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

It is currently 05 May 2015, 18:16

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x and y are integers, does x^y * y^(-x) = 1?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
3 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 5459
Location: Pune, India
Followers: 1336

Kudos [?]: 6795 [3] , given: 177

If x and y are integers, does x^y * y^(-x) = 1? [#permalink] New post 06 Jun 2012, 22:44
3
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

42% (02:14) correct 58% (01:22) wrong based on 34 sessions
If x and y are integers, does x^y * y^(-x) = 1?

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

SOLUTION:
[Reveal] Spoiler:
Let's re-arrange the question first:
Is \((x)^y * (y)^{-x} = 1\)?
Is \((x)^y = (y)^x\)?

Check this post for a detailed discussion on this: try-this-one-700-level-number-properties-103461.html#p805817

So, \((x)^y = (y)^x\) when x = y or x and y take values 2,4 or -2,-4

Look at the statements now:

(1) \((x)^x > y\)
We know this relation is true for many random values of x and y e.g. x = 4, y = 5 etc. So the answer to the question is NO in this case. \((x)^y\) is not equal to \((y)^x\).
But does it hold for any values which will make \((x)^y = (y)^x\)?
Yes it does! If x = y, x^x > y is true for say, x = y = 3. 3^3 is greater than 3. So x and y can take values which will give the answer YES.
Not sufficient.

(2) \(x > (y)^y\)
Again, it holds for many random values of x and y e.g. x = 10, y = 2 etc. So the answer to the question is NO in this case.
But does it hold for any values which will make \((x)^y = (y)^x\)?
Let's see. If x = y, x cannot be greater than \(y^y\). Check for a few values to figure out the pattern.
If x = 4 and y = 2, x is not greater than \(y^y\).
Similarly, it doesn't work for x = -2, y = -4 and x = -4 and y = -2 since x will be negative while y^y will be positive.
Therefore, if \(x > (y)^y\), \((x)^y = (y)^x\) cannot hold for any values of x and y. Hence answer to the question stays NO.
Sufficient.

Answer (B).
[Reveal] Spoiler: OA

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29!

Veritas Prep Reviews

Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
Senior Manager
Senior Manager
User avatar
Joined: 01 Nov 2010
Posts: 286
Location: India
Concentration: Technology, Marketing
GMAT Date: 08-27-2012
GPA: 3.8
WE: Marketing (Manufacturing)
Followers: 8

Kudos [?]: 61 [0], given: 43

Re: If x and y are integers, does x^y * y^(-x) = 1? [#permalink] New post 06 Jun 2012, 22:58
Thank you Karishma for such a detailed reply.

Thanks.
_________________

kudos me if you like my post.

Attitude determine everything.
all the best and God bless you.

Manager
Manager
User avatar
Affiliations: Project Management Professional (PMP)
Joined: 30 Jun 2011
Posts: 213
Location: New Delhi, India
Followers: 3

Kudos [?]: 36 [0], given: 12

Re: If x and y are integers, does x^y * y^(-x) = 1? [#permalink] New post 06 Jun 2012, 23:28
VeritasPrepKarishma wrote:
Responding to a pm:

Question: If x and y are integers, does (x)^y * (y)^-x = 1?

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

Let's re-arrange the question first:
Is \((x)^y * (y)^{-x} = 1\)?
Is \((x)^y = (y)^x\)?

Check this post for a detailed discussion on this: try-this-one-700-level-number-properties-103461.html#p805817

So, \((x)^y = (y)^x\) when x = y or x and y take values 2,4 or -2,-4

Look at the statements now:

(1) \((x)^x > y\)
We know this relation is true for many random values of x and y e.g. x = 4, y = 5 etc. So the answer to the question is NO in this case. \((x)^y\) is not equal to \((y)^x\).
But does it hold for any values which will make \((x)^y = (y)^x\)?
Yes it does! If x = y, x^x > y is true for say, x = y = 3. 3^3 is greater than 3. So x and y can take values which will give the answer YES.
Not sufficient.

(2) \(x > (y)^y\)
Again, it holds for many random values of x and y e.g. x = 10, y = 2 etc. So the answer to the question is NO in this case.
But does it hold for any values which will make \((x)^y = (y)^x\)?
Let's see. If x = y, x cannot be greater than \(y^y\). Check for a few values to figure out the pattern.
If x = 4 and y = 2, x is not greater than \(y^y\).
Similarly, it doesn't work for x = -2, y = -4 and x = -4 and y = -2 since x will be negative while y^y will be positive.
Therefore, if \(x > (y)^y\), \((x)^y = (y)^x\) cannot hold for any values of x and y. Hence answer to the question stays NO.
Sufficient.

Answer (B).

good Q.. thanks for the explanation...
_________________

Best
Vaibhav

If you found my contribution helpful, please click the +1 Kudos button on the left, Thanks

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 4781
Followers: 296

Kudos [?]: 52 [0], given: 0

Premium Member
Re: If x and y are integers, does x^y * y^(-x) = 1? [#permalink] New post 31 Jan 2015, 16:47
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If x and y are integers, does x^y * y^(-x) = 1?   [#permalink] 31 Jan 2015, 16:47
    Similar topics Author Replies Last post
Similar
Topics:
Is 1/(x-y) < (y-x) ? alphonsa 0 09 Aug 2014, 03:43
If X and Y are positive, is x/y +y/x >2 ? 1. X does not sondenso 8 14 May 2008, 01:06
Experts publish their posts in the topic If X and Y are positive, is X/Y + Y/X > 2? 1. x does not bmwhype2 7 21 Nov 2007, 06:00
If x and y are integers, does x^y . y^(-x) = 1? (1) x^x mm007 5 20 Dec 2006, 13:55
x and y are positive integers, is X^y <= Y^x? 1. X = y^2 M8 4 14 Aug 2006, 22:05
Display posts from previous: Sort by

If x and y are integers, does x^y * y^(-x) = 1?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.