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

It is currently 21 Jun 2018, 18:46

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

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

Hide Tags

1 KUDOS received
Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 514
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
If x and y are integers, does x^y * y^(-x) = 1? [#permalink]

Show Tags

New post Updated on: 31 Aug 2015, 00:27
1
1
10
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

34% (01:38) correct 66% (01:35) wrong based on 238 sessions

HideShow timer Statistics

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

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

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730


Originally posted by enigma123 on 02 Nov 2011, 15:14.
Last edited by Bunuel on 31 Aug 2015, 00:27, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
Manager
avatar
Joined: 29 Oct 2011
Posts: 166
Concentration: General Management, Technology
Schools: Sloan '16 (D)
GMAT 1: 760 Q49 V44
GPA: 3.76
Re: If x and y are integers, does x^y * y^(-x) = 1? [#permalink]

Show Tags

New post Updated on: 02 Nov 2011, 17:43
Original attempt (or as I would have done it on a GMAT never having seen this question before). For a more thorough solution see below.

First, rewrite the original equation. \(x^y*y^{-x}=1 -> (x^y)/(y^x)=1 -> x^y = y^x\)
I worked it using sample numbers.

Case (1): x=2, y=2 works in original equation
x = 2, y=1 does not work
Insufficient

Case (2): I couldn't quickly come up with 2 numbers that would satisfy the original equation so I assumed that it would be sufficient to say that the original equation will not be equal to 1. This is how I would guess on a GMAT.

I'd say B.

Originally posted by kostyan5 on 02 Nov 2011, 15:42.
Last edited by kostyan5 on 02 Nov 2011, 17:43, edited 3 times in total.
Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 514
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: If x and y are integers, does x^y * y^(-x) = 1? [#permalink]

Show Tags

New post 02 Nov 2011, 16:06
Sorry Kostyan - i am not very clear on the explanation on statement 2. can you please elaborate?
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Manager
Manager
avatar
Joined: 29 Oct 2011
Posts: 166
Concentration: General Management, Technology
Schools: Sloan '16 (D)
GMAT 1: 760 Q49 V44
GPA: 3.76
Re: If x and y are integers, does x^y * y^(-x) = 1? [#permalink]

Show Tags

New post 02 Nov 2011, 16:37
For B, I plugged in a few sets of numbers and all resulted in the original equation not holding true. Instead of wasting time trying to solve it, I decided to simulate the test conditions and simply assume that none of the numbers would work for the original equation. Therefore, B would be sufficient to say that the original equation will not hold true.

I will work out the actual solving at a later time.
Manager
Manager
avatar
Joined: 29 Oct 2011
Posts: 166
Concentration: General Management, Technology
Schools: Sloan '16 (D)
GMAT 1: 760 Q49 V44
GPA: 3.76
Re: If x and y are integers, does x^y * y^(-x) = 1? [#permalink]

Show Tags

New post 02 Nov 2011, 17:41
Continuing from previous post, the integer solutions to \(x^y=y^x\) are X=Y, (2,4), (4,2), (-2,-4), and (-4,-2).

(1) \(x^x>y\): It is possible to find solutions that both work for (1) and for original equation. It is also possible to find solutions that work for (1) but not for original equation. Therefore, (1) is insufficient to answer.

(2), \(x>y^y\): None of the solutions to the original equation work for (2). That means, given (2), there is no possible way to make the original equation work. Therefore, (2) is sufficient to answer whether \(x^y = y^x\), and that is NO.

So the answer to the question is B: (2) alone is sufficient and (1) is not sufficient.
1 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 1900
Re: If x and y are integers, does x^y * y^(-x) = 1? [#permalink]

Show Tags

New post 03 Nov 2011, 01:15
1
enigma123 wrote:
If x and y are integers, does x^y*y^-x=1

1. x^x>y
2. x>y^y


Guys - any idea the approach to solve this question please?


The above explanation is good enough. I'll just add some text to it.

Q: Is x^y=y^x

In other words:
Is x=y OR Is (x,y) any of the pairs: (2, 4), (4, 2), (-2, -4), (-4, -2)

1. x^x>y
Say (x,y)=(4,2)
x^x=4^4>2; Good. Answer to the question=Yes, x^y is equal to y^x as (x, y) is one of the mentioned pairs.

But say (x,y)=(5,2)
x^x=5^5>2; Good. Answer to the question=No

Not Sufficient.

2. x>y^y

Now,
We can definitely say that x NOT equal to Y.
Let's see whether they can be any of the mentioned pairs.
(x,y)=(2,4); No;
(x,y)=(4,2); No;
(x,y)=(-2,-4); No; as -2 < (-4)^(-4)
(x,y)=(-4,-2); No; as -4 < (-2)^(-2)

So, (x,y) is not one of the pairs that will make the expression true. So, we can definitely conclude that x^y*y^-x NOT equal to 1
A definite NO proves sufficiency.
Sufficient.

Ans: "B"
**********************************
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
avatar
Joined: 08 Sep 2011
Posts: 60
Concentration: Finance, Strategy
Re: If x and y are integers, does x^y * y^(-x) = 1? [#permalink]

Show Tags

New post 15 Nov 2011, 15:10
I got B. Because x>y^y than 2 and 4 or are not an option. Therefore by the fraction made by the negative exponent will not = 1 whether it is postive or negative. Good question took me 1:47 seconds, a little longer than I would like to spend on 600-700. kudos
Expert Post
6 KUDOS received
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India
If x and y are integers, does x^y * y^(-x) = 1? [#permalink]

Show Tags

New post 06 Jun 2012, 23:44
6
9
If x and y are integers, does x^y * y^(-x) = 1?

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

SOLUTION:

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).
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7013
Premium Member
Re: If x and y are integers, does x^y * y^(-x) = 1? [#permalink]

Show Tags

New post 28 Dec 2017, 22:47
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] 28 Dec 2017, 22:47
Display posts from previous: Sort by

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

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


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

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®.