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A bar of gold with dimensions 12 inches by 18 inches by 15 inches is m

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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
[Reveal] Spoiler: OA

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Option A : volume of original gold bar I'd 3240 in^3. All the other choice of options gives volume equal to 3240. But A volumes to 3300 which is not possible

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New post 05 Apr 2017, 22:27
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 fastest way to approach this problem is to notice that product of 12 inches by 18 inches by 15 inches has a single and only multiple of 5 i.e. 15

all the options have single multiple of 5 except A which has 2 multiples i.e. 10 and 15

Hence option A is correct
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Re: A bar of gold with dimensions 12 inches by 18 inches by 15 inches is m [#permalink]

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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.
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Re: A bar of gold with dimensions 12 inches by 18 inches by 15 inches is m [#permalink]

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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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Re: A bar of gold with dimensions 12 inches by 18 inches by 15 inches is m [#permalink]

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New post 24 Nov 2017, 14:01
Hi All,

We're told that 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. We're also told that 4 of the 5 answers choices ARE possible dimensions of the new gold bar. We're asked to find the one that's NOT. We can actually use the answer choices 'against' the prompt and TEST THE ANSWERS.

To start, this question involves the VOLUME of the gold bar - although we don't actually have to calculate the entire volume. Notice the dimensions (12 by 18 by 15)...

Answer A: 10 by 15 by 22

This Answer includes a 15 (the same as the original bar had), so we can 'ignore' those 15s and focus on what's left: (10 by 22) vs. (12 by 18)....
(10 by 22) = 220
(12 by 18) = 216
These are NOT the same results. The volume of Answer A would be BIGGER than the volume of the original bar, so this result is NOT possible and Answer A must be the answer.

Final Answer:
[Reveal] Spoiler:
A


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Re: A bar of gold with dimensions 12 inches by 18 inches by 15 inches is m   [#permalink] 24 Nov 2017, 14:01
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A bar of gold with dimensions 12 inches by 18 inches by 15 inches is m

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