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

It is currently 29 Jul 2015, 06:02
GMAT Club Tests

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 positive integers, is x^2*y^2 even ? (1) x +

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Senior Manager
Senior Manager
avatar
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 328
Followers: 1

Kudos [?]: 147 [1] , given: 193

If x and y are positive integers, is x^2*y^2 even ? (1) x + [#permalink] New post 19 Oct 2010, 09:23
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

50% (02:11) correct 50% (01:05) wrong based on 32 sessions
If x and y are positive integers, is x^2*y^2 even ?

(1) x + 5 is a prime number

(2) y + 1 is a prime number
[Reveal] Spoiler: OA

_________________

I'm the Dumbest of All !!


Last edited by Bunuel on 20 Oct 2010, 12:47, edited 1 time in total.
Edited the stem.
Current Student
avatar
Joined: 29 Sep 2010
Posts: 13
Schools: IMD '16 (A)
GMAT 1: 730 Q47 V44
Followers: 0

Kudos [?]: 5 [0], given: 1

Re: Number properties [#permalink] New post 19 Oct 2010, 09:36
A for me.

First off, an even number squared will give an even number(2^2 = 4, 4^2 = 16 etc). An odd number squared will give an odd number (3^2 = 9, 5^2 = 25 etc). Also, for the multiplication between two numbers to come out even, at least one of the numbers must be even.

We know all primes except for 2 are odd. Since x and y are positive, the only way for x + 5 to be prime will be if x is even (i.e. if x = 1 then x + 5 = 6 which is not prime. But if x = 2 then x + 5 = 7 which is prime). Therefore, x^2 will also be even and x^2y^2 will also be even regardless of what y is. statement 1 is sufficient.

Using a similar approach for condition 2, we can set y = 1 (y + 1 = 2 which is prime) or y = 2 (y + 2 = 3 which is also prime). So we see with this condition, y can be both even or odd. So statement 2 alone is not sufficient.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28751
Followers: 4583

Kudos [?]: 47233 [0], given: 7115

Re: Number properties [#permalink] New post 19 Oct 2010, 09:37
Expert's post
shrive555 wrote:
If x and y are positive integers, is x2y2 even ?

(1) x + 5 is a prime number

(2) y + 1 is a prime number


In order \(x^2y^2\) to be even at least one of the unknowns must be even.

(1) \(x+5=prime\) --> as \(x\) is a positive integer then this prime can not be the only even prime 2 (in this case \(x+5=2\) --> \(x=-3=negative\)), so \(x+5=prime=odd\) --> \(x=odd-5=odd-odd=even\). Sufficient.

(2) y + 1 is a prime number --> \(y\) could be 1, so odd, and we won't be sure whether \(x^2y^2=even\) or \(y\) could be even (for example 2) and then \(x^2y^2=even\). Not sufficient.

Answer: A.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Current Student
User avatar
Joined: 15 Jul 2010
Posts: 259
GMAT 1: 750 Q49 V42
Followers: 7

Kudos [?]: 110 [0], given: 65

Re: Number properties [#permalink] New post 20 Oct 2010, 12:45
A.

Kind of trivial but I was staring at x2y2 for 20 seconds.

edit it to x^2y^2 for others maybe?
_________________

Consider KUDOS if my post was helpful. :-D

My Debrief: 750-q49v42-105591.html#p825487

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5679
Followers: 321

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

Premium Member
Re: If x and y are positive integers, is x^2*y^2 even ? (1) x + [#permalink] New post 12 Apr 2015, 20:20
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If x and y are positive integers, is x^2*y^2 even ? (1) x +   [#permalink] 12 Apr 2015, 20:20
    Similar topics Author Replies Last post
Similar
Topics:
6 Experts publish their posts in the topic If x is a positive integer, is (x^2 + y^2)^1/2 an integer? Bunuel 5 24 Mar 2015, 03:30
3 Experts publish their posts in the topic If x and y are positive integers such that x^2+y^2 is a prim mun23 3 27 Feb 2013, 13:19
What is the value of x^2 + y^2? 1) x^2 + y^2 = 2xy + 1 2) youven 6 24 Jul 2010, 07:50
1 Experts publish their posts in the topic Is x^2 - y^2 divisible by 8? 1. x and y are even integers. study 16 07 Dec 2009, 02:15
7 Experts publish their posts in the topic Is x^2 – y^2 a positive number ? topmbaseeker 7 02 Oct 2008, 05:47
Display posts from previous: Sort by

If x and y are positive integers, is x^2*y^2 even ? (1) x +

  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®.