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3^20 - 3^19
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12 Aug 2017, 09:54
12 Aug 2017, 09:54
Expert Reply
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Question Stats:
78% (00:37) correct
21% (00:55) wrong based on 290 sessions
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Quantity A |
Quantity B |
\(\frac{(3^{20} - 3^{19})}{3}\) |
\(3^{18} + 3^{18}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Posts: 6218
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Re: 3^20 - 3^19
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13 Aug 2017, 05:30
13 Aug 2017, 05:30
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Carcass wrote:
Quantity A |
Quantity B |
\(\frac{(3^{20} - 3^{19})}{3}\) |
\(3^{18} + 3^{18}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Given:
Quantity A: (3^20 - 3^19)/3
Quantity B: 3^18 + 3^18
Factor Quantity A and combine the terms in Quantity B to get:
Quantity A: 3^19(3^1 - 1)/3
Quantity B: 2(3^18)
Simplify the numerator of Quantity A to get:
Quantity A: 3^19(2)/3
Quantity B: 2(3^18)
3^19 divided by 3 = 3^18. So, we get:
Simplify the numerator of Quantity A to get:
Quantity A: (3^18)(2)
Quantity B: 2(3^18)
Answer: C
Cheers,
Brent
Re: 3^20 - 3^19
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26 Nov 2020, 11:43
26 Nov 2020, 11:43
4
Much easier way would be to simply Quantity A:
1. Pull out \(3^{19}\)
\(\frac{3^{19}(3-1)}{3} = \frac{(2)3^{19}}{3} \)
2. Cancel out 3
\((2)3^{18}\)
You can see \((2)3^{18}\) is equal to Quantity B, which is \(3^{18} + 3^{18}\).
The answer is C.
1. Pull out \(3^{19}\)
\(\frac{3^{19}(3-1)}{3} = \frac{(2)3^{19}}{3} \)
2. Cancel out 3
\((2)3^{18}\)
You can see \((2)3^{18}\) is equal to Quantity B, which is \(3^{18} + 3^{18}\).
The answer is C.
