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

It is currently 11 Dec 2018, 03:53

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

If x, y and z are positive integers, is xz 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: 51098
If x, y and z are positive integers, is xz even?  [#permalink]

Show Tags

New post 01 Oct 2018, 03:55
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

67% (01:20) correct 33% (02:18) wrong based on 39 sessions

HideShow timer Statistics

CEO
CEO
User avatar
P
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2710
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: If x, y and z are positive integers, is xz even?  [#permalink]

Show Tags

New post 01 Oct 2018, 04:06
Bunuel wrote:
If x, y and z are positive integers, is xz even?

(1) (2xy − x) is even
(2) (x^2 + xz) is eve


Given: If x, y and z are positive integers

Question: is xz even?

Statement 1: (2xy − x) is even
i.e. \(x(2y-1) = Even\)
But (2y-1) = Even - 1 = Odd therefore,
x = Even
i.e. xz = even
SUFFICIENT

Statement 2: \((x^2 + xz)\) is even

\((x^2 + xz) = x(x+z) = even\)
Case 1: x = even and z is odd i.e. xz = even
Case 2: x = even and z is Even
Case 3: x = Odd and z is Odd i.e. xz = Odd
NOT SUFFICIENT

Answer: Option A
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3228
Location: Canada
If x, y and z are positive integers, is xz even?  [#permalink]

Show Tags

New post 01 Oct 2018, 05:50
Top Contributor
Bunuel wrote:
If x, y and z are positive integers, is xz even?

(1) (2xy − x) is even
(2) (x² + xz) is even


Some important rules:
#1. ODD +/- ODD = EVEN
#2. ODD +/- EVEN = ODD
#3. EVEN +/- EVEN = EVEN

#4. (ODD)(ODD) = ODD
#5. (ODD)(EVEN) = EVEN
#6. (EVEN)(EVEN) = EVEN


Target question: Is xz even?

Given: x, y and z are positive integers

Statement 1: (2xy − x) is even
Notice that 2xy will be EVEN for all values of x and y.
So, statement 1 is really telling us that EVEN - x = EVEN, which we can rewrite as: EVEN + EVEN = x
By rule #3, we can conclude that x is EVEN
If x is EVEN, them we can be certain (from rules #5 and #6) that xz is EVEN
So, the answer to the target question is YES, xz is even
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: (x² + xz) is even
There are several values of x and z that satisfy statement 2. Here are two:
Case a: x = 2 and z = 1. Notice that x² + xz = 2² + (2)(1) = 6, which is even. In this case, xz = (2)(1) = 2. So, the answer to the target question is YES, xz IS even
Case b: x = 1 and z = 1. Notice that x² + xz = 1² + (1)(1) = 2, which is even. In this case, xz = (1)(1) = 1. So, the answer to the target question is NO, xz is NOT even
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com
Image

Director
Director
User avatar
P
Joined: 31 Oct 2013
Posts: 852
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If x, y and z are positive integers, is xz even?  [#permalink]

Show Tags

New post 01 Oct 2018, 06:14
Bunuel wrote:
If x, y and z are positive integers, is xz even?

(1) (2xy − x) is even
(2) (x^2 + xz) is even


even - even = even

odd + odd = even.

Statement 1:

2xy = even. So x has to be even. Thus xz must be even. Sufficient.

Statement 2:

case 1:

let x be 2 and

\(x^2 = even\)

xz = even.

case 2:

x = 3 and z = 3

\(3^2 + 3*3 = 18\)

but 3*3 = 9 , which is odd.

Thus not sufficient .

The best answer is A.
GMAT Club Bot
Re: If x, y and z are positive integers, is xz even? &nbs [#permalink] 01 Oct 2018, 06:14
Display posts from previous: Sort by

If x, y and z are positive integers, is xz 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®.