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16 Sep 2014, 00:26
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If \(g\) is an integer, what is the value of \((-1)^{g^4 - 1}\)?
(1) \(g^2 \lt 1\)
(2) \(g^2+2g=0\)
(1) \(g^2 \lt 1\)
(2) \(g^2+2g=0\)
16 Sep 2014, 00:26
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Official Solution:
If \(g\) is an integer, what is the value of \((-1)^{g^4 - 1}\)?
(1) \(g^2 \lt 1\).
This statement implies that \(-1 \lt g \lt 1\).
Since given that \(g\) is an integer, the only possible value for \(g\) is 0. This information is sufficient to calculate the value of \((-1)^{g^4 - 1}\).
(2) \(g^2+2g=0\)
Factoring the equation gives \(g(g+2)=0\).
This implies that \(g=0\) or \(g=-2\). Since both potential values of \(g\) are even, it follows that \((-1)^{g^4 - 1}=(-1)^{\text{even}-1}=(-1)^{\text{odd} }=-1\). Sufficient.
Answer: D
If \(g\) is an integer, what is the value of \((-1)^{g^4 - 1}\)?
(1) \(g^2 \lt 1\).
This statement implies that \(-1 \lt g \lt 1\).
Since given that \(g\) is an integer, the only possible value for \(g\) is 0. This information is sufficient to calculate the value of \((-1)^{g^4 - 1}\).
(2) \(g^2+2g=0\)
Factoring the equation gives \(g(g+2)=0\).
This implies that \(g=0\) or \(g=-2\). Since both potential values of \(g\) are even, it follows that \((-1)^{g^4 - 1}=(-1)^{\text{even}-1}=(-1)^{\text{odd} }=-1\). Sufficient.
Answer: D
General Discussion
12 Oct 2017, 00:09
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I don't understand the explanation to solution (2).
(2) seems to assume another question - one that asks about whether (−1)g^(4−1) is even or odd or non-negative. However, the question ask for a value. Since (2) tells us that the solution to the equation could be 0 or 8, this doesn't seem to answer the question. Could you let me know if my logic is off here?
(2) seems to assume another question - one that asks about whether (−1)g^(4−1) is even or odd or non-negative. However, the question ask for a value. Since (2) tells us that the solution to the equation could be 0 or 8, this doesn't seem to answer the question. Could you let me know if my logic is off here?
