If x and y are both integers, which is larger, x^x or y^y? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 04:08

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 both integers, which is larger, x^x or y^y?

Author Message
TAGS:

Hide Tags

Manager
Joined: 03 Oct 2009
Posts: 62
Followers: 0

Kudos [?]: 101 [2] , given: 8

If x and y are both integers, which is larger, x^x or y^y? [#permalink]

Show Tags

18 Feb 2012, 08:33
2
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

54% (01:56) correct 46% (00:57) wrong based on 37 sessions

HideShow timer Statistics

If x and y are both integers, which is larger, x^x or y^y?

(1) x = y + 1
(2) x^y > x and x is positive.
[Reveal] Spoiler: OA
Manager
Status: Employed
Joined: 17 Nov 2011
Posts: 100
Location: Pakistan
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 7

Kudos [?]: 136 [2] , given: 10

Re: Which is larger, x^x or y^y? [#permalink]

Show Tags

18 Feb 2012, 10:38
2
KUDOS
Answer should be C. Here is how:

If $$x$$ and $$y$$ are both integers, which is larger, $$x^x$$ or $$y^y$$ ?

Statement A: $$x=y+1$$

So $$x$$ and $$y$$ are consecutive integers. Remember they can be positive, negative or $$0$$ (from the question stem).

Suppose $$y=1$$ and $$x=2$$ , then $$x^x$$ is larger , but suppose $$y=-2$$ and $$x =-1$$ then $$y^y$$ is larger.

Hence Insufficient.

Statement B: $$x^y>x$$ and $$x$$ is positive.

Knowing that $$x>0$$, $$x^y>x$$ is only possible if $$y>1$$ . Please note even when $$y=0$$ , $$x>0$$ and $$x$$ is an integer. So now we know that $$y$$ is positive and $$x$$ is positive but we do not know which is larger. Hence Insufficient

Combined:

From Statement 2 we know that $$x$$ and $$y$$ are both $$>0$$ and from Statement 1 we know that $$x$$ is bigger. So YES. $$x^x$$ is bigger than $$y^y$$

Sufficient. Hence Answer C . Seriously Kudos Hungry
_________________

"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde

Math Expert
Joined: 02 Sep 2009
Posts: 36625
Followers: 7104

Kudos [?]: 93624 [0], given: 10583

Re: Which is larger, x^x or y^y? [#permalink]

Show Tags

18 Feb 2012, 11:08
omerrauf wrote:
Answer should be C. Here is how:

If $$x$$ and $$y$$ are both integers, which is larger, $$x^x$$ or $$y^y$$ ?

Statement A: $$x=y+1$$

So $$x$$ and $$y$$ are consecutive integers. Remember they can be positive, negative or $$0$$ (from the question stem).

Suppose $$y=1$$ and $$x=2$$ , then $$x^x$$ is larger , but suppose $$y=-2$$ and $$x =-1$$ then $$y^y$$ is larger.

Hence Insufficient.

Statement B: $$x^y>x$$ and $$x$$ is positive.

Let's re-arrage this a bit.

$$x^y>x$$ so $$x^y-x>0$$ so x*(y-1)>0 and we know that x is +ve
Now in order for $$x*(y-1)>0$$ the factor $$(y-1)$$ has to be $$>0$$ so we know that $$y>1$$ but we do not know which is bigger, $$x$$ or $$y$$.

Hence Insufficient

Combined:

From Statement 2 we know that $$x$$ and $$y$$ are both $$>0$$ and from Statement 1 we know that x is bigger. So YES. $$x^x$$ is bigger than $$y^y$$

Sufficient. Hence Answer C Seriously Kudos Hungry

The red part is not correct.

If x and y are both integers, which is larger, x^x or y^y?

(1) x = y + 1 --> if $$y$$ is positive integer then $$x^x=(y+1)^{y+1}>y^y$$ but if $$y=-2$$ then $$x=-1$$ and $$x^x=-1<\frac{1}{4}=y^y$$

(2) x^y > x and x is positive --> since $$x$$ is positive then $$x^{y-1}>1$$ --> since $$x$$ and $$y$$ are integers then $$y>1$$. If $$x=1$$ and $$y=2$$ then $$x^x<y^y$$ but if $$x=3$$ and $$y=2$$ then $$x^x>y^y$$. Not sufficient.

(1)+(2) From (2) $$y>1$$, so it's a positive integer then from (1) $$x^x=(y+1)^{y+1}>y^y$$. Sufficient.

P.S. Not a GMAT style question.
_________________
Manager
Status: Employed
Joined: 17 Nov 2011
Posts: 100
Location: Pakistan
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 7

Kudos [?]: 136 [0], given: 10

Re: If x and y are both integers, which is larger, x^x or y^y? [#permalink]

Show Tags

18 Feb 2012, 20:05
Had already corrected that before you wrote bunuel. While writing the solution I mistakenly took $$x^y-x$$ for $$xy-x$$ but corrected it when i was reading my solution after I had posted. Thankyou anyways!
_________________

"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde

Manager
Joined: 03 Oct 2009
Posts: 62
Followers: 0

Kudos [?]: 101 [0], given: 8

Show Tags

04 Mar 2012, 09:15
If x and y are both integers, which is larger, x^x or y^y?

x = y + 1
x^y > x and x is positive.
Senior Manager
Joined: 23 Mar 2011
Posts: 473
Location: India
GPA: 2.5
WE: Operations (Hospitality and Tourism)
Followers: 20

Kudos [?]: 216 [0], given: 59

Show Tags

04 Mar 2012, 09:43
St 1:
x=y+1
eg; y=2; then x= 2+1 = 3
then 3^3 > 2^2

y=-3 then x= -3+1 = -2
then -2^-2 > -3^-3

Sufficient

St 2:
x^y>x

eg; x = 2 y = 3 then x^y>x

Thus, x^x < y^y

However, if x = 4 and y = 3 then also x^y> x
But, x^x > y^y

Not sufficient

ANS: A

I dont know if this is the best approach.
_________________

"When the going gets tough, the tough gets going!"

Bring ON SOME KUDOS MATES+++

-----------------------------

My GMAT journey begins: http://gmatclub.com/forum/my-gmat-journey-begins-122251.html

Moderator
Joined: 10 May 2010
Posts: 825
Followers: 24

Kudos [?]: 401 [0], given: 192

Show Tags

04 Mar 2012, 12:34
http://www.platinumgmat.com/practice_gm ... on_id=2197
_________________

The question is not can you rise up to iconic! The real question is will you ?

Current Student
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 62

Kudos [?]: 594 [0], given: 355

Re: Which is larger, x^x or y^y? [#permalink]

Show Tags

27 Dec 2013, 09:09
Bunuel wrote:
omerrauf wrote:
Answer should be C. Here is how:

If $$x$$ and $$y$$ are both integers, which is larger, $$x^x$$ or $$y^y$$ ?

Statement A: $$x=y+1$$

So $$x$$ and $$y$$ are consecutive integers. Remember they can be positive, negative or $$0$$ (from the question stem).

Suppose $$y=1$$ and $$x=2$$ , then $$x^x$$ is larger , but suppose $$y=-2$$ and $$x =-1$$ then $$y^y$$ is larger.

Hence Insufficient.

Statement B: $$x^y>x$$ and $$x$$ is positive.

Let's re-arrage this a bit.

$$x^y>x$$ so $$x^y-x>0$$ so x*(y-1)>0 and we know that x is +ve
Now in order for $$x*(y-1)>0$$ the factor $$(y-1)$$ has to be $$>0$$ so we know that $$y>1$$ but we do not know which is bigger, $$x$$ or $$y$$.

Hence Insufficient

Combined:

From Statement 2 we know that $$x$$ and $$y$$ are both $$>0$$ and from Statement 1 we know that x is bigger. So YES. $$x^x$$ is bigger than $$y^y$$

Sufficient. Hence Answer C Seriously Kudos Hungry

The red part is not correct.

If x and y are both integers, which is larger, x^x or y^y?

(1) x = y + 1 --> if $$y$$ is positive integer then $$x^x=(y+1)^{y+1}>y^y$$ but if $$y=-2$$ then $$x=-1$$ and $$x^x=-1<\frac{1}{4}=y^y$$

(2) x^y > x and x is positive --> since $$x$$ is positive then $$x^{y-1}>1$$ --> since $$x$$ and $$y$$ are integers then $$y>1$$. If $$x=1$$ and $$y=2$$ then $$x^x<y^y$$ but if $$x=3$$ and $$y=2$$ then $$x^x>y^y$$. Not sufficient.

(1)+(2) From (2) $$y>1$$, so it's a positive integer then from (1) $$x^x=(y+1)^{y+1}>y^y$$. Sufficient.

P.S. Not a GMAT style question.

Just curious, why not a GMAT style question?

Thanks

Cheers!
J
Re: Which is larger, x^x or y^y?   [#permalink] 27 Dec 2013, 09:09
Similar topics Replies Last post
Similar
Topics:
1 Are both x and y integers? 2 29 Nov 2016, 00:44
13 Is |x|/x > |y|/y? 6 19 May 2016, 21:35
1 If x and y are both integers, which is larger, x^x or y^y? 6 26 Aug 2011, 15:09
2 If x and y are both integers, which is larger, x^x or y^y? 7 23 Jul 2011, 01:25
10 Given that both x and y are positive integers, and that y = 5 17 Jun 2011, 06:12
Display posts from previous: Sort by