NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 19:58 It is currently 23 Apr 2024, 19:58
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If x and y are integers and x y is odd, which of the following must

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618613 [24]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
If x and y are integers and x y is odd, which of the following must [#permalink] New post   30 Jul 2018, 00:26
5
Kudos
19
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

84% (01:13) correct 16% (01:22) wrong based on 1878 sessions
Hide Show timer Statistics
If x and y are integers and x − y is odd, which of the following must be true?

I. xy is even.
II. x^2 + y^2 is odd.
II. (x + y)^2 is even.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


(PS01120)
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
D
KSBGC
VP
VP
Joined: 31 Oct 2013
Posts: 1260
Own Kudos [?]: 1153 [5]
Given Kudos: 635
Concentration: Accounting, Finance
GPA: 3.68
WE:Analyst (Accounting)
Send PM
Re: If x and y are integers and x y is odd, which of the following must [#permalink] New post   30 Jul 2018, 01:08
3
Kudos
2
Bookmarks
Bunuel wrote:
If x and y are integers and x − y is odd, which of the following must be true?

I. xy is even.
II. x^2 + y^2 is odd.
II. (x + y)^2 is even.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


NEW question from GMAT® Quantitative Review 2019


(PS01120)


Given

x - y = odd

In this case either x or y must be even and another must be odd.

I. xy = even. True . (3*2)= 6

II.\(x^2 + y^2 = odd\). True. \((2)^2 + (3)^2 = 13\)

III. \((3+2)^2 = 25\) . False.

The best answer is D.
General Discussion
avatar
B
bhanu88
Intern
Intern
Joined: 22 Dec 2010
Posts: 11
Own Kudos [?]: 5 [1]
Given Kudos: 5
Location: India
Schools: Kellogg 1YR '20 (S)
GMAT 1: 750 Q49 V44
GPA: 3.7
Send PM
Re: If x and y are integers and x y is odd, which of the following must [#permalink] New post   30 Jul 2018, 01:12
1
Kudos
D...odd-even or even-odd is odd...
I. One is even so xy will be even
II. Odd+even is odd/ even +odd is odd
III... Odd+even is odd ...sqaure can't be even ..will be odd

Sent from my MI MAX 2 using GMAT Club Forum mobile app
User avatar
L
dave13
VP
VP
Joined: 09 Mar 2016
Posts: 1160
Own Kudos [?]: 1017 [0]
Given Kudos: 3851
Send PM
Re: If x and y are integers and x y is odd, which of the following must [#permalink] New post   30 Jul 2018, 02:55
Bunuel wrote:
If x and y are integers and x − y is odd, which of the following must be true?

I. xy is even.
II. x^2 + y^2 is odd.
II. (x + y)^2 is even.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


NEW question from GMAT® Quantitative Review 2019


(PS01120)



IMO D must be correct answer :-)

Let X = 7 and Y = 2

I. xy is even ( 7*2 = 14 ) correct :)

II. x^2 + y^2 is odd. \(7^2+2^2 = 53\) TRUE

II. (x + y)^2 is even. \((7+ 2)^2 = 49+4 =53\) FALSE

EDIT
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18753
Own Kudos [?]: 22041 [1]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: If x and y are integers and x y is odd, which of the following must [#permalink] New post   10 Aug 2018, 18:54
Expert Reply
Bunuel wrote:
If x and y are integers and x − y is odd, which of the following must be true?

I. xy is even.
II. x^2 + y^2 is odd.
II. (x + y)^2 is even.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III



The only way to get an odd sum or difference of two integers is if one integer is odd and the other integer is even. Since x - y is odd, then x is even and y is odd OR x is odd and y is even.

We recall that even x odd = even. Thus, xy must be even. Thus, Roman numeral I is true.

Since odd + even = odd, we see that x^2 + y^2 must be odd, and (x + y)^2 must be odd. Thus, Roman numeral II is true and Roman numeral III is false.

Answer: D
User avatar
G
Salsanousi
Senior Manager
Senior Manager
Joined: 19 Oct 2013
Posts: 412
Own Kudos [?]: 306 [0]
Given Kudos: 117
Location: Kuwait
GPA: 3.2
WE:Engineering (Real Estate)
Send PM
GMAT ToolKit User
Re: If x and y are integers and x y is odd, which of the following must [#permalink] New post   16 Oct 2018, 14:02
Bunuel wrote:
If x and y are integers and x − y is odd, which of the following must be true?

I. xy is even.
II. x^2 + y^2 is odd.
II. (x + y)^2 is even.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


NEW question from GMAT® Quantitative Review 2019


(PS01120)


Can be solved much faster and without any substitution if we know that even - odd = odd. From this we know that one number must be even. What applies to subtraction in terms of even/odd applies to addition.

even * odd = even

Having a power does not change whether the number is odd or even.

only I and II are true.
User avatar
S
TheGuyDangerous
Current Student
Joined: 10 Sep 2019
Posts: 137
Own Kudos [?]: 33 [0]
Given Kudos: 59
Location: India
Concentration: Social Entrepreneurship, Healthcare
Schools: Fuqua '24 (D) ISB '23 (A) Darden '24 (D) Johnson '24 (D) Kenan-Flagler '24 (I) McDonough '24 (S) Tepper '24 (S)
GMAT 1: 680 Q49 V33
GMAT 2: 720 Q50 V37
GRE 1: Q167 V159
GPA: 2.59
WE:Project Management (Non-Profit and Government)
Send PM
Reviews Badge
Re: If x and y are integers and x y is odd, which of the following must [#permalink] New post   25 Nov 2019, 04:59
Input numbers 3&2 and 5&2.

Smash D
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16831 [0]
Given Kudos: 165
Send PM
Re: If x and y are integers and x y is odd, which of the following must [#permalink] New post   25 Nov 2019, 20:24
Expert Reply
Given
    • x and y are integers and x − y is odd
      o One of x and y is even and another is odd.

To find
    • The correct option.

Approach and Working out

I – xy is even
    • Multiplication of one even and one integer is always even.

II - x^2 + y^2 is odd.
    • Even ^2 + Odd^2 = Even + Odd = Odd

III - (x + y)^2 is even.
    • Odd^2 = Odd
    • Not true

Thus, option D is the correct answer.

Correct Answer: Option D
avatar
B
perryzhu
Intern
Intern
Joined: 14 Mar 2020
Posts: 1
Own Kudos [?]: 2 [2]
Given Kudos: 0
Send PM
Re: If x and y are integers and x y is odd, which of the following must [#permalink] New post   26 May 2020, 16:47
2
Kudos
EgmatQuantExpert wrote:
Given
    • x and y are integers and x − y is odd
      o One of x and y is even and another is odd.

To find
    • The correct option.

Approach and Working out

I – xy is even
    • Multiplication of one even and one integer is always even.

II - x^2 + y^2 is odd.
    • Even ^2 + Odd^2 = Even + Odd = Odd

III - (x + y)^2 is even.
    • Odd^2 = Odd
    • Not true

Thus, option D is the correct answer.

Correct Answer: Option D



Hi Payal

why don't we need to consider 0 here? it is an integer right?

3-0=3 but 3x0=0 is not even.
User avatar
G
Basshead
Director
Director
Joined: 09 Jan 2020
Posts: 967
Own Kudos [?]: 223 [0]
Given Kudos: 434
Location: United States
Send PM
Re: If x and y are integers and x y is odd, which of the following must [#permalink] New post   06 Nov 2020, 19:34
\(\)If x and y are integers and x − y is odd, which of the following must be true?

For x - y to be odd, x and y must be odd/even or even/odd.

I. \(xy\) is even. -- MUST BE TRUE
II. \(x^2 + y^2\) is odd. -- MUST BE TRUE
II. \((x + y)^2\) is even. -- FALSE

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

Answer is D.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32632
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: If x and y are integers and x y is odd, which of the following must [#permalink] New post   06 Nov 2023, 21:26
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 Bot
gmatclubot
Re: If x and y are integers and x y is odd, which of the following must [#permalink]
06 Nov 2023, 21:26
Moderators:
Bunuel
Math Expert
92883 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions