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

It is currently 16 Oct 2018, 05:13

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

If x and y are positive integers, is xy even?

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49909
If x and y are positive integers, is xy even?  [#permalink]

Show Tags

New post 26 Jun 2017, 02:43
2
5
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

76% (01:40) correct 24% (01:48) wrong based on 440 sessions

HideShow timer Statistics

Intern
Intern
avatar
Joined: 27 May 2017
Posts: 12
Re: If x and y are positive integers, is xy even?  [#permalink]

Show Tags

New post Updated on: 25 Jul 2017, 04:36
1
Statement 1
X^2 +Y^2 - 1 is divisible by 4. can be 3^2 + 5^2 - 1 = 24 or 4^2 + 1^2 - 1 = 16 S
Statement 2. X+Y = odd. it has to be one even and one odd number. Suff

Ans D

Sent from my SM-G935F using GMAT Club Forum mobile app

Originally posted by Ejiroosa on 26 Jun 2017, 02:50.
Last edited by Ejiroosa on 25 Jul 2017, 04:36, edited 1 time in total.
Intern
Intern
avatar
B
Joined: 26 Feb 2017
Posts: 3
Re: If x and y are positive integers, is xy even?  [#permalink]

Show Tags

New post 26 Jun 2017, 02:54
1
x^2 + y^2 - 1 has to be even to be divisible by 4.
Hence x^2 + y^2 is odd.
This means either x or y has to be even. Statement 1 is sufficient.
Similarly for x+y to be odd, either x or y has to be even. Hence product xy is even.
Statement 2 is also sufficient.
Answer - D

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
Director
Director
User avatar
D
Joined: 04 Dec 2015
Posts: 701
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
GMAT ToolKit User
If x and y are positive integers, is xy even?  [#permalink]

Show Tags

New post 26 Jun 2017, 02:59
1
Bunuel wrote:
If x and y are positive integers, is xy even?

(1) x^2 + y^2 − 1 is divisible by 4.
(2) x + y is odd.


(1) \(x^2 + y^2 − 1\) is divisible by 4.

Let (\(x^2 + y^2\) ) be \(z\).

\(z - 1\) is divisible by \(4\).

Only even number is divisible by \(4\). Hence \(z - 1\) should be even.

Odd - Odd = Even.

Therefore \((x^2 - y^2)\) should be Odd. (\(Odd^2\) will be Odd. \(Even^2\) will be Even)

Even - Odd = Odd

Therefore either \(x\) or \(y\) should be even. Therefore \(xy\) will be even. I is Sufficient.

(2) \(x + y\) is odd.

Even + Odd = Odd.

Therefore either \(x\) or \(y\) should be even. Therefore \(xy\) will be even. II is Sufficient.

Answer (D)...
Retired Moderator
User avatar
P
Joined: 19 Mar 2014
Posts: 948
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
GMAT ToolKit User Premium Member
Re: If x and y are positive integers, is xy even?  [#permalink]

Show Tags

New post 26 Jun 2017, 03:07
1
If x and y are positive integers, is \(xy\)even?

(1) \(x^2 + y^2 − 1\) is divisible by 4

This means that either x or y has to be odd.

As you know ODD * EVEN = EVEN

Question - Is xy EVEN ? is TRUE =====> Eq. (1) SUFFICIENT

(2) \(x + y\) is odd

As we know, ODD + EVEN = ODD

And ODD * EVEN = EVEN

Question - Is xy EVEN ? is TRUE =====> Eq. (2) SUFFICIENT

Hence, the answer is D
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Intern
Intern
avatar
Joined: 27 May 2017
Posts: 12
Re: If x and y are positive integers, is xy even?  [#permalink]

Show Tags

New post 26 Jun 2017, 04:30
Ans is D used 5 instead of 4....

Sent from my SM-G935F using GMAT Club Forum mobile app
Director
Director
avatar
S
Joined: 12 Nov 2016
Posts: 749
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: If x and y are positive integers, is xy even?  [#permalink]

Show Tags

New post 17 Jul 2017, 22:45
Bunuel wrote:
If x and y are positive integers, is xy even?

(1) x^2 + y^2 − 1 is divisible by 4.
(2) x + y is odd.


St 1

(x^2 + y^2 − 1) /4 = some integer - therefore some odd number minus 1 is divisible by 4

x^2 + y^2= some odd number... in order for this to be true either X and Y must be some even and odd mix

(1)^2 +(2)^2= 5 odd

knowing x and y must be different ( even and odd) x and y must odd

St 2

Even + Odd = Odd so

Suff

D
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3825
Location: United States (CA)
Re: If x and y are positive integers, is xy even?  [#permalink]

Show Tags

New post 30 Jul 2017, 17:31
Bunuel wrote:
If x and y are positive integers, is xy even?

(1) x^2 + y^2 − 1 is divisible by 4.
(2) x + y is odd.


We need to determine whether the product of x and y is even.

Statement One Alone:

x^2 + y^2 − 1 is divisible by 4.

Since 4 is an even number, we need x^2 + y^2 − 1 to be even. In order for x^2 + y^2 − 1 to be even, we need x^2 + y^2 to be odd. If the sum of two squares is odd, one of them must be odd and the other must be even. This means that either x = odd and y = even OR x = even and y = odd. In either case, the product of x and y will be even. Statement one alone is sufficient to answer the question.

Statement Two Alone:

x + y is odd.

Since x + y = odd, either x = odd and y = even OR x = even and y = odd. In either case, the product of x and y will be even. Statement two alone is sufficient to answer the question.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Study Buddy Forum Moderator
User avatar
D
Joined: 04 Sep 2016
Posts: 1207
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
If x and y are positive integers, is xy even?  [#permalink]

Show Tags

New post 13 Mar 2018, 21:18
Bunuel pushpitkc niks18 Hatakekakashi
amanvermagmat

How about this approach?

\(x^2\) + \(y^2\) - 1 = 4 *(m) where m is an integer since there is no remainder (given)

or

\(x^2\) + \(y^2\) = odd

or

x + y = odd (a positive odd / even no when squared will give odd and even values respectively)

This is only possible when either of x or y is odd.

Does that help to make St 1 suff?
_________________

It's the journey that brings us happiness not the destination.

DS Forum Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1348
Location: India
Premium Member
Re: If x and y are positive integers, is xy even?  [#permalink]

Show Tags

New post 13 Mar 2018, 21:54
1
adkikani wrote:
Bunuel pushpitkc niks18 Hatakekakashi
amanvermagmat

How about this approach?

\(x^2\) + \(y^2\) - 1 = 4 *(m) where m is an integer since there is no remainder (given)

or

\(x^2\) + \(y^2\) = odd

or

x + y = odd (a positive odd / even no when squared will give odd and even values respectively)

This is only possible when either of x or y is odd.

Does that help to make St 1 suff?


Hello

yes i think this approach is correct
BSchool Forum Moderator
User avatar
G
Joined: 07 Jan 2016
Posts: 760
Location: India
Schools: ISB '20 (II)
GMAT 1: 710 Q49 V36
Reviews Badge
Re: If x and y are positive integers, is xy even?  [#permalink]

Show Tags

New post 14 Mar 2018, 00:21
adkikani wrote:
Bunuel pushpitkc niks18 Hatakekakashi
amanvermagmat

How about this approach?

\(x^2\) + \(y^2\) - 1 = 4 *(m) where m is an integer since there is no remainder (given)

or

\(x^2\) + \(y^2\) = odd

or

x + y = odd (a positive odd / even no when squared will give odd and even values respectively)

This is only possible when either of x or y is odd.

Does that help to make St 1 suff?


this approach is correct :)

good usage of basic concepts (Y)
GMAT Club Bot
Re: If x and y are positive integers, is xy even? &nbs [#permalink] 14 Mar 2018, 00:21
Display posts from previous: Sort by

If x and y are positive integers, is xy even?

  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®.