GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Aug 2018, 23:42

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Manager
Joined: 14 May 2009
Posts: 187
Schools: Stanford, Harvard, Berkeley, INSEAD
If X is an integer, X even? (1) X^{X} <= |X| (2) X^{3}  [#permalink]

### Show Tags

Updated on: 03 Jun 2009, 02:07
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions

### HideShow timer Statistics

If $$X$$ is an integer, $$X$$ even?

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

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

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

Hades

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
Re: Tough DS 10  [#permalink]

### Show Tags

03 Jun 2009, 01:32
simple..answer E..

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
Schools: Stanford, Harvard, Berkeley, INSEAD
Re: Tough DS 10  [#permalink]

### Show Tags

03 Jun 2009, 01:34
Nope, try again...
_________________

Hades

Manager
Joined: 14 May 2009
Posts: 187
Schools: Stanford, Harvard, Berkeley, INSEAD
Re: Tough DS 10  [#permalink]

### Show Tags

03 Jun 2009, 02:07
My bad, yes you were correct, but I typed it in wrong-- try again
_________________

Hades

VP
Joined: 28 Dec 2005
Posts: 1477
Re: Tough DS 10  [#permalink]

### Show Tags

03 Jun 2009, 08:08
so is the answer E then ?
VP
Joined: 28 Dec 2005
Posts: 1477
Re: Tough DS 10  [#permalink]

### Show Tags

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)
Re: Tough DS 10  [#permalink]

### Show Tags

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
_________________

Lahoosaher

Manager
Joined: 14 May 2009
Posts: 187
Schools: Stanford, Harvard, Berkeley, INSEAD
Re: Tough DS 10  [#permalink]

### Show Tags

03 Jun 2009, 16:49
Hades wrote:
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, $$A$$.
_________________

Hades

Senior Manager
Joined: 15 Jan 2008
Posts: 261
Re: Tough DS 10  [#permalink]

### Show Tags

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
Re: Tough DS 10  [#permalink]

### Show Tags

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
Re: Tough DS 10  [#permalink]

### Show Tags

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
Posts: 2420
Re: Tough DS 10  [#permalink]

### Show Tags

24 Jul 2009, 10:43
Hades wrote:
Hades wrote:
$$0^0 = 1 > |0|$$

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.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Re: Tough DS 10 &nbs [#permalink] 24 Jul 2009, 10:43
Display posts from previous: Sort by

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

 post reply Question banks Downloads My Bookmarks Reviews Important topics

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.