Problem Solving

EconomistGMATTutor 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

Can some experts find the best Option?

OA A

Hi lheiannie07,
Let's take a look at your question.

Volume of the bar of gold can be represented as:
$$=12\times18\times15inches^3$$

Write it as a product of prime factors.
$$=2\times2\times3\times2\times3\times3\times3\times5\ inches^3$$
$$=2^3\times3^4\times5\ inches^3$$

Let's now write the given options as a product of their prime factors and check which one of these is different from the volume of gold bar.
Option A:
10 inches by 15 inches by 22 inches
$$=10\times15\times22\ inches^3$$
$$=2\times5\times3\times5\times2\times11\ inches^3$$
$$=2^2\times3\times5^2\times11\ inches^3$$

This does not represent the volume of the gold bar as it is different from $$2^3\times3^4\times5\ inches^3$$ .

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.

Jay@ManhattanReview wrote:

lheiannie07 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

Can some experts find the best Option?

OA A

The volume of the reformed bar must be equal to the original bar.

Volume of the original bar = 12 * 18 * 15; let's factorize it into prime factors.

12 * 18 * 15 = (2^2 * 3) * (2 * 3^2) * (3 * 5) = 2^3 * 3^4 * 5

The option that does not have prime factors of their volume = 2^3 * 3^4 * 5 is the correct answer.

We see that one of the dimensions of option A is 22 inches; this will give a prime factor 11, which is not there is the volume of the original bar, thus, it is the correct answer.

The correct answer: A

Hope this helps!

-Jay
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[email protected] wrote:Hi lheiannie07,

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: A

GMAT assassins aren't born, they're made,
Rich