If x is an integer, is x|x|<2^x ? : GMAT Data Sufficiency (DS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 07 Dec 2016, 21:39

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x is an integer, is x|x|<2^x ?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178
Followers: 5

Kudos [?]: 2206 [4] , given: 0

If x is an integer, is x|x|<2^x ? [#permalink]

### Show Tags

18 Dec 2012, 07:31
4
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

85% (01:50) correct 15% (01:03) wrong based on 1041 sessions

### HideShow timer Statistics

If x is an integer, is x|x|<2^x ?

(1) x < 0
(2) x = -10
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 35912
Followers: 6851

Kudos [?]: 90032 [4] , given: 10402

Re: If x is an integer, is x|x|<2^x ? [#permalink]

### Show Tags

18 Dec 2012, 07:35
4
KUDOS
Expert's post
4
This post was
BOOKMARKED
If x is an integer, is x|x|<2^x ?

(1) x < 0
(2) x= -10

If x is an integer, is x|x|<2^x ?

Notice that the RHS (right hand side) of the expression is always positive ($$2^x>0$$), but the LHS is positive when $$x>0$$ ($$x>0$$ --> $$x*|x|=x^2$$), negative when $$x<0$$ ($$x<0$$ --> $$x*|x|=-x^2$$) and equals to zero when $$x={0}$$.

(1) x < 0. According to the above $$x*|x|<0<2^x$$. Sufficient.

(2) x = -10. The same here $$x*|x|=-100<0<\frac{1}{2^{10}}$$. Sufficient.

_________________
Manager
Joined: 21 Aug 2013
Posts: 113
Schools: ISB '15
Followers: 2

Kudos [?]: 28 [0], given: 60

### Show Tags

30 Dec 2013, 10:42
If x is an integer, is x |x| < 2^x ?

(1) x < 0
(2) x = –10

DS from OG.
_________________

Veritas Prep - 650
MGMAT 1 590
MGMAT 2 640 (V48/Q31)

Last edited by seabhi on 31 Dec 2013, 01:45, edited 1 time in total.
Intern
Joined: 05 Dec 2013
Posts: 16
Followers: 0

Kudos [?]: 10 [1] , given: 1

### Show Tags

30 Dec 2013, 11:02
1
KUDOS
seabhi wrote:
If x is an integer, is x |x| < 2x ?

(1) x < 0
(2) x = –10

DS from OG.

OA is D for the following reasons:
When you first see a DS question, see if there is anyway to simplify the question stem
In this case, since |x| is positive, we can divide both sides by |x| giving us a new question stem --> is x < 2?

S1: x<0, therefore x must be <2 = sufficient
S2: x = -10 and -10 < 2 = sufficient

Let me know if this helps!
Intern
Joined: 03 Dec 2013
Posts: 16
Location: Uzbekistan
Concentration: Finance, Entrepreneurship
GMAT 1: 620 Q42 V33
GRE 1: 600 Q790 V400
GPA: 3.4
WE: Analyst (Commercial Banking)
Followers: 0

Kudos [?]: 13 [1] , given: 57

### Show Tags

30 Dec 2013, 20:36
1
KUDOS
bparrish89 wrote:
seabhi wrote:
If x is an integer, is x |x| < 2x ?

(1) x < 0
(2) x = –10

DS from OG.

OA is D for the following reasons:
When you first see a DS question, see if there is anyway to simplify the question stem
In this case, since |x| is positive, we can divide both sides by |x| giving us a new question stem --> is x < 2?

S1: x<0, therefore x must be <2 = sufficient
S2: x = -10 and -10 < 2 = sufficient

Let me know if this helps!

The OA is wrong here because of the following reasons:

(1) if x=-10 then -100<-20, on the other hand if x= -1, x<0 then the inequality changes from < to >, namely, -1 > -2 ; This statement is absolutely insufficient!

(2) This statement is obviously sufficient!

So, the correct answer is notD, but B
Manager
Joined: 21 Aug 2013
Posts: 113
Schools: ISB '15
Followers: 2

Kudos [?]: 28 [0], given: 60

### Show Tags

31 Dec 2013, 01:46
Apologies for the confusion, the Question has been corrected.
It was not 2x but 2^x
_________________

Veritas Prep - 650
MGMAT 1 590
MGMAT 2 640 (V48/Q31)

Math Expert
Joined: 02 Sep 2009
Posts: 35912
Followers: 6851

Kudos [?]: 90032 [0], given: 10402

### Show Tags

31 Dec 2013, 03:07
seabhi wrote:
If x is an integer, is x |x| < 2^x ?

(1) x < 0
(2) x = –10

DS from OG.

Merging similar topics. Please refer tot the solutions above. All OG13 questions are here: the-official-guide-quantitative-question-directory-143450.html
_________________
Intern
Joined: 22 Nov 2014
Posts: 6
Concentration: Entrepreneurship, Marketing
GPA: 3.2
Followers: 2

Kudos [?]: 11 [1] , given: 48

If x is an integer, is x|x|<2^x ? [#permalink]

### Show Tags

27 Jul 2015, 05:40
1
KUDOS
If x is an integer, is x|x|<2^x ?

(1) x < 0
(2) x = -10
VP
Joined: 08 Jul 2010
Posts: 1432
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 65

Kudos [?]: 1340 [0], given: 42

If x is an integer, is x|x|<2^x ? [#permalink]

### Show Tags

27 Jul 2015, 05:43
reza52520 wrote:
If x is an integer, is x|x|<2^x ?

(1) x < 0
(2) x = -10

Question : Is x|x|<2^x ?

Statement 1: x < 0

For x to be Negative LHS i.e. x|x| will always be NEGATIVE
and 2^x will be positive for any value of x
i.e. x|x|<2^x will always be true
SUFFICIENT

Statement 1: x = -10
For x =-10 LHS i.e. x|x| will always be NEGATIVE (-100)
and 2^x will be positive for given x (1/2^10)
i.e. x|x|<2^x will always be true
SUFFICIENT

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772
http://www.GMATinsight.com/testimonials.html

Feel free to give a Kudos if it is a useful post .

Last edited by GMATinsight on 27 Jul 2015, 05:44, edited 1 time in total.
Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4138
Followers: 306

Kudos [?]: 3249 [0], given: 100

Re: If x is an integer, is x|x|<2^x ? [#permalink]

### Show Tags

27 Jul 2015, 05:44
reza52520 wrote:
If x is an integer, is x|x|<2^x ?

(1) x < 0
(2) x = -10

Hi,
we have an equation and the RHS 2^x will be positive irrespective of value of x and LHS xlxl will depend on the value of x..
1) x is -ive .. so LHS is -ive and RHS is +ive.. suff
2) x=-10... again LHS is -ive and RHS is +ive.. suff
ans D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Senior Manager
Joined: 11 Nov 2014
Posts: 374
Location: India
WE: Project Management (Telecommunications)
Followers: 2

Kudos [?]: 19 [0], given: 17

Re: If x is an integer, is x|x|<2^x ? [#permalink]

### Show Tags

13 Dec 2015, 10:47
For,
and 2^x will be positive for any value of x

2 power x, X can be negative no?
since its x, we dont know positive or negative..
What am I missing?
Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2648
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 113

Kudos [?]: 1310 [0], given: 786

Re: If x is an integer, is x|x|<2^x ? [#permalink]

### Show Tags

13 Dec 2015, 11:04
paidlukkha wrote:
For,
and 2^x will be positive for any value of x

2 power x, X can be negative no?
since its x, we dont know positive or negative..
What am I missing?

You are missing a crucial thing here. Even if x is <0, $$2^x$$ with x<0 = $$1/2^x$$ , it is still >0...(1)

Thus with x<0, |x| = -x and hence x|x| = -$$x^2$$

As, x^2 is always $$\geq$$ 0 for all x, -$$x^2$$<0 ...(2)

Thus, from (1) and (2), you get a definite "yes" for the question "is $$x|x| < 2^x$$" for x<0.

Hope this helps.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Manager
Joined: 17 Nov 2013
Posts: 180
Followers: 0

Kudos [?]: 8 [0], given: 14

Re: If x is an integer, is x|x|<2^x ? [#permalink]

### Show Tags

24 Apr 2016, 14:22
This question can be solved as follows.

stmt1) it says that x /x/ < 2^x. and also we are told that x< 0. So if x is zero and the abs of x is always positive then we know that x/x/ will be negative. In addition to that, we know that 2^negative number will be positive because it will be in the form of 1/2^x, it will be less than 1 but it will be greater than a negative number. So stmt1 is SUFF.

stmt2) this is a repetition of stmt1 because the left side is negative and the right side is positive. SUFF.

Intern
Joined: 04 Jul 2016
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: If x is an integer, is x|x|<2^x ? [#permalink]

### Show Tags

24 Nov 2016, 05:03
I would say statement 1 is insufficient... Am I doing something incorrect?

$$x |x| < 2^x$$

$$|x| < \frac{2^x}{x}$$

For x = -1

$$|-1| < \frac{1}{2}/-1$$
$$1 < - \frac{1}{2}$$
Math Expert
Joined: 02 Sep 2009
Posts: 35912
Followers: 6851

Kudos [?]: 90032 [0], given: 10402

Re: If x is an integer, is x|x|<2^x ? [#permalink]

### Show Tags

24 Nov 2016, 06:17
Drblabla wrote:
I would say statement 1 is insufficient... Am I doing something incorrect?

$$x |x| < 2^x$$

$$|x| < \frac{2^x}{x}$$

For x = -1

$$|-1| < \frac{1}{2}/-1$$
$$1 < - \frac{1}{2}$$

When you divide by negative value you should flip the sign...
_________________
Re: If x is an integer, is x|x|<2^x ?   [#permalink] 24 Nov 2016, 06:17
Similar topics Replies Last post
Similar
Topics:
3 Is y < 2x? 4 08 May 2015, 03:02
4 If x is a positive integer, is (x)(x + 2)(x + 4) div by 12? 4 26 Nov 2012, 08:40
1 If x and y are both integers, which is larger, x^x or y^y? 7 23 Jul 2011, 01:25
5 If x is an integer, is x|x| < 2^x? 9 17 Jan 2007, 15:27
4 If x is an integer, is x|x| < 2^x? 8 22 Mar 2010, 20:59
Display posts from previous: Sort by