of-alloy-of-aluminum-and-silver-measures-2-x-15-mm-it-is-98446.html

Hope it helps.
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I think this is a high-quality question and I agree with explanation.

I think this is a high-quality question and I agree with explanation.

I think this is a high-quality question and I agree with explanation.

I think this is a high-quality question and I agree with explanation

hey davidbeckham

please note that the volume of aluminum in the alloy equals that of silver not weight.
A and S stands for weight & silver is twice as heavy as aluminum; hence S becomes 2A.

hi Bunuel

One suggestion if one of the options can be changed to 80 gms. this can set up a trap for people who understand "if silver is twice as heavy as aluminum" in an opposite way. this would a good learning for folks who don't read the text carefully and make silly mistakes!

Hi,
second coin is 1mm thick and 30mm diameter, and first coin is 2mm thick and 15mm diameter. I didn't understand why second coin is double weight.