It is currently 26 Jun 2017, 16:10

### 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

# Is z an integer?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 09 Sep 2013
Posts: 20

### Show Tags

24 Jan 2014, 02:27
1
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

65% (01:45) correct 35% (00:41) wrong based on 142 sessions

### HideShow timer Statistics

Is z an integer?

(1) 2z is an even number.

(2) 4z is an even number.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39702
Re: Is z an integer? [#permalink]

### Show Tags

24 Jan 2014, 03:02
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
Is z an integer?

(1) 2z is an even number --> $$2z=even$$ --> $$z=\frac{even}{2}=integer$$. Sufficient.

(2) 4z is an even number --> $$4z=even$$ --> $$z=\frac{even}{4}$$: if that even number is a multiple of 4 (for example 4), then z will be an integer but if that even number is even but not a multiple of 4 (for example 2), then z will not be an integer. Not sufficient.

Hope it's clear.
_________________
Intern
Joined: 09 Sep 2013
Posts: 20
Re: Is z an integer? [#permalink]

### Show Tags

24 Jan 2014, 05:20
Bunuel wrote:
Is z an integer?

(1) 2z is an even number --> $$2z=even$$ --> $$z=\frac{even}{2}=integer$$. Sufficient.

(2) 4z is an even number --> $$4z=even$$ --> $$z=\frac{even}{4}$$: if that even number is a multiple of 4 (for example 4), then z will be an integer but if that even number is even but not a multiple of 4 (for example 2), then z will not be an integer. Not sufficient.

Hope it's clear.

But what is z=4.3?? 2z=8.6 which is an even number but z is not an integer here
Math Expert
Joined: 02 Sep 2009
Posts: 39702
Re: Is z an integer? [#permalink]

### Show Tags

24 Jan 2014, 06:28
Expert's post
1
This post was
BOOKMARKED
nfr007 wrote:
Bunuel wrote:
Is z an integer?

(1) 2z is an even number --> $$2z=even$$ --> $$z=\frac{even}{2}=integer$$. Sufficient.

(2) 4z is an even number --> $$4z=even$$ --> $$z=\frac{even}{4}$$: if that even number is a multiple of 4 (for example 4), then z will be an integer but if that even number is even but not a multiple of 4 (for example 2), then z will not be an integer. Not sufficient.

Hope it's clear.

But what is z=4.3?? 2z=8.6 which is an even number but z is not an integer here

4.3 is not even. Only integers can be even or odd:

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.

An odd number is an integer that is not evenly divisible by 2.

Theory on Number Properties: math-number-theory-88376.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

Hope this helps.
_________________
Senior Manager
Joined: 20 Dec 2013
Posts: 267
Location: India
Re: Is z an integer? [#permalink]

### Show Tags

24 Jan 2014, 08:30
Statement 1 is sufficient.
S1 says 2z is even.Thus,if z is fractional,it could be .5,1.5,2.5... to make 2z an integer.But even then 2z will be odd only,not even.
Therefore,only when z is an integer,2z will be even integer.
In statement 2,4z could be even if z=.5,1.5... Or z=1,2,3...On this basis we cannot conclude that z is an integer.Not sufficient.
Ans.A

Posted from my mobile device
Manager
Joined: 25 Oct 2013
Posts: 169
Re: Is z an integer? [#permalink]

### Show Tags

01 Feb 2014, 05:57
Stmt1: For 2z to be even z has to be integer. For a non-integer 2z cannot be even. SUFF
Stmt2: 4z is even. Now if z=1.5(a non-integer) 4z=6 (even number). if z=2, 4z=8(even number). INSUFF.
_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Manager
Joined: 03 Aug 2015
Posts: 64
Concentration: Strategy, Technology
Schools: ISB '18, SPJ GMBA '17
GMAT 1: 680 Q48 V35
Re: Is z an integer? [#permalink]

### Show Tags

14 Sep 2015, 04:08
Hi,

What if i substitute Z=4/2....Then also ''2z=4'' is an even no.?

So, i can't Understand Hw statement one is sufficient? Pls help....

Thanks,
Arun
Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)

### Show Tags

14 Sep 2015, 04:44
1
KUDOS
Expert's post
ArunpriyanJ wrote:
Hi,

What if i substitute Z=4/2....Then also ''2z=4'' is an even no.?

So, i can't Understand Hw statement one is sufficient? Pls help....

Thanks,
Arun

Even if you substitute z=4/2 you still are going to get z = 4/2 =2 , an integer.

A fraction MUST Be reduced to simplest terms for the final answer. A fraction is a true fraction ONLY when the numerator and the denominator have 1 as the only commmon factor. In the case of 4/2, apart from 1 , you also have 2 as the common factor and thus this value of 4/2 is actually=2. Hence statement 1 is sufficient.

Hope this helps.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 3460
GPA: 3.82
Re: Is z an integer? [#permalink]

### Show Tags

15 Sep 2015, 09:14
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

Is z an integer?

(1) 2z is an even number.

(2) 4z is an even number.

In the original condition we have 1 variable (z) and thus we need 1 equation to match the number of variables and equations. Since there is 1 each in 1) and 2), there is high probability that D is the answer.

In case of 1), 2z=even=2m(m is some integer), z=m therefore the answer is yes and the condition is suffi
In case of 2), 4z=even=2n(n is some integer), z=n/2, 4z=2, z=1/2 the answer is no, while for 4z=4, z=1 the answer is yes. Therefore the condition is not sufficient

Normally for cases where we need 1 more equation, such as original conditions with 1 variable, or 2 variables and 1 equation, or 3 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15985
Re: Is z an integer? [#permalink]

### Show Tags

30 May 2017, 12:15
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.
_________________
Intern
Joined: 21 Feb 2017
Posts: 34
Re: Is z an integer? [#permalink]

### Show Tags

30 May 2017, 12:26
Bunuel wrote:
Is z an integer?

(1) 2z is an even number --> $$2z=even$$ --> $$z=\frac{even}{2}=integer$$. Sufficient.

(2) 4z is an even number --> $$4z=even$$ --> $$z=\frac{even}{4}$$: if that even number is a multiple of 4 (for example 4), then z will be an integer but if that even number is even but not a multiple of 4 (for example 2), then z will not be an integer. Not sufficient.

Hope it's clear.

Hi, I am not getting here... Statement 1 says 2Z=even and it can be anything integer or fraction, so 2Z=1.4 or 2Z=4 or anything. This can give Z as integer as well as non integer. So 1 is not sufficient.

Same way 2 is not sufficient.

What is my mistake?

Thanks.

Sent from my XT1663 using GMAT Club Forum mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 39702
Re: Is z an integer? [#permalink]

### Show Tags

30 May 2017, 12:31
goalMBA1990 wrote:
Bunuel wrote:
Is z an integer?

(1) 2z is an even number --> $$2z=even$$ --> $$z=\frac{even}{2}=integer$$. Sufficient.

(2) 4z is an even number --> $$4z=even$$ --> $$z=\frac{even}{4}$$: if that even number is a multiple of 4 (for example 4), then z will be an integer but if that even number is even but not a multiple of 4 (for example 2), then z will not be an integer. Not sufficient.

Hope it's clear.

Hi, I am not getting here... Statement 1 says 2Z=even and it can be anything integer or fraction, so 2Z=1.4 or 2Z=4 or anything. This can give Z as integer as well as non integer. So 1 is not sufficient.

Same way 2 is not sufficient.

What is my mistake?

Thanks.

Sent from my XT1663 using GMAT Club Forum mobile app

1.4 is not an even number. Only integers can be even or odd:

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.

An odd number is an integer that is not evenly divisible by 2.

Theory on Number Properties: http://gmatclub.com/forum/math-number-theory-88376.html

All DS Number Properties Problems to practice: http://gmatclub.com/forum/search.php?se ... &tag_id=38
All PS Number Properties Problems to practice: http://gmatclub.com/forum/search.php?se ... &tag_id=59

Hope this helps.
_________________
Re: Is z an integer?   [#permalink] 30 May 2017, 12:31
Similar topics Replies Last post
Similar
Topics:
1 If z is an integer, is z even? 4 22 May 2015, 20:17
5 If z is an integer, is z even? 3 20 Dec 2016, 16:48
21 If Z is an integer, is Z prime? 9 02 May 2017, 07:20
5 If z is an integer, is z even? 14 01 Jan 2017, 12:03
5 If Z is an integer, is Z prime? 12 03 Nov 2011, 18:41
Display posts from previous: Sort by