It is currently 18 Oct 2017, 07:55

# Live Now:

### 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 distinct positive integers

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

### Hide Tags

Manager
Joined: 24 Aug 2012
Posts: 140

Kudos [?]: 275 [0], given: 2

If x and y are distinct positive integers [#permalink]

### Show Tags

06 Nov 2012, 18:37
2
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:24) correct 41% (01:18) wrong based on 205 sessions

### HideShow timer Statistics

If x and y are distinct positive integers, what is the value of x^4 - y^4?

(1) (y^2 + x^2)(y + x)(x - y) = 240
(2) x^y = y^x and x > y
[Reveal] Spoiler: OA

_________________

Push +1 kudos button please, if you like my post

Kudos [?]: 275 [0], given: 2

Intern
Status: wants to beat the gmat
Joined: 18 Jul 2012
Posts: 20

Kudos [?]: 9 [0], given: 1

Location: United States
Re: If x and y are distinct positive integers [#permalink]

### Show Tags

06 Nov 2012, 18:50
1. sufficient b/c doing the algebra, comes out to be x^4 - y^4 = 240.
2. sufficient b/c only case this works is when x = 4 and y = 2
4^2 = 2^4

Kudos [?]: 9 [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128720 [1], given: 12182

Re: If x and y are distinct positive integers [#permalink]

### Show Tags

07 Nov 2012, 03:40
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
If x and y are distinct positive integers, what is the value of x^4 - y^4?

(1) (y^2 + x^2)(y + x)(x - y) = 240 --> $$(x^2 +y^2)(x^2 - y^2) = 240$$ --> $$x^4-y^4= 240$$. Sufficient.

(2) x^y = y^x and x > y. With trial and error we can find that, since x and y are positive integers and x>y, then x=4 and y=2. Sufficient.

_________________

Kudos [?]: 128720 [1], given: 12182

Intern
Status: Studying
Joined: 09 Dec 2012
Posts: 27

Kudos [?]: 34 [0], given: 1

Location: Russian Federation
Concentration: Finance, Strategy
GMAT Date: 04-06-2013
GPA: 3.6
WE: Consulting (Insurance)
Re: If x and y are distinct positive integers [#permalink]

### Show Tags

27 Apr 2013, 02:04
bunuel

ok, 1 is pretty much understandable, but for 2, how do you get there? what is the mind process here, in similar problems on the actual test, how do you get there in under 2 minutes? do you start just plugging the numbers in?

Kudos [?]: 34 [0], given: 1

MBA Section Director
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 4699

Kudos [?]: 3706 [0], given: 2420

Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
WE: Business Development (Manufacturing)
Re: If x and y are distinct positive integers [#permalink]

### Show Tags

13 Aug 2013, 08:50
lololol650 wrote:
bunuel

ok, 1 is pretty much understandable, but for 2, how do you get there? what is the mind process here, in similar problems on the actual test, how do you get there in under 2 minutes? do you start just plugging the numbers in?

Statement 2 is sufficient because, only one pair of integers that can satisfy the condition $$X^y = Y^x$$ is 4 and 2. $$(4^2 = 2^4)$$. So whenever you see such equation you can rest assured that one integer must be 4 and other one be 2.

Hope that helps.
_________________

Kudos [?]: 3706 [0], given: 2420

Current Student
Joined: 06 Sep 2013
Posts: 1978

Kudos [?]: 719 [0], given: 355

Concentration: Finance
Re: If x and y are distinct positive integers [#permalink]

### Show Tags

21 Jan 2014, 07:26
Narenn wrote:
lololol650 wrote:
bunuel

ok, 1 is pretty much understandable, but for 2, how do you get there? what is the mind process here, in similar problems on the actual test, how do you get there in under 2 minutes? do you start just plugging the numbers in?

Statement 2 is sufficient because, only one pair of integers that can satisfy the condition $$X^y = Y^x$$ is 4 and 2. $$(4^2 = 2^4)$$. So whenever you see such equation you can rest assured that one integer must be 4 and other one be 2.

Hope that helps.

Not really, they have to specify that such numbers must be positive integers otherwise one could have 4 combinations of 2 and 4

Kudos [?]: 719 [0], given: 355

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16707

Kudos [?]: 273 [0], given: 0

Re: If x and y are distinct positive integers [#permalink]

### Show Tags

24 Feb 2017, 05:22
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.
_________________

Kudos [?]: 273 [0], given: 0

Re: If x and y are distinct positive integers   [#permalink] 24 Feb 2017, 05:22
Display posts from previous: Sort by

# If x and y are distinct positive integers

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

 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®.