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

It is currently 14 Dec 2018, 09:55

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 in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Typical Day of a UCLA MBA Student - Recording of Webinar with UCLA Adcom and Student

     December 14, 2018

     December 14, 2018

     10:00 PM PST

     11:00 PM PST

    Carolyn and Brett - nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.
  • Free GMAT Strategy Webinar

     December 15, 2018

     December 15, 2018

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

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
Manager
User avatar
Joined: 24 Aug 2012
Posts: 116
Reviews Badge
If x and y are distinct positive integers  [#permalink]

Show Tags

New post 06 Nov 2012, 17:37
4
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (01:55) correct 40% (01:56) wrong based on 254 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

_________________

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

Intern
Intern
avatar
Status: wants to beat the gmat
Joined: 18 Jul 2012
Posts: 19
Location: United States
Re: If x and y are distinct positive integers  [#permalink]

Show Tags

New post 06 Nov 2012, 17:50
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

answer D
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51215
Re: If x and y are distinct positive integers  [#permalink]

Show Tags

New post 07 Nov 2012, 02:40
1
2
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.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Status: Studying
Joined: 09 Dec 2012
Posts: 26
Location: Russian Federation
Concentration: Finance, Strategy
GMAT Date: 04-06-2013
GPA: 3.6
WE: Consulting (Insurance)
GMAT ToolKit User
Re: If x and y are distinct positive integers  [#permalink]

Show Tags

New post 27 Apr 2013, 01:04
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?
MBA Section Director
User avatar
V
Affiliations: GMAT Club
Joined: 21 Feb 2012
Posts: 5886
City: Pune
GMAT ToolKit User Premium Member
Re: If x and y are distinct positive integers  [#permalink]

Show Tags

New post 13 Aug 2013, 07:50
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.
_________________

Chances of Getting Admitted After an Interview [Data Crunch]


Must Read Forum Topics Before You Kick Off Your MBA Application

New GMAT Club Decision Tracker - Real Time Decision Updates

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1721
Concentration: Finance
GMAT ToolKit User
Re: If x and y are distinct positive integers  [#permalink]

Show Tags

New post 21 Jan 2014, 06:26
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
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9159
Premium Member
Re: If x and y are distinct positive integers  [#permalink]

Show Tags

New post 03 Jul 2018, 19:14
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

GMAT Club Bot
Re: If x and y are distinct positive integers &nbs [#permalink] 03 Jul 2018, 19:14
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  


Copyright

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®.