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 volume of the two gold bars will remain the same.

Volume = 12 * 18 * 15

Volume = 2 * 2 * 2 * 3 * 3 * 3 * 3 * 5

Any other dimensions of the bar would use the same number of same prime factors. You will have three 2s, four 3s and one 5. Check for each option.

Option (A) has only two 2s, only one 3, two 5s and an 11. All wrong!

Hence option (A) cannot be the dimensions.

_________________

Karishma

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