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

It is currently 28 Aug 2015, 16:31
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 integers, is xy even?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 21 Dec 2011
Posts: 21
Location: India
Concentration: Strategy, Leadership
GMAT 1: 680 Q V
GRE 1: 1330 Q720 V610
WE: Information Technology (Other)
Followers: 1

Kudos [?]: 5 [0], given: 6

GMAT ToolKit User CAT Tests
If x and y are integers, is xy even? [#permalink] New post 19 Aug 2012, 07:03
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

73% (01:46) correct 27% (00:51) wrong based on 526 sessions
If x and y are integers, is xy even?

(1) x = y + 1.
(2) x/y is an even integer.

[Reveal] Spoiler:
Official answer is that both these statements are independently sufficient (D), with the following explanations :-
(1)- since x and y are consecutive numbers, so one of these would be even and thus xy is also even.
(2) if the fraction is even, then it means x is even and hence xy is also even..

Here is my doubt...

I chose option (B), meaning (2) alone is sufficient but (1) is not.
Explanation: x and y are integers which means x could be 0 as well, in that case y will be 1, or x could be -1 and then y would be 0.
in both these cases the product xy will not be even.

Can someone please help me in clarifying this doubt!

TIA
[Reveal] Spoiler: OA

_________________

Everybody says I'm Fine!


Last edited by Bunuel on 13 Dec 2012, 05:03, edited 2 times in total.
Edited the question.
Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29100
Followers: 4724

Kudos [?]: 49662 [5] , given: 7400

Re: If x and Y are integers, is xy even? [#permalink] New post 19 Aug 2012, 07:27
5
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
If x and Y are integers, is xy even?

In order the product of two integers to be even either (or both) of them must be even. So, the question basically asks whether either x or y is even.

(1) x = y + 1. If x is odd then y is even and vise-versa. Sufficient.
(2) x/y is an even integer --> \(\frac{x}{y}=even\) --> \(x=y*even=even\). Sufficient.

Answer: D.

As for your doubt: if either x or y is zero, then xy=0=even, because zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

Hope it helps.
_________________

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

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29100
Followers: 4724

Kudos [?]: 49662 [1] , given: 7400

Re: If x and Y are integers, is xy even? [#permalink] New post 20 Apr 2013, 03:45
1
This post received
KUDOS
Expert's post
vicky4113 wrote:
Hi bunuel... what if y=-1 and x=0 in case 1 ?

Bunuel wrote:
If x and Y are integers, is xy even?

In order the product of two integers to be even either (or both) of them must be even. So, the question basically asks whether either x or y is even.

(1) x = y + 1. If x is odd then y is even and vise-versa. Sufficient.
(2) x/y is an even integer --> \(\frac{x}{y}=even\) --> \(x=y*even=even\). Sufficient.

Answer: D.

As for your doubt: if either x or y is zero, then xy=0=even, because zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

Hope it helps.


For (1) if y=-1 and x=0, then xy=0=even.

Zero is an even integer.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

Hope it's clear.
_________________

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

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29100
Followers: 4724

Kudos [?]: 49662 [1] , given: 7400

Re: If x and y are integers, is xy even? [#permalink] New post 13 Aug 2013, 23:36
1
This post received
KUDOS
Expert's post
pvaller1 wrote:
It is not explicitly mentioned that x cannot equal y!

In this case :

X/Y yields 1 and XY would therefore yield 1 -> an odd number

I would have expected an extra constraints saying that X doesn't equal Y to make it a 100% clear - or am I missing out something?


For (2) x/y cannot be 1, because (2) says that x/y is even and 1 is odd.

Does this make sense?
_________________

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

Intern
Intern
avatar
Joined: 21 Dec 2011
Posts: 21
Location: India
Concentration: Strategy, Leadership
GMAT 1: 680 Q V
GRE 1: 1330 Q720 V610
WE: Information Technology (Other)
Followers: 1

Kudos [?]: 5 [0], given: 6

GMAT ToolKit User CAT Tests
Re: If x and Y are integers, is xy even? [#permalink] New post 19 Aug 2012, 08:17
thank you Bunnel, this is what happens when you don't brush up your basics before preparing for quant!

I was not considering 0 as an even number.
_________________

Everybody says I'm Fine!

Intern
Intern
avatar
Joined: 14 Dec 2011
Posts: 7
GMAT 1: 670 Q49 V32
GMAT 2: 710 Q47 V41
Followers: 0

Kudos [?]: 0 [0], given: 52

Re: If x and Y are integers, is xy even? [#permalink] New post 19 Apr 2013, 10:35
Hi bunuel... what if y=-1 and x=0 in case 1 ?

Bunuel wrote:
If x and Y are integers, is xy even?

In order the product of two integers to be even either (or both) of them must be even. So, the question basically asks whether either x or y is even.

(1) x = y + 1. If x is odd then y is even and vise-versa. Sufficient.
(2) x/y is an even integer --> \(\frac{x}{y}=even\) --> \(x=y*even=even\). Sufficient.

Answer: D.

As for your doubt: if either x or y is zero, then xy=0=even, because zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

Hope it helps.
Intern
Intern
avatar
Joined: 05 Jun 2013
Posts: 4
Followers: 0

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

Re: If x and y are integers, is xy even? [#permalink] New post 13 Aug 2013, 12:47
It is not explicitly mentioned that x cannot equal y!

In this case :

X/Y yields 1 and XY would therefore yield 1 -> an odd number

I would have expected an extra constraints saying that X doesn't equal Y to make it a 100% clear - or am I missing out something?
Intern
Intern
avatar
Joined: 05 Jun 2013
Posts: 4
Followers: 0

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

Re: If x and y are integers, is xy even? [#permalink] New post 14 Aug 2013, 07:33
Bunuel wrote:
pvaller1 wrote:
It is not explicitly mentioned that x cannot equal y!

In this case :

X/Y yields 1 and XY would therefore yield 1 -> an odd number

I would have expected an extra constraints saying that X doesn't equal Y to make it a 100% clear - or am I missing out something?


For (2) x/y cannot be 1, because (2) says that x/y is even and 1 is odd.

Does this make sense?



Hi Bunuel - makes perfectly sense.. I somehow missed that it says even integer.
Thank you for your answer :)
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6096
Followers: 340

Kudos [?]: 68 [0], given: 0

Premium Member
Re: If x and y are integers, is xy even? [#permalink] New post 19 Aug 2014, 02:13
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

Intern
Intern
avatar
Joined: 25 Mar 2013
Posts: 1
Followers: 0

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

Re: If x and y are integers, is xy even? [#permalink] New post 27 Feb 2015, 15:30
Am I missing something? Part 2 says x/y is even. Odd / Odd is even. Even / Even is even. Even / Odd is also even (24/3=8). How can we be sure what x & y are?
Expert Post
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 3436
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 148

Kudos [?]: 925 [0], given: 56

Re: If x and y are integers, is xy even? [#permalink] New post 27 Feb 2015, 18:06
Expert's post
Hi hersheykitts,

You have to be careful with your 'generalizations' and Number Properties.

hersheykitts wrote:
Am I missing something? Part 2 says x/y is even. Odd / Odd is even. Even / Even is even. Even / Odd is also even (24/3=8). How can we be sure what x & y are?


First off, ODD/ODD is NOT an even.... it's either ODD or it's a non-integer (which means it's neither even nor odd)

Here are some examples:

3/3 = 1
9/3 = 3
7/5 = 1.4

In that same way, EVEN/EVEN is usually even or a non-integer....but COULD be odd (if the two evens are the SAME NUMBER)....

2/2 = 1
4/2 = 2
6/4 = 1.5

EVEN/ODD is either even or a non-integer....

2/1 = 2
12/3 = 4
4/3 = 1.33333

To answer your question, the prompt tells us that X and Y are integers and Fact 2 tells us that X/Y is an EVEN INTEGER. This means that AT LEAST one of the two variables is even....

4/1 = 4
6/3 = 2
4/2 = 2
Etc.

The question asks if XY is even. Since one or both of the variables will be even in this situation, the answer to the question is ALWAYS YES. Fact 2 is SUFFICIENT.

GMAT assassins aren't born, they're made,
Rich
_________________

Official Guide 2016 Question Breakdown:
http://gmatclub.com/forum/empowergmat-blog-198415.html#p1527977

Rich Cohen
Rich.C@empowergmat.com
http://www.empowergmat.com

GMAT Club Verified Reviews for EMPOWERgmat & Special Discount

EMPOWERgmat Podcast - A Wild Secret About The GMAT Algorithm


Re: If x and y are integers, is xy even?   [#permalink] 27 Feb 2015, 18:06
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic If x and y are integers, is xy even? mpcostello 5 19 Apr 2015, 10:32
1 Experts publish their posts in the topic If x is a positive integer, is (x+y) even? ananthpatri 4 05 Aug 2012, 22:02
4 Experts publish their posts in the topic if x and y are integers , is x an even integer a) x(y+5) anilnandyala 2 09 Jan 2011, 07:45
If x and y are integers, is xy even? 1) x=y+1 2) x/y is an mitzieee 2 22 Mar 2010, 01:54
6 If x and y are positive integers , is the product xy even krishan 3 29 Jan 2009, 04:47
Display posts from previous: Sort by

If x and y are integers, is xy even?

  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®.