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# If g is an integer what is the value of (-1)^(g^4-1)

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Director
Joined: 01 Aug 2008
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Kudos [?]: 868 [0], given: 99

If g is an integer what is the value of (-1)^(g^4-1) [#permalink]

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21 Dec 2008, 09:55
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If $$g$$ is an integer what is the value of $$(-1)^{g^4 - 1}$$ ?

(1) $$g^2<{1}$$
(2) $$g^2+2 g=0$$

Source: GMAT Club Tests - hardest GMAT questions

Last edited by Bunuel on 13 Dec 2013, 07:08, edited 2 times in total.
Updated.

Kudos [?]: 868 [0], given: 99

Math Expert
Joined: 02 Sep 2009
Posts: 42338

Kudos [?]: 133122 [3], given: 12415

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

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19 Dec 2012, 06:40
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ugimba wrote:
What is the value of $$(-1)^{g^4 + g - 1}$$ ?

1. $$g$$ is an integer
2. $$g$$ is even

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

shouldn't we consider negative values for option 1? ( 'g' is integer)? in this case, then A wont fit right?

BELOW IS REVISED VERSION OF THIS QUESTION:
If $$g$$ is an integer what is the value of $$(-1)^{g^4 - 1}$$ ?

(1) $$g^2<{1}$$
(2) $$g^2+2 g=0$$

SOLUTION:
(1) $$g^2<{1}$$ --> 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 $$(-1)^{even^4 - 1}=(-1)^{even-1}=(-1)^{odd}=-1$$. Sufficient.

_________________

Kudos [?]: 133122 [3], given: 12415

VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1078

Kudos [?]: 663 [0], given: 70

Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Re: What is the value of (-1)^{g^4 + g - 1} ? 1. g is an [#permalink]

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19 Dec 2012, 17:14
good question really tricky, i went on select B in hurry

Kudos [?]: 663 [0], given: 70

VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1078

Kudos [?]: 663 [0], given: 70

Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Re: What is the value of (-1)^{g^4 + g - 1} ? 1. g is an [#permalink]

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19 Dec 2012, 17:19
Bunuel wrote:
ugimba wrote:
What is the value of $$(-1)^{g^4 + g - 1}$$ ?

1. $$g$$ is an integer
2. $$g$$ is even

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

shouldn't we consider negative values for option 1? ( 'g' is integer)? in this case, then A wont fit right?

BELOW IS REVISED VERSION OF THIS QUESTION:
If $$g$$ is an integer what is the value of $$(-1)^{g^4 - 1}$$ ?

(1) $$g^2<{1}$$
(2) $$g^2+2 g=0$$

SOLUTION:
(1) $$g^2<{1}$$ --> 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 $$(-1)^{even^4 - 1}=(-1)^{even-1}=(-1)^{odd}=-1$$. Sufficient.

Superb question, since g^2<1 g cannot have any value except zero had it been g<1 than the answer would have been B

Kudos [?]: 663 [0], given: 70

Re: What is the value of (-1)^{g^4 + g - 1} ? 1. g is an   [#permalink] 19 Dec 2012, 17:19
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# If g is an integer what is the value of (-1)^(g^4-1)

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