Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 65785

If x and y are positive integers, is xy even?
[#permalink]
Show Tags
26 Jun 2017, 01:43
Question Stats:
75% (01:40) correct 25% (01:51) wrong based on 1424 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11394
Location: United States (CA)

Re: If x and y are positive integers, is xy even?
[#permalink]
Show Tags
30 Jul 2017, 16:31
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
_________________
★
★
★
★
★
250 REVIEWS
5STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE
NOW WITH GMAT VERBAL (BETA)
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews




Intern
Joined: 26 Feb 2017
Posts: 3

Re: If x and y are positive integers, is xy even?
[#permalink]
Show Tags
26 Jun 2017, 01:54
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




Intern
Joined: 27 May 2017
Posts: 12

Re: If x and y are positive integers, is xy even?
[#permalink]
Show Tags
Updated on: 25 Jul 2017, 03:36
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 SMG935F using GMAT Club Forum mobile app
Originally posted by Ejiroosa on 26 Jun 2017, 01:50.
Last edited by Ejiroosa on 25 Jul 2017, 03:36, edited 1 time in total.



Director
Joined: 04 Dec 2015
Posts: 723
Location: India
Concentration: Technology, Strategy
Schools: HEC Sept19 intake, ISB '19, Rotman '21, NUS '21, IIMA , IIMB, NTU '20, Bocconi '21, XLRI, Trinity MBA '20, Smurfit "21
WE: Information Technology (Consulting)

If x and y are positive integers, is xy even?
[#permalink]
Show Tags
26 Jun 2017, 01:59
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
Joined: 19 Mar 2014
Posts: 904
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5

Re: If x and y are positive integers, is xy even?
[#permalink]
Show Tags
26 Jun 2017, 02:07
If x and y are positive integers, is \(xy\)even? (1) \(x^2 + y^2 − 1\) is divisible by 4This means that either x or y has to be odd. As you know ODD * EVEN = EVENQuestion  Is xy EVEN ? is TRUE =====> Eq. (1) SUFFICIENT(2) \(x + y\) is oddAs we know, ODD + EVEN = ODDAnd ODD * EVEN = EVENQuestion  Is xy EVEN ? is TRUE =====> Eq. (2) SUFFICIENTHence, 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/howtoget60awamyguide64327.html#p470475



Intern
Joined: 27 May 2017
Posts: 12

Re: If x and y are positive integers, is xy even?
[#permalink]
Show Tags
26 Jun 2017, 03:30
Ans is D used 5 instead of 4.... Sent from my SMG935F using GMAT Club Forum mobile app



Director
Joined: 12 Nov 2016
Posts: 663
Location: United States
GPA: 2.66

Re: If x and y are positive integers, is xy even?
[#permalink]
Show Tags
17 Jul 2017, 21:45
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



IIMA, IIMC School Moderator
Joined: 04 Sep 2016
Posts: 1428
Location: India
WE: Engineering (Other)

If x and y are positive integers, is xy even?
[#permalink]
Show Tags
13 Mar 2018, 20:18
Bunuel pushpitkc niks18 HatakekakashiamanvermagmatHow 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. Feeling stressed, you are not alone!!



Retired Moderator
Joined: 21 Aug 2013
Posts: 1355
Location: India

Re: If x and y are positive integers, is xy even?
[#permalink]
Show Tags
13 Mar 2018, 20:54
adkikani wrote: Bunuel pushpitkc niks18 HatakekakashiamanvermagmatHow 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



Current Student
Joined: 07 Jan 2016
Posts: 1082
Location: India

Re: If x and y are positive integers, is xy even?
[#permalink]
Show Tags
13 Mar 2018, 23:21
adkikani wrote: Bunuel pushpitkc niks18 HatakekakashiamanvermagmatHow 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)



Senior Manager
Status: Student
Joined: 14 Jul 2019
Posts: 438
Location: United States
Concentration: Accounting, Finance
GPA: 3.9
WE: Education (Accounting)

Re: If x and y are positive integers, is xy even?
[#permalink]
Show Tags
06 Apr 2020, 15:33
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 is odd. So, one of x and y will be even which will make xy even Sufficient 2) same as 1. Sufficient. D is the answer.



GMAT Club Legend
Status: GMAT/GRE Tutor l Admission Consultant l OnDemand Course creator l A learner forever :)
Joined: 08 Jul 2010
Posts: 4512
Location: India
GMAT: QUANT EXPERT
WE: Education (Education)

Re: If x and y are positive integers, is xy even?
[#permalink]
Show Tags
07 Apr 2020, 00:19
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. Question: Is x*y even?STatement 1: x^2 + y^2 − 1 = 4ai.e. x^2 + y^2 = 4a + 1 = ODD i.e. one of x and y must be even and other must be odd i.e. x*y = even SUFFICIENT Statement 2: x + y = oddi.e. one of x and y must be even and other must be odd SUFFICIENT ANswer: Option D
_________________



Manager
Status: When going gets tough, tough gets going_GMAT2020
Joined: 05 Feb 2020
Posts: 79
Location: India
Concentration: Finance, Entrepreneurship
WE: Engineering (Military & Defense)

Re: If x and y are positive integers, is xy even?
[#permalink]
Show Tags
21 Apr 2020, 03:28
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. **************** x,y>0 , is xy even? xy can be even when x and y both are even or either x or y is even (1) x^2 + y^2 − 1 is divisible by 4, therefore, x^2 + y^2 − 1=4I (I is an integer) x^2 + y^2 =4I+ 1 ( can you correlate it with 2n+1) for x^2 + y^2 to be odd, both x and y should be odd. Odd*Odd=Odd Sufficient. (2) x + y is odd (Refer above). Sufficient. Answer is D
_________________
*************Krishh******************* It's all about dreams because they are free... *************************************




Re: If x and y are positive integers, is xy even?
[#permalink]
21 Apr 2020, 03:28




