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

 It is currently 16 Oct 2018, 17:59

### 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

# Is x^(k+1) > x^k?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Current Student
Joined: 22 Jul 2014
Posts: 123
Concentration: General Management, Finance
GMAT 1: 670 Q48 V34
WE: Engineering (Energy and Utilities)
Is x^(k+1) > x^k?  [#permalink]

### Show Tags

Updated on: 18 Aug 2014, 09:47
12
00:00

Difficulty:

75% (hard)

Question Stats:

55% (02:12) correct 45% (01:52) wrong based on 162 sessions

### HideShow timer Statistics

Is x^(k+1) > x^k ?

(1) |x| > 1

(2) k+1 is divisible by 6

source: 4gmat

Originally posted by alphonsa on 18 Aug 2014, 08:57.
Last edited by Bunuel on 18 Aug 2014, 09:47, edited 1 time in total.
Edited the question
Intern
Joined: 14 May 2012
Posts: 5
Re: Is x^(k+1) > x^k?  [#permalink]

### Show Tags

18 Aug 2014, 09:10
alphonsa wrote:
Is $$x^(k+1) > x^k$$ ?

1) |x| >1

2) k+1 is divisible by 6

source: 4gmat

C)

i) NS,

since X could be positive or negative, and since (k+1) could be odd or even.

ii) NS

Since X could be a fraction

i) + ii)

Sufficient since i) makes sure X it is not a fraction <1, and, ii) makes sure (k+1) is even.
Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 610
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: Is x^(k+1) > x^k?  [#permalink]

### Show Tags

18 Aug 2014, 09:27
1
STAT1
means that x < -1 or x > 1
If x is +ve then x^(k+1) will be > x^k for all values of k ...(1)
If x is -ve then x^(k+1) will be > x^k for all odd values of k ....(2)
If x is -ve then x^(k+1) will be < x^k for all even values of k
So, INSUFFICIENT

STAT2
k+1 is divisible by 6 means k+1 is either 0 or even, so k will be odd
For x=0 x^(k+1) = x^k =0
So, other values of x we can get x^(k+1) > x^k and also, x^(k+1) < x^k
So, INSUFFICIENT

STAT1 and STAT2 together we have only ...(1) and ...(2) possible
so, x^(k+1) will be > x^k
so, SUFFICIENT

Hence, Answer will be C

Hope it helps!
_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Director
Joined: 25 Apr 2012
Posts: 692
Location: India
GPA: 3.21
WE: Business Development (Other)
Re: Is x^(k+1) > x^k?  [#permalink]

### Show Tags

19 Aug 2014, 00:03
3
alphonsa wrote:
Is x^(k+1) > x^k ?

(1) |x| > 1

(2) k+1 is divisible by 6

source: 4gmat

The question can be reduced $$x^{k}(x-1)>0$$

St 1 says |x|>1 or x>1 or x<-1....Now if x<-1 and k is odd then the expression will be greater than zero but x<-1, K is even then the expression is less than zero. Since 2 ans are possible st1 is not sufficient

St 2 says $$\frac{K+1}{6}=I$$ , Where I is an Integer. So K=6I-1 or K =even-odd=odd

So we know K is odd but we don't know anything about x not sufficient.

Combined we have, x>1 or x<-1 and k is odd
Case 1: x>1 and k is odd, the expression is postive
Case: x<-1 and k is odd so we have $$x^{k}$$ negative and $$(x-1)$$ also negative..so the expression will be positive.

Ans is C
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Manager
Joined: 16 May 2016
Posts: 152
Location: India
Concentration: Marketing, Healthcare
GPA: 3.5
WE: Analyst (Consulting)
Re: Is x^(k+1) > x^k?  [#permalink]

### Show Tags

20 Sep 2018, 19:45
alphonsa wrote:
Is x^(k+1) > x^k ?

(1) |x| > 1

(2) k+1 is divisible by 6

source: 4gmat

Bunuel, I am not understanding why the answer is C.
Here is my reasoning:
1.
X can be positive or negative, x is not equal to zero. X can be any number except 0 and greater than 1 and less than -1
Insufficient

2. K+1 is even so K is odd.
If X is 0 , x^(k+1) = x^k=0
If X is +ve,x^(k+1) > x^k
If X is negative, x^(k+1) > x^k
Also, there is condition for fractions
Insufficient

1+2
If X is +ve,x^(k+1) > x^k
If X is negative, x^(k+1) > x^k
and for fractions the statement changes.

Ans: E
I do not know why we are not considering fractions
_________________

Not Giving UP! Kudos if you like the question

Math Expert
Joined: 02 Sep 2009
Posts: 49915
Re: Is x^(k+1) > x^k?  [#permalink]

### Show Tags

20 Sep 2018, 20:34
Cbirole wrote:
alphonsa wrote:
Is x^(k+1) > x^k ?

(1) |x| > 1

(2) k+1 is divisible by 6

source: 4gmat

Bunuel, I am not understanding why the answer is C.
Here is my reasoning:
1.
X can be positive or negative, x is not equal to zero. X can be any number except 0 and greater than 1 and less than -1
Insufficient

2. K+1 is even so K is odd.
If X is 0 , x^(k+1) = x^k=0
If X is +ve,x^(k+1) > x^k
If X is negative, x^(k+1) > x^k
Also, there is condition for fractions
Insufficient

1+2
If X is +ve,x^(k+1) > x^k
If X is negative, x^(k+1) > x^k
and for fractions the statement changes.

Ans: E
I do not know why we are not considering fractions

Not clear how you concluded the red part there.

This following post shows why the answer is C: answerhttps://gmatclub.com/forum/is-x-k ... l#p1394406
_________________
Director
Joined: 14 Dec 2017
Posts: 500
GMAT 1: 640 Q49 V28
Re: Is x^(k+1) > x^k?  [#permalink]

### Show Tags

20 Sep 2018, 23:10
alphonsa wrote:
Is x^(k+1) > x^k ?

(1) |x| > 1

(2) k+1 is divisible by 6

source: 4gmat

Simplifying the prompt we get,

$$x^k*(x - 1) > 0$$

Hence , we have 3 cases
i) x > 0, k - odd/even, then the given Expression is > 0
ii) x < 0, k - odd, then the given Expression is > 0
iii)x < 0, k - even, then the given Expression is < 0

Statement 1 - |x| > 1, hence x < -1 or x > 1

However, No information about k

Statement 1 alone is Not Sufficient.

Statement 2: (k + 1) = 6p, hence k = 6p - 1 = (even) - 1.
k = odd

However, No information about x

Statement 2 alone is Not Sufficient.

Combining both, we get x > 1 or x < -1 & k = odd

We can see from the 3 cases above, the given conditions satisfy cases i) & ii).

Hence the given expression > 0

Combining is Sufficient.

Hence Answer is C.

Thanks,
GyM
_________________
Re: Is x^(k+1) > x^k? &nbs [#permalink] 20 Sep 2018, 23:10
Display posts from previous: Sort by

# Is x^(k+1) > x^k?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.