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1/-1^x or 0
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05 Jan 2022, 06:19
05 Jan 2022, 06:19
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72% (00:56) correct
27% (00:54) wrong based on 11 sessions
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\(x\) is an integer
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.
Kudos for the right answer and explanation
See more on this topic Exponents
Quantity A |
Quantity B |
\(\frac{1}{(-1)^x}-(-1)^x\) |
0 |
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.
Kudos for the right answer and explanation
See more on this topic Exponents
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
1/-1^x or 0
[#permalink]
05 Jan 2022, 06:34
05 Jan 2022, 06:34
Carcass wrote:
\(x\) is an integer
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.
Kudos for the right answer and explanation
See more on this topic Exponents
Quantity A |
Quantity B |
\(\frac{1}{(-1)^x}-(-1)^x\) |
\(0\) |
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.
Kudos for the right answer and explanation
See more on this topic Exponents
The key concept here is that \(\frac{1}{(-1)^x} = (-1)^x\). Here's why:
Since x must be either odd or even, we can consider both cases.
If x is ODD, then \(\frac{1}{(-1)^x} = \frac{1}{-1} = -1\)
If x is ODD, then \((-1)^x = -1\)
So, when x is ODD, \(\frac{1}{(-1)^x} = (-1)^x\)
If x is EVEN, then \(\frac{1}{(-1)^x} = \frac{1}{1} = 1\)
If x is EVEN, then \((-1)^x = 1\)
So, when x is EVEN, \(\frac{1}{(-1)^x} = (-1)^x\)
Since we have analyzed both possible cases, we can be certain that \(\frac{1}{(-1)^x} = (-1)^x\), which means...
QUANTITY A: \(\frac{1}{(-1)^x}-(-1)^x = 0\)
QUANTITY B: \(0\)
Answer: C
gmatclubot
1/-1^x or 0 [#permalink]
05 Jan 2022, 06:34
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