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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
3^{40} + 3^{40} + +3^{40} vs 6^{40}
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20 Feb 2020, 07:41
20 Feb 2020, 07:41
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Question Stats:
83% (00:27) correct
16% (00:38) wrong based on 68 sessions
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Quantity A |
Quantity B |
\(3^{40}+3^{40}+3^{40}\) |
\(6^{40}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: 3^{40} + 3^{40} + +3^{40} vs 6^{40}
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21 Feb 2020, 07:26
21 Feb 2020, 07:26
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GreenlightTestPrep wrote:
Quantity A |
Quantity B |
\(3^{40}+3^{40}+3^{40}\) |
\(6^{40}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Useful property: \((xy)^n = (x^n)(y^n)\)
QUANTITY A: \(3^{40}+3^{40}+3^{40}\)
In the same way that k + k + k = 3k, we can also say that \(3^{40}+3^{40}+3^{40}=3(3^{40})\)
QUANTITY B: \(6^{40}\)
We can rewrite 6 as follows: \((2 \times 3)^{40}\)
Then we can apply the above property to get: \((2^{40})(3^{40})\)
So we now have:
QUANTITY A: \(3(3^{40})\)
QUANTITY B: \((2^{40})(3^{40})\)
At this point, we can divide both quantities by \(3^{40}\) to get:
QUANTITY A: \(3\)
QUANTITY B: \(2^{40}\)
At this point it is clear that, Quantity B is greater.
Answer: B
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