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

It is currently 23 Oct 2014, 01:44

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Manager
Manager
avatar
Joined: 10 Jul 2009
Posts: 172
Followers: 1

Kudos [?]: 35 [2] , given: 8

If x, y and z are integers and xy + z is an odd integer, is [#permalink] New post 28 Jul 2009, 21:25
2
This post received
KUDOS
10
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

42% (03:17) correct 58% (02:19) wrong based on 382 sessions
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
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Mar 2013, 01:10, edited 1 time in total.
Edited the question and added the OA.
23 KUDOS received
Director
Director
User avatar
Joined: 03 Jun 2009
Posts: 805
Location: New Delhi
WE 1: 5.5 yrs in IT
Followers: 64

Kudos [?]: 414 [23] , given: 56

Re: DS - Is x even? [#permalink] New post 28 Jul 2009, 22:14
23
This post received
KUDOS
5
This post was
BOOKMARKED
IMO A

1. xy + xz is an even integer - SUFFICIENT
Given:
xy + z is odd ...(i)
xy + xz is even ...(ii)

subtracting (ii) from (i)
we get xz - z, which should be odd (* since odd - even = odd)
=> z(x-1) is odd
=> both z and (x-1) is odd
=> since (x-1) is odd, x must be even.

2. y + xz is an odd integer -INSUFFICIENT
Given:
xy + z is odd ...(i)
y + xz is odd ...(ii)

subtracting (ii) from (i)
we get xy + z - y - xz
= (x-1)(y-z) , which should be even
=> either (x-1) is even or (y-z) is even ....insufficient to determine
_________________

ISB 2011-12 thread | Ask ISB Alumni @ ThinkISB
All information related to Indian candidates and B-schools | Indian B-schools accepting GMAT scores
Self evaluation for Why MBA?

GMAT Instructor
avatar
Joined: 24 Jun 2008
Posts: 978
Location: Toronto
Followers: 261

Kudos [?]: 707 [0], given: 3

Re: GMAT Prep...How much time did u take to solve this one ?? [#permalink] New post 26 Sep 2009, 21:52
You can look at Statement 1 conceptually: when we add z to xy, we get something odd. However, when we add xz to xy, we get something even. So certainly one of z or xz is odd, the other even. Now if xz is different from z, then multiplying by x must have changed z, and that could only happen if x is even and z odd. That's a bit tricky to explain, but I hope that's clear.

Or you can proceed algebraically - notice the similarity between the expression in the question and in Statement 1. We know that xy + xz is even, and xy + z is odd. When you subtract this second expression from the first, you're subtracting an odd from an even, so must get an odd: xy + xz - (xy + z) = xz - z = z(x-1) is odd. Since this is a product, z must be odd, and x-1 must be odd, so x is even. Sufficient.

For Statement 2, all the letters could be odd, so not sufficient.
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

Manager
Manager
User avatar
Joined: 25 Mar 2009
Posts: 56
Followers: 1

Kudos [?]: 10 [0], given: 9

Re: GMAT Prep...How much time did u take to solve this one ?? [#permalink] New post 27 Sep 2009, 08:58
IanStewart wrote:
You can look at Statement 1 conceptually: when we add z to xy, we get something odd. However, when we add xz to xy, we get something even. So certainly one of z or xz is odd, the other even. Now if xz is different from z, then multiplying by x must have changed z, and that could only happen if x is even and z odd. That's a bit tricky to explain, but I hope that's clear.

Or you can proceed algebraically - notice the similarity between the expression in the question and in Statement 1. We know that xy + xz is even, and xy + z is odd. When you subtract this second expression from the first, you're subtracting an odd from an even, so must get an odd: xy + xz - (xy + z) = xz - z = z(x-1) is odd. Since this is a product, z must be odd, and x-1 must be odd, so x is even. Sufficient.

For Statement 2, all the letters could be odd, so not sufficient.


Fr St2,
y+xz odd
xy+z odd
=> y+zx+xy+z even
=> y(x+1)+z(x+1) even
=> (y+z)(x+1) event
x+1 can be odd or even means that x can be even or odd, insuff
Director
Director
avatar
Joined: 01 Jan 2008
Posts: 629
Followers: 3

Kudos [?]: 133 [0], given: 1

Re: GMAT Prep...How much time did u take to solve this one ?? [#permalink] New post 28 Sep 2009, 04:34
It took me 15 seconds.

1) sufficient (x is even)
2) insufficient (try even y, odd x, odd z; even x, odd y, z)

A
Manager
Manager
User avatar
Joined: 21 May 2009
Posts: 136
Followers: 1

Kudos [?]: 9 [0], given: 48

Re: GMAT Prep...How much time did u take to solve this one ?? [#permalink] New post 29 Sep 2009, 18:26
Took me less than a min

if XY+Z is odd
these are the possiblities

X Y Z

E E O
O E O
E O O
O O E

so substituting these values in Option A gives the solution write away as Even.
in B we have 2 diff results so

Answer is A
1 KUDOS received
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1748
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 14

Kudos [?]: 192 [1] , given: 299

GMAT ToolKit User
Re: If x, y and z are integers and xy + z is an odd integer, is [#permalink] New post 31 Jan 2014, 08:31
1
This post received
KUDOS
Aleehsgonji 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



Odd/Even questions can be usually solved quite easily if one tries some operations with the statements

We want to know if x is even integer

We are given that xy+z is odd

Statement 1

xq + xz is even

Subtracting

z(x+1) is odd

Therefore, x+1 should be odd and x should be even

Sufficient

Statement 2

Not sufficient

Answer is A

Just my 2c

Cheers
J
Intern
Intern
avatar
Joined: 12 Apr 2013
Posts: 5
Followers: 0

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

Re: If x, y and z are integers and xy + z is an odd integer, is [#permalink] New post 19 Mar 2014, 18:41
Given condition:
xy + z = odd
implies either xy = odd (x =odd and y = odd) and z = even or xy = even (x or y can be odd and even respectively and vice versa) and z = odd

condition 1:

xy + xz = even; Implies x(y+z) = even which again implies the following:

i) x even and y+z = odd - where again y or z can be odd and even respectively and vice versa
ii) x odd and y +z = even - where again y and z has to be both odd or both even

inconclusive

condition 2:

y + xz = odd

again inconclusive
1 + 2:
Add xy + z + y + xz = odd + odd
implies: (x + 1)(y+z) = even
and x (y+z) is also even according to 2.. so y + z = even <y and z both even or y + z both odd>, x can be odd or even
but by 1 xy + z = odd which means y and z both odd, so x is even.

C is the answer
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23394
Followers: 3607

Kudos [?]: 28814 [2] , given: 2852

Re: If x, y and z are integers and xy + z is an odd integer, is [#permalink] New post 20 Mar 2014, 05:09
2
This post received
KUDOS
Expert's post
Mountain14 wrote:
jlgdr wrote:
Aleehsgonji 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



Odd/Even questions can be usually solved quite easily if one tries some operations with the statements

We want to know if x is even integer

We are given that xy+z is odd

Statement 1

xq + xz is even

Subtracting

z(x+1) is odd

Therefore, x+1 should be odd and x should be even


Sufficient

Statement 2

Not sufficient

Answer is A

Just my 2c

Cheers
J



I am not clear with the red part.


When you subtract xy + z=odd from xy+xz=even you'll get: xz-z=even-odd=odd --> z(x-1)=odd. For the product of two integers to be odd, both of them must be odd --> z and x-1 are odd. If x-1=odd, then x must be even: x-1=x-odd=odd --> x=odd+odd=even.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 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 NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
1 KUDOS received
Moderator
Moderator
User avatar
Joined: 20 Dec 2013
Posts: 159
GMAT 1: 720 Q49 V40
Followers: 1

Kudos [?]: 24 [1] , given: 62

GMAT ToolKit User Premium Member Reviews Badge
Re: If x, y and z are integers and xy + z is an odd integer, is [#permalink] New post 21 Mar 2014, 19:46
1
This post received
KUDOS
Expert's post
Odd(O) Even (E)
given:
x,y,z integers
xy+z=O
so only the following scenarios can fulfill the constraints
a) EO+O
b) EE+O
c) OE+O
d) OO+E

question:
x=E?

1) x(y+z)=E
i. (E)(O+O) --> fits scenario a -->yes, x can be even
ii. (O)(E+E) --> n/a - doesn't fit any scenarios
iii. (O)(O+O) --> n/a - doesn't fit any scenarios

stop testing, x can't be odd, sufficient

2) y+xz = O
i. E+(O)(O) --> fits scenario a -->yes, x can be even
ii. O+(E)(E) --> n/a - doesn't fit any scenarios
iii. O+(O)(E) --> fits scenario d -->no, x can be odd

stop testing, x can be either even or odd

insufficient

A
_________________

MY GMAT BLOG - ADVICE - OPINIONS - ANALYSIS

Intern
Intern
avatar
Joined: 29 Sep 2014
Posts: 2
Followers: 0

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

Re: GMAT Prep...How much time did u take to solve this one ?? [#permalink] New post 30 Sep 2014, 04:10
nikhilpoddar wrote:
Please solve...


took me 4 seconds, but I got it wrong :(
Re: GMAT Prep...How much time did u take to solve this one ??   [#permalink] 30 Sep 2014, 04:10
    Similar topics Author Replies Last post
Similar
Topics:
1 if x,y,z are integers is x(y^2 + z^3) even? vr4indian 2 29 Sep 2008, 10:40
1 If x, y, and z are consecutive odd integers such that 31 sarzan 2 24 Aug 2008, 12:50
4 Experts publish their posts in the topic If x y, and z are integers and xy + z is an odd integer, is mbawaters 8 22 May 2008, 05:26
Are x, y, z odd integers? 1) x+y+z is odd 2) x*y*z is a withme 2 18 Jan 2007, 07:39
If x, y, and z are integers and xy + z is an odd integer, is macca 9 12 Apr 2006, 06:35
Display posts from previous: Sort by

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

  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®.