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If X is an integer, X even? (1) X^{X} <= |X| (2) X^{3}

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Manager
Joined: 14 May 2009
Posts: 187
If X is an integer, X even? (1) X^{X} <= |X| (2) X^{3}  [#permalink]

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Updated on: 03 Jun 2009, 02:07
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If $$X$$ is an integer, $$X$$ even?

(1) $$X^{X} <= |X|$$

(2) $$X^{3} < 0$$

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Originally posted by Hades on 03 Jun 2009, 01:26.
Last edited by Hades on 03 Jun 2009, 02:07, edited 1 time in total.
Senior Manager
Joined: 15 Jan 2008
Posts: 261

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03 Jun 2009, 01:32

1, insufficient.. scenario possible for both X even or odd..
2, infusfficent, scneario possible for both X even or odd...

combined .. dont provide much info abt Z being even or odd..

hence ansewr is E
Manager
Joined: 14 May 2009
Posts: 187

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03 Jun 2009, 01:34
Nope, try again...
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Manager
Joined: 14 May 2009
Posts: 187

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03 Jun 2009, 02:07
My bad, yes you were correct, but I typed it in wrong-- try again
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VP
Joined: 28 Dec 2005
Posts: 1477

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03 Jun 2009, 08:08
so is the answer E then ?
VP
Joined: 28 Dec 2005
Posts: 1477

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03 Jun 2009, 09:22
Hm, ok, lets try again

From statement 2, you know that X is negative. Great, but no info on whether its odd or even. insuff

From statement 1, X=1 and -1 both work, and they're both odd. Even numbers, both positive and negative, dont satisfy the inequality. So X must be odd. suff.

Therefore, I now say A
Senior Manager
Joined: 16 Jan 2009
Posts: 339
Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE: Sales (Telecommunications)

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03 Jun 2009, 16:22
IMO A

x^x<=|x|
for x^x=|x|
x=1
for x^x<|x|
x has negative odd values
in both the cases x is odd
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Lahoosaher

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Joined: 14 May 2009
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03 Jun 2009, 16:49
If $$X$$ is an integer, $$X$$ even?

(1) $$X^{X} \leq |X|$$

(2) $$X^{3} < 0$$

Question:($$X$$ EVEN)?

(1) $$X^{X} \leq |X|$$

Let's assume X is any integer for now, so $$X = ...,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,...$$

Notice that $$2^{2} = 4 > |2| = 2$$ which is contrary to fact #1, and likewise any number bigger than 2. So we're down to:

$$X = ...,-8,-7,-6,-5,-4,-3,-2,-1,0,1$$

Consider $$X=0$$

$$0^0 = 1 > |0|$$, so $$X=0$$ doesn't hold.

So $$X = ...,-8,-7,-6,-5,-4,-3,-2,-1,1$$

$$X=-1$$ holds as $$(-1)^{-1} = -1 \leq |-1| = 1$$.

$$X=-2$$ doesn't hold as raising a negative number to an even exponent makes it positive, and a positive integer raised to itself will always be bigger than itself, hence no negative even numbers will hold.

And we're down to

$$X = ...,-7,-5,-3,-1,1$$

Which is always odd.

$$\longrightarrow SUFFICIENT$$.

(2) $$X^{3} < 0$$

This doesn't tell us much, just that X is negative-- X can still be even or odd.

$$\longrightarrow INSUFFICIENT$$.

Final Answer, $$A$$.
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Senior Manager
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03 Jun 2009, 22:50
i differ...

X = -2 doesn't hold as raising a negative number to an even exponent makes it positive, and a positive integer raised to itself will always be bigger than itself, hence no negative even numbers will hold.

for X = -2, X^X = .25..
and .25 is less than 2.. it holds..

So still not defined..

I stick with my answer... E..
Manager
Joined: 07 Apr 2009
Posts: 143

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23 Jul 2009, 14:01
Quote:
i differ...

X = -2 doesn't hold as raising a negative number to an even exponent makes it positive, and a positive integer raised to itself will always be bigger than itself, hence no negative even numbers will hold.

for X = -2, X^X = .25..
and .25 is less than 2.. it holds..

So still not defined..

I stick with my answer... E..

I know , Sorry to exhume this thread again !
Manager
Joined: 05 Jul 2008
Posts: 131
GMAT 2: 740 Q51 V38

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24 Jul 2009, 02:46
Neochronic wrote:
i differ...

X = -2 doesn't hold as raising a negative number to an even exponent makes it positive, and a positive integer raised to itself will always be bigger than itself, hence no negative even numbers will hold.

for X = -2, X^X = .25..
and .25 is less than 2.. it holds..

So still not defined..

I stick with my answer... E..

I agree.
Let X be -A (A>0 and A is an integer)
(-A) ^(-A)= (1/-A) ^A < 1 (A is an integer so 1/-A <1 )
So X^X <1 if X <0 while |X| is always >= 1 (except X=0)
SVP
Joined: 29 Aug 2007
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24 Jul 2009, 10:43
$$0^0 = 1 > |0|$$

Few things:

1. $$0^0$$ is not defined.

Quote:
$$X=-2$$ doesn't hold as raising a negative number to an even exponent makes it positive, and a positive integer raised to itself will always be bigger than itself, hence no negative even numbers will hold.

2. If $$x=-2$$, $$x^x = (-2)^(-2) = 1/(-2)^(2)= 1/4$$ which is always < 2.

OA should be E not A.

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Re: Tough DS 10 &nbs [#permalink] 24 Jul 2009, 10:43
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