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Number properties

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Number properties

by sud21 » Fri Oct 09, 2015 7:57 pm
Suppose x is an integer such that (x ^ 2 −x−1)^ (x+2) =1 . How many possible values of x exist?

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by GMATinsight » Fri Oct 09, 2015 9:05 pm
sud21 wrote:Suppose x is an integer such that (x ^ 2 −x−1)^ (x+2) =1 . How many possible values of x exist?

1

2

3

4

5
(x ^ 2 −x−1)^ (x+2) =1 is possible only when

Either (x ^ 2 −x−1)=1 i.e. x = 2 or -1

OR (x+2) =0 i.e. x = -2

Or x=0

i.e. Possible values of x = 0, 2, -1 and -2

Answer: option D
Last edited by GMATinsight on Fri Oct 09, 2015 10:31 pm, edited 1 time in total.
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by [email protected] » Fri Oct 09, 2015 10:24 pm
Hi sud21,

As complex as this question looks, it's really just about some fundamental Exponent rules.

Before working through the Algebra, it's important to define HOW the given Exponent-equation can equal 1:

1) (1)^(any) = 1
2) (any)^(0) = 1
3) (-1)^(even) = 1

Knowing these rules, how many distinct values of X fit the given equation? Remember to be thorough with your Algebra....

Final Answer: D

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