If x and y are distinct positive integers, what is the value : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 20 Jan 2017, 09:45

### 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, what is the value

Author Message
TAGS:

### Hide Tags

Intern
Joined: 19 Feb 2010
Posts: 10
Followers: 0

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

If x and y are distinct positive integers, what is the value [#permalink]

### Show Tags

18 Jul 2010, 07:11
11
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:30) correct 45% (01:25) wrong based on 389 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
Math Expert
Joined: 02 Sep 2009
Posts: 36582
Followers: 7086

Kudos [?]: 93266 [2] , given: 10555

### Show Tags

18 Jul 2010, 07:28
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
ankitmania wrote:
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. $$x^y = y^x and x > y$$

Important property to know: $$x^2-y^2=(x+y)(x-y)$$.

Given: $$x$$ and $$y$$ are distinct positive integers. Question: $$x^4-y^4=?$$

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

(2) $$x^y = y^x$$ and $$x>y$$, also $$x$$ and $$y$$ are distinct positive integers --> only one such pair is possible $$x=4>y=2$$: $$x^y=4^2=16=2^4=y^x$$ --> $$x^4-y^4=240$$. Sufficient.

_________________
Intern
Joined: 19 Dec 2009
Posts: 37
Followers: 0

Kudos [?]: 10 [0], given: 8

### Show Tags

18 Jul 2010, 08:33
Bunuel wrote:
only one such pair is possible $$x=4>y=2$$: $$x^y=4^2=16=2^4=y^x$$ --> $$x^4-y^4=240$$. Sufficient.

How do you come to this conclusion? Just picking numbers/knowing or is there some mathematical rule for this? I understand that it revolves around the power of 2, but can't put my finger on it.
Math Expert
Joined: 02 Sep 2009
Posts: 36582
Followers: 7086

Kudos [?]: 93266 [4] , given: 10555

### Show Tags

18 Jul 2010, 10:05
4
KUDOS
Expert's post
4
This post was
BOOKMARKED
Suvorov wrote:
Bunuel wrote:
only one such pair is possible $$x=4>y=2$$: $$x^y=4^2=16=2^4=y^x$$ --> $$x^4-y^4=240$$. Sufficient.

How do you come to this conclusion? Just picking numbers/knowing or is there some mathematical rule for this? I understand that it revolves around the power of 2, but can't put my finger on it.

I think it's worth remembering that $$4^2=16=2^4$$, I've seen several GMAT questions on number properties using this (another useful property $$8^2=4^3=2^6=64$$).

But if you don't know this property:

Given: $$x^y = y^x$$ and $$x>y$$, also $$x$$ and $$y$$ are distinct positive integers.
Couple of things:
$$x$$ and $$y$$ must be either distinct positive odd integers or distinct positive even integers (as odd in ANY positive integer power is odd and even in ANY positive integer power is even).

After testing several options you'll see that $$x=4$$ and $$y=2$$ is the only possible scenario: because, when $$y\geq{2}$$ and $$x>{4}$$, then $$x^y$$ (bigger value in smaller power) will be always less than $$y^x$$ (smaller value in bigger power): $$5^3<3^5$$, or $$6^2<2^6$$, or $$8^2<2^8$$, or $$10^2<2^{10}$$, ....
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13463
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If x and y are distinct positive integers, what is the value [#permalink]

### Show Tags

15 Oct 2013, 05:20
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 Club Legend
Joined: 09 Sep 2013
Posts: 13463
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If x and y are distinct positive integers, what is the value [#permalink]

### Show Tags

20 Nov 2014, 12:45
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.
_________________
Senior Manager
Joined: 01 Nov 2013
Posts: 357
GMAT 1: 690 Q45 V39
WE: General Management (Energy and Utilities)
Followers: 6

Kudos [?]: 166 [0], given: 403

Re: If x and y are distinct positive integers, what is the value [#permalink]

### Show Tags

10 Mar 2015, 01:46
Bunuel wrote:
Suvorov wrote:
Bunuel wrote:
only one such pair is possible $$x=4>y=2$$: $$x^y=4^2=16=2^4=y^x$$ --> $$x^4-y^4=240$$. Sufficient.

How do you come to this conclusion? Just picking numbers/knowing or is there some mathematical rule for this? I understand that it revolves around the power of 2, but can't put my finger on it.

I think it's worth remembering that $$4^2=16=2^4$$, I've seen several GMAT questions on number properties using this (another useful property $$8^2=4^3=2^6=64$$).

But if you don't know this property:

Given: $$x^y = y^x$$ and $$x>y$$, also $$x$$ and $$y$$ are distinct positive integers.
Couple of things:
$$x$$ and $$y$$ must be either distinct positive odd integers or distinct positive even integers (as odd in ANY positive integer power is odd and even in ANY positive integer power is even).

After testing several options you'll see that $$x=4$$ and $$y=2$$ is the only possible scenario: because, when $$y\geq{2}$$ and $$x>{4}$$, then $$x^y$$ (bigger value in smaller power) will be always less than $$y^x$$ (smaller value in bigger power): $$5^3<3^5$$, or $$6^2<2^6$$, or $$8^2<2^8$$, or $$10^2<2^{10}$$, ....

Want to solve a GMAT like problem using this property 8^2=4^3=2^6=64 ??? Do you have any in your arsenal??Pls share
_________________

Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time.

I hated every minute of training, but I said, 'Don't quit. Suffer now and live the rest of your life as a champion.-Mohammad Ali

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13463
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If x and y are distinct positive integers, what is the value [#permalink]

### Show Tags

19 Apr 2016, 04:06
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.
_________________
SVP
Joined: 17 Jul 2014
Posts: 2201
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '19 (S)
GMAT 1: 560 Q42 V26
GMAT 2: 550 Q39 V27
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Followers: 20

Kudos [?]: 270 [0], given: 140

Re: If x and y are distinct positive integers, what is the value [#permalink]

### Show Tags

10 Nov 2016, 15:36
ankitmania wrote:
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 $$x > y$$

$$x^4 - y^4$$
i started by factoring out...
this basically equals: $$(y^2 + x^2)(y + x)(x - y)$$

1. we are given the exact answer...sufficient.

2. we must have multiples of 2..otherwise it would not work..
i started with x=4 and y=2
4^2 = 2^4
2^4 = 2^4. works
tried few more options, don't work.

2 is sufficient.

Re: If x and y are distinct positive integers, what is the value   [#permalink] 10 Nov 2016, 15:36
Similar topics Replies Last post
Similar
Topics:
If x and y are positive integers, what is the value of x? 2 08 Jan 2017, 06:51
3 If x and y are distinct positive integers. . . 5 11 Nov 2016, 04:50
1 What is the value of X, if X and Y are two distinct integers and their 2 14 Mar 2016, 07:07
3 If x and y are distinct positive integers, what is the value of .... 1 10 Sep 2015, 14:00
If x and y are distinct positive integers 5 06 Nov 2012, 17:37
Display posts from previous: Sort by