AbdurRakib wrote:

A bar of gold with dimensions 12 inches by 18 inches by 15 inches is melted down and re-formed into a bar of different dimensions. All of the following are possible dimensions of the new gold bar EXCEPT:

A. 10 inches by 15 inches by 22 inches

B. 12 inches by 10 inches by 27 inches

C. 6 inches by 18 inches by 30 inches

D.24 inches by 27 inches by 5 inches

E. 9 inches by 24 inches by 15 inches

The key to solving this problem is to notice that when we melt and re-form the gold bar, the volume of the original gold bar will be the same as the re-formed gold bar. Therefore, we must compare the volumes of the answer choices with the volume of the given gold bar.

A helpful way to solve this problem is to recognize that we can factor the answer choices to determine any difference between the factors of the dimensions in those choices and the given dimensions of 12 by 18 by 15. The original bar’s dimensions factor to 2^3 x 3^4 x 5^1. In scanning the answer choices, we see that answer choice A has dimensions of 10 by 15 by 22. Thus, those dimensions contain a factor of 11. Since the original dimensions of 12 by 18 by 15 DO NOT contain a factor of 11, answer choice A is correct.

Answer: A

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