Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 05 Feb 2016, 14:18

### 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?

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Manager
Joined: 03 Oct 2009
Posts: 62
Followers: 0

Kudos [?]: 68 [2] , given: 8

If x and y are both integers, which is larger, x^x or y^y? [#permalink]  18 Feb 2012, 08:33
2
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

51% (01:53) correct 49% (00:57) wrong based on 35 sessions
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
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 5

Kudos [?]: 107 [2] , given: 10

Re: Which is larger, x^x or y^y? [#permalink]  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: 31223
Followers: 5341

Kudos [?]: 62011 [0], given: 9426

Re: Which is larger, x^x or y^y? [#permalink]  18 Feb 2012, 11:08
Expert's post
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
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 5

Kudos [?]: 107 [0], given: 10

Re: If x and y are both integers, which is larger, x^x or y^y? [#permalink]  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 [?]: 68 [0], given: 8

Exponents [#permalink]  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: 16

Kudos [?]: 164 [0], given: 59

Re: Exponents [#permalink]  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+++

-----------------------------
Quant Notes consolidated: consolodited-quant-guides-of-forum-most-helpful-in-preps-151067.html#p1217652

My GMAT journey begins: my-gmat-journey-begins-122251.html

Moderator
Joined: 10 May 2010
Posts: 823
Followers: 25

Kudos [?]: 368 [0], given: 192

Re: Exponents [#permalink]  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: 2036
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 39

Kudos [?]: 432 [0], given: 355

Re: Which is larger, x^x or y^y? [#permalink]  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 If x and y are both integers, which is larger, x^x or y^y? 6 26 Aug 2011, 15:09
8 If both x and y are positive integers that are divisible by 15 26 Aug 2011, 01:16
1 If x and y are both integers, which is larger, x^x or y^y? 7 23 Jul 2011, 01:25
3 Given that both x and y are positive integers, and that y = 4 17 Jun 2011, 06:12
If denotes a mathematical operation, does x y=y x for all x 3 01 Apr 2010, 11:33
Display posts from previous: Sort by

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

 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®.