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# M06-04

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Math Expert
Joined: 02 Sep 2009
Posts: 52971

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15 Sep 2014, 23:26
3
8
00:00

Difficulty:

85% (hard)

Question Stats:

49% (00:49) correct 51% (01:15) wrong based on 158 sessions

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If $$g$$ is an integer what is the value of $$(-1)^{g^4 - 1}$$?

(1) $$g^2 \lt 1$$

(2) $$g^2+2g=0$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52971

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15 Sep 2014, 23:26
2
1
Official Solution:

(1) $$g^2 \lt 1$$. This statement tells that $$-1 \lt g \lt 1$$. Since $$g$$ is an integer then $$g=0$$. Sufficient to calculate the value of $$(-1)^{g^4 - 1}$$.

(2) $$g^2+2g=0$$

$$g(g+2)=0$$

$$g=0$$ or $$g=-2$$. Since both possible values of $$g$$ are even then $$(-1)^{\text{even}^4 - 1}=(-1)^{\text{even}-1}=(-1)^{\text{odd}}=-1$$. Sufficient.

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Joined: 06 Jun 2017
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11 Oct 2017, 23:09
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?
Math Expert
Joined: 02 Sep 2009
Posts: 52971

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11 Oct 2017, 23:15
1
PRein wrote:
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?

Let me put it in another way.

We want to find the value of $$(-1)^{g^4 - 1}$$.

(2) says that g = 0 or g = -2.

For either of these values, 0 or -2, $$(-1)^{g^4 - 1}=-1$$.

Hope it's clear.
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Joined: 06 Jun 2017
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11 Oct 2017, 23:23
Bunuel wrote:
PRein wrote:
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?

Let me put it in another way.

We want to find the value of $$(-1)^{g^4 - 1}$$.

(2) says that g = 0 or g = -2.

For either of these values, 0 or -2, $$(-1)^{g^4 - 1}=-1$$.

Hope it's clear.

Thanks for the clarification. I miss-read the formula as (-1)*g^(4-1) instead of (-1)^((g^4)-1).
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Joined: 14 May 2017
Posts: 47

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25 Dec 2017, 09:45
I think this is a high-quality question and I agree with explanation.
Re M06-04   [#permalink] 25 Dec 2017, 09:45
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# M06-04

Moderators: chetan2u, Bunuel

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