Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 24 May 2017, 12:06

### 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 and y are nonzero integers, is x^y<y^x?

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

### Hide Tags

Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 633
Followers: 44

Kudos [?]: 969 [0], given: 39

If x and y are nonzero integers, is x^y<y^x? [#permalink]

### Show Tags

18 Jun 2011, 09:20
4
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

67% (02:25) correct 33% (01:16) wrong based on 63 sessions

### HideShow timer Statistics

If x and y are nonzero integers, is x^y<y^x?

(1) x = y^2
(2) y>2

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-nonzero-integers-is-x-y-y-x-168279.html
[Reveal] Spoiler: OA

_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Current Student
Joined: 26 May 2005
Posts: 565
Followers: 18

Kudos [?]: 215 [1] , given: 13

Re: If x and y are nonzero integers, is x^y<y^x? [#permalink]

### Show Tags

18 Jun 2011, 09:31
1
KUDOS
Baten80 wrote:
If x and y are nonzero integers, is x^y<y^x?
(1) x = y^2
(2) y>2

St1. Let Y = 1 X = 1
1^1 is not less than 1^1................. insufficient ( even 2..2^4 is not less than 4^2)

St2: nothing abt X ... insuffcient

1&2 we know Y >2 and integer
Y = 3 X = 9
9^3< 3^9... true

sufficient hence C
Manager
Joined: 08 Sep 2010
Posts: 58
Followers: 0

Kudos [?]: 31 [0], given: 4

Re: If x and y are nonzero integers, is x^y<y^x? [#permalink]

### Show Tags

18 Jun 2011, 10:17
Baten80 wrote:
If x and y are nonzero integers, is x^y<y^x?
(1) x = y^2
(2) y>2

(1) x=y^2 ..... basically translates the original equation to....

(y.y)^y < y^(y.y)

if y = 1, is x^y<y^x? No!
if y = 3, is x^y<y^x? Yes!

Hence insufficient.

(2) y>2 ...... lets say y = 3....translates the original equation to....

x^3 < 3^x

if x = 1, is x^3 < 3^x ? No!
if x = 4, is x^3 < 3^x ? Yes!

Hence insufficient.

Together:

we know the original translates into (y.y)^y < y^(y.y)

and based on (2), the minimum value for y = 3....so lets plug it in

(3.3)^3 < 3^(3.3) ? <<<<< - will be the same regardless of what value you plugin for y as long as its > 2

9^3 < 3^9 .... without doing this long calculated simply simplify the exponents

3^2(3) < 3^3

eliminate the base 6 < 9 ??? YES!!!!

Hence (C)
_________________

Don't forget to give me ****KUDOS****

Last edited by 386390 on 18 Jun 2011, 10:40, edited 2 times in total.
Manager
Status: GMAT BATTLE - WIN OR DIE
Joined: 02 May 2011
Posts: 167
Concentration: General Management, Entrepreneurship
GMAT Date: 12-22-2011
GPA: 3.81
WE: General Management (Hospitality and Tourism)
Followers: 2

Kudos [?]: 89 [1] , given: 13

Re: If x and y are nonzero integers, is x^y<y^x? [#permalink]

### Show Tags

18 Jun 2011, 10:25
1
KUDOS
my answer is C
x^y<y^x
1)
x=y^2
so put in this x^y<y^x
obtained
y^2y<y^(y^2)
or simplified
2y<y^2

not you can check
y=1, 2<1 - incorrect
y=2, 4<4 - incorrect
y=3, 6<9 - correct

so insufficient

2)
y>2

insufficient because no information about X

1)+2)

y=3, 6<9 - correct

Sufficient
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 633
Followers: 44

Kudos [?]: 969 [0], given: 39

Re: If x and y are nonzero integers, is x^y<y^x? [#permalink]

### Show Tags

18 Jun 2011, 10:34
sudhir18n wrote:
Baten80 wrote:
If x and y are nonzero integers, is x^y<y^x?
(1) x = y^2
(2) y>2

St1. Let Y = 1 X = 1
1^1 is not less than 1^1................. insufficient ( even 2..2^4 is not less than 4^2)

St2: nothing abt X ... insuffcient

1&2 we know Y >2 and integer
Y = 3 X = 9
9^3< 3^9... true

sufficient hence C

See you missed y is equal to could be 3 and thus x = 9 for option 1.
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15429
Followers: 649

Kudos [?]: 207 [0], given: 0

Re: If x and y are nonzero integers, is x^y<y^x? [#permalink]

### Show Tags

20 Apr 2016, 13:27
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 38856
Followers: 7726

Kudos [?]: 106032 [0], given: 11602

Re: If x and y are nonzero integers, is x^y<y^x? [#permalink]

### Show Tags

21 Apr 2016, 00:00
Expert's post
1
This post was
BOOKMARKED
Baten80 wrote:
If x and y are nonzero integers, is x^y<y^x?

(1) x = y^2
(2) y>2

If x and y are nonzero integers, is x^y < y^x ?

(1) x = y^2 --> if $$x=y=1$$, then $$x^y=1=y^x$$, so the answer would be NO BUT if $$y=3$$ and $$x=9$$, then $$x^y=9^3<y^x=3^9$$, so the answer would be YES. Not sufficient.

(2) y > 2. No info about $$x$$, not sufficient.

(1)+(2) From (1) $$x = y^2$$, thus the question becomes: is $$(y^2)^y<y^{(y^2)}$$? --> is $$y^{2y}<y^{(y^2)}$$? Now, since from (2) $$y=integer>2$$, then $$2y$$ will always be less than $$y^2$$, therefore $$y^{2y}$$ will be less than $$y^{(y^2)}$$. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-nonzero-integers-is-x-y-y-x-168279.html
_________________
Re: If x and y are nonzero integers, is x^y<y^x?   [#permalink] 21 Apr 2016, 00:00
Similar topics Replies Last post
Similar
Topics:
5 Is |x|*y - x*|y| > x*y, where x and y are non-zero integers 7 22 Feb 2017, 00:01
If x and y are nonzero integers, is x/y > 0? 1 29 Apr 2016, 06:51
If x and y are both nonzero integers, is 25% of xy greater than x? 2 06 Mar 2016, 04:09
46 If x and y are nonzero integers, is x^y < y^x ? 14 24 Jan 2017, 00:11
6 If x and y are nonzero integers, is x/y an integer? 8 26 Oct 2016, 10:07
Display posts from previous: Sort by

# If x and y are nonzero integers, is x^y<y^x?

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO 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®.