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What is the value of (-1)^{g^4 + g - 1} ? 1. g is an integer

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Manager
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What is the value of (-1)^{g^4 + g - 1} ? 1. g is an integer [#permalink]

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18 Jan 2008, 00:34
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What is the value of (-1)^{g^4 + g - 1} ?

1. g is an integer
2. g is even

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

i just get 2 is sufficient, OA is D. i keep seeing that pending it being even or odd, the result will be either -1 or 1. details would be nice =D.
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Kudos [?]: 3050 [0], given: 360

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18 Jan 2008, 00:41

D

$$(-1)^{odd}=-1$$
$$(-1)^{even}=1$$

1. $$(-1)^{g^4 + g - 1}$$

a $$odd^4 + odd - 1 = odd$$
b $$even^4 + even - 1 = odd$$
SUFF.

2. $$(-1)^{g^4 + g - 1}$$
$$even^4 + even - 1 = odd$$
SUFF.
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Manager
Joined: 15 Nov 2007
Posts: 135
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Kudos [?]: 46 [0], given: 2

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18 Jan 2008, 01:07
+1... question though: doesn't odd^4 = 4*odd (and hence, even) since it's an exponent raised to an exponent?
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 499

Kudos [?]: 3050 [0], given: 360

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18 Jan 2008, 01:23
dominion wrote:
+1... question though: doesn't odd^4 = 4*odd (and hence, even) since it's an exponent raised to an exponent?

$$1^4=1*1*1*1=1 (odd)$$
$$4*1=4 (even)$$
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18 Jan 2008, 07:52
the function is equal to -1 for any integer. Therefore, either of those statements is sufficient.
Re: walker.... exponent question   [#permalink] 18 Jan 2008, 07:52
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