It is currently 24 Jun 2017, 17:26

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x y, and z are integers and xy + z is an odd integer, is

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 07 Jan 2008
Posts: 289
If x y, and z are integers and xy + z is an odd integer, is [#permalink]

### Show Tags

22 May 2008, 06:26
3
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

47% (02:23) correct 53% (01:40) wrong based on 167 sessions

### HideShow timer Statistics

If x, y and z are integers and xy + z is an odd integer, is x an even integer?

(1) xy + xz is an even integer
(2) y + xz is an odd integer

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-y-and-z-are-integers-and-xy-z-is-an-odd-integer-is-81562.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Aug 2014, 04:07, edited 3 times in total.
Edited the question and added the OA.
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12
Re: If x y, and z are integers and xy + z is an odd integer, is [#permalink]

### Show Tags

22 May 2008, 06:33
question is missing is x or z or what is an integer??
Director
Joined: 23 Sep 2007
Posts: 783
Re: If x y, and z are integers and xy + z is an odd integer, is [#permalink]

### Show Tags

22 May 2008, 09:54
mbawaters wrote:
If x y, and z are integers and xy + z is an odd integer, is x an even integer?

1) xy + xz is an even integer.

2) y + xz is an odd integer.

** Edited **

I am 0 for 2 when answering this question. 7-t60544
CEO
Joined: 29 Mar 2007
Posts: 2559
Re: If x y, and z are integers and xy + z is an odd integer, is [#permalink]

### Show Tags

22 May 2008, 10:21
mbawaters wrote:
If x y, and z are integers and xy + z is an odd integer, is x an even integer?

1) xy + xz is an even integer.

2) y + xz is an odd integer.

** Edited **

I believe the answer is D.

I tried several numbers. Although im not proud of how long it took me.
Senior Manager
Joined: 19 Apr 2008
Posts: 316
Re: If x y, and z are integers and xy + z is an odd integer, is [#permalink]

### Show Tags

22 May 2008, 13:06
6
KUDOS
2
This post was
BOOKMARKED

you can represent any odd number by 2n+1 and even number by 2n , I have realized using this property helps me a lot in solving odd/even questions

First piece of infomation xy + z is odd so xy+z = 2n+1

1) xy + xz is an even integer.

re- write it as (xy+z)-z+xz = 2n+1 + z(x-1) = even ....since 2n+1 is odd ...the term z(x-1) must be odd and so (x-1) must be odd , this tells us that x must be even .

2) 2) y + xz is an odd integer.

re-write it as

y+(xy+z)-(xy+z)+xz = 2n+1 +(x-1)(z-y) = odd ...for this to be true (x-1)(z-y) must be even and so either (x-1) is even or (z-y) even or both are even ....insuff

I did this in less than a minute time ....
Intern
Joined: 26 Jul 2007
Posts: 32
Re: If x y, and z are integers and xy + z is an odd integer, is [#permalink]

### Show Tags

23 May 2008, 05:05
rpmodi wrote:

you can represent any odd number by 2n+1 and even number by 2n , I have realized using this property helps me a lot in solving odd/even questions

First piece of infomation xy + z is odd so xy+z = 2n+1

1) xy + xz is an even integer.

re- write it as (xy+z)-z+xz = 2n+1 + z(x-1) = even ....since 2n+1 is odd ...the term z(x-1) must be odd and so (x-1) must be odd , this tells us that x must be even .

2) 2) y + xz is an odd integer.

re-write it as

y+(xy+z)-(xy+z)+xz = 2n+1 +(x-1)(z-y) = odd ...for this to be true (x-1)(z-y) must be even and so either (x-1) is even or (z-y) even or both are even ....insuff

I did this in less than a minute time ....

Hello,

I tried also to use the same pattern but what i'm not sure about is this : so (x-1) must be odd in your explaining from stmt 1
Because if z(x-1) is odd, it doesn't necessarily lead to (x-1) odd ?
Senior Manager
Joined: 19 Apr 2008
Posts: 316
Re: If x y, and z are integers and xy + z is an odd integer, is [#permalink]

### Show Tags

25 May 2008, 08:41
Poullo , if product of two terms is odd , both the terms are odd .

try any combination ; if one of the number is even product will be even . HTH
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15956
Re: If x y, and z are integers and xy + z is an odd integer, is [#permalink]

### Show Tags

28 Aug 2014, 02:41
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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 39662
Re: If x y, and z are integers and xy + z is an odd integer, is [#permalink]

### Show Tags

28 Aug 2014, 04:08
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-y-and-z-are-integers-and-xy-z-is-an-odd-integer-is-81562.html
_________________
Re: If x y, and z are integers and xy + z is an odd integer, is   [#permalink] 28 Aug 2014, 04:08
Similar topics Replies Last post
Similar
Topics:
2 If X, Y, Z are positive integers where X>Y>Z, is X*Y*Z an odd integer 4 15 Oct 2016, 06:59
3 If x, y, and z are positive integers, is (x!)(y!) > z! ? 3 29 Jan 2017, 12:27
8 For non-negative integers x, y, and z, is x^z odd? 9 21 Nov 2016, 02:50
8 If x, y and z are integers, is x odd? 7 14 Sep 2015, 07:43
158 If x, y and z are integers and xy + z is an odd integer, is 20 26 May 2017, 09:25
Display posts from previous: Sort by