Last visit was: 12 Sep 2024, 01:25 It is currently 12 Sep 2024, 01:25
Toolkit
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.
Request Expert Reply

# Is the positive integer n odd?

SORT BY:
Tags:
Show Tags
Hide Tags
Senior Manager
Joined: 11 May 2014
Status:I don't stop when I'm Tired,I stop when I'm done
Posts: 473
Own Kudos [?]: 39816 [48]
Given Kudos: 220
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE:Business Development (Real Estate)
Most Helpful Reply
Alum
Joined: 12 Aug 2015
Posts: 2267
Own Kudos [?]: 3238 [19]
Given Kudos: 893
GRE 1: Q169 V154
Math Expert
Joined: 02 Sep 2009
Posts: 95464
Own Kudos [?]: 657815 [13]
Given Kudos: 87247
General Discussion
Manager
Joined: 02 Mar 2012
Posts: 198
Own Kudos [?]: 302 [0]
Given Kudos: 4
Schools: Schulich '16
Re: Is the positive integer n odd? [#permalink]
D
given x is positive integer
only odd integer(n) satisfy both equations
Alum
Joined: 12 Aug 2015
Posts: 2267
Own Kudos [?]: 3238 [5]
Given Kudos: 893
GRE 1: Q169 V154
Re: Is the positive integer n odd? [#permalink]
5
Kudos
Nice Question
Here we can use the property that POWER does not effect the even or odd nature of any integer
Hence statement 1=> 3n+odd=even => n is odd=> suff
Statement 2=> -n-5=even=> n=even-odd=> odd => suff

Smash that D
Intern
Joined: 02 Nov 2012
Posts: 21
Own Kudos [?]: 7 [0]
Given Kudos: 12
Location: India
Concentration: Finance, International Business
GMAT 1: 690 Q49 V36
GPA: 3.9
WE:Analyst (Retail Banking)
Re: Is the positive integer n odd? [#permalink]
Correct answer is D.

Statement 1 :- N can only be odd.

as for the statement to be even either all the numbers have to even or there should be a pair of odd numbers i.e.

E+E+E = E
or O+E+O = E

Now as they are consecutive numbers first scenario is not possible. Hence second scenario is correct. Therefore N is odd.

Statement 2 :- Same explanation. Addition or subtraction dont make a difference in even and odd rule.
Intern
Joined: 18 Mar 2017
Posts: 33
Own Kudos [?]: 6 [0]
Given Kudos: 14
Re: Is the positive integer n odd? [#permalink]
stonecold
Nice Question
Here we can use the property that POWER does not effect the even or odd nature of any integer
Hence statement 1=> 3n+odd=even => n is odd=> suff
Statement 2=> -n-5=even=> n=even-odd=> odd => suff

Smash that D

stonecold - I am quite a bit lost on this question. Could you just explain a lil bit more how you get to "3n + odd = even" / "-n-5=even"?

Thanks in advance!
p
IIM School Moderator
Joined: 04 Sep 2016
Posts: 1247
Own Kudos [?]: 1271 [0]
Given Kudos: 1207
Location: India
WE:Engineering (Other)
Re: Is the positive integer n odd? [#permalink]
Hi stonecold Bunuel

I understood your explanation but can you suggest flaw in my approach:

I started with : Assuming n is even if st 1 is satisfied:
If n is even, then n+1 is odd and n+2 is even
so we have:
LHS=e+o+e = o ; whereeas RHS is even. Where did I do wrong?
Manager
Joined: 27 Jan 2016
Posts: 100
Own Kudos [?]: 294 [3]
Given Kudos: 124
Schools: ISB '18
GMAT 1: 700 Q50 V34
Re: Is the positive integer n odd? [#permalink]
2
Kudos
1
Bookmarks
Stmnt 1)
If n is odd
O+E+O = E satisifies

If n is even
E+O+E = O does not satisfy
Hence N is odd

Stmnt 2)
If N is Odd
O-E-O = E satisfies

If N is even
E-O-E = O does not satisfy

Hence answr D
IIM School Moderator
Joined: 04 Sep 2016
Posts: 1247
Own Kudos [?]: 1271 [0]
Given Kudos: 1207
Location: India
WE:Engineering (Other)
Re: Is the positive integer n odd? [#permalink]
hi srikanth9502

thanks for chipping in.
You mean to say that we are looking for unique property of n as even or odd.
Since n is odd satisfies both hence n is odd
Since n is even does not satisfy both hence n is even is not correct
Since I got two answers for n as odd / even for st 1 i rejected it.
Senior Manager
Joined: 19 Oct 2013
Posts: 407
Own Kudos [?]: 318 [1]
Given Kudos: 117
Location: Kuwait
GPA: 3.2
WE:Engineering (Real Estate)
Re: Is the positive integer n odd? [#permalink]
1
Kudos
AbdurRakib
Is the positive integer n odd?

(1) $$n^2+(n+1)^2+(n+2)^2$$ is even
(2) $$n^2-(n+1)^2-(n+2)^2$$ is even

OG Q 2017 New Question(Book Question: 194)

Because powers don't affect whether the integer is odd or even.

it can be rewritten as n + n +1 + n + 2 = 3n + 3. Only way to get that as a even is if n is odd.

Sufficient.

Apply the same for statement 2

n - n - 1 -n - 2 = -n - 3 is even. the only way for it to be even is if n is odd.

Sufficient.

Answer choice D
Manager
Joined: 28 Jun 2018
Posts: 94
Own Kudos [?]: 224 [0]
Given Kudos: 329
Location: Bouvet Island
GMAT 1: 640 Q47 V30
GMAT 2: 670 Q50 V31
GMAT 3: 700 Q49 V36
GMAT 4: 490 Q39 V18
GPA: 4
Is the positive integer n odd? [#permalink]
adkikani
hi srikanth9502

thanks for chipping in.
You mean to say that we are looking for unique property of n as even or odd.
Since n is odd satisfies both hence n is odd
Since n is even does not satisfy both hence n is even is not correct
Since I got two answers for n as odd / even for st 1 i rejected it.

Hey adkikani
What is "both" that u are referring to?

Question - Is n odd?
If we answer a YES or NO for that then it is sufficient.

Statement 1)
For N to satisfy statement one.
N has to be odd.
So it answers our main question. Yes N is odd.

Statement 2)
For N to satisfy statement two.
N has to be odd here too.
So again it answers our main question. Yes N is odd.

Note - You dont even have to check for statement 2 because all the EVEN and ODD properties for addition are same as that for subtraction.
Example:
2 + 1 = 3 ---------- EVEN + ODD = ODD
2 - 1 = 1 ---------- EVEN - ODD = ODD

Hope it helps.
Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 953
Own Kudos [?]: 5076 [0]
Given Kudos: 690
Concentration: Accounting
Is the positive integer n odd? [#permalink]
Top Contributor
AbdurRakib
Is the positive integer n odd?

(1) $$n^2+(n+1)^2+(n+2)^2$$ is even
(2) $$n^2-(n+1)^2-(n+2)^2$$ is even

(1) If $$n=1, 1+2^2+3^2=14=Even$$, n is Odd.

if $$n=2, 2+3^2+4^2=4+9+16=25=Odd$$, n is even and contradictory with the condition.

The answer n is ODD, Sufficient.

(2) If $$n=1, 1-2^2-3^2=1-4-9=-12=Even$$ n is Odd.

if $$n=2, 2-3^2-4^2=4-9-16=-21=Odd$$, n is even and contradictory with the condition.

The answer n is ODD, Sufficient.

The answer is D.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19444
Own Kudos [?]: 23196 [2]
Given Kudos: 286
Location: United States (CA)
Re: Is the positive integer n odd? [#permalink]
2
Kudos
Expert Reply
AbdurRakib
Is the positive integer n odd?

(1) $$n^2+(n+1)^2+(n+2)^2$$ is even
(2) $$n^2-(n+1)^2-(n+2)^2$$ is even

OG Q 2017 New Question(Book Question: 194)
Solution:

Question Stem Analysis:

We need to determine whether positive integer n is odd.

Let’s review a few even/odd rules:
If n is odd, then (n + 1) is even, and (n + 2) is odd
Odd x odd = odd, even x even = even, and even x odd = even
Odd + odd = even, even + even = even, and odd + even = odd

Statement One Alone:

If n is odd, then n^2 is odd, (n + 1)^2 is even, and (n + 2)^2 is odd. The sum n^2 + (n + 1)^2 + (n + 2)^2 = odd + even + odd = even.

If n is even, then n^2 is even, (n + 1)^2 is odd, and (n + 2)^2 is even. The sum n^2 + (n + 1)^2 + (n + 2)^2 = even + odd + even = odd.

From the above, we see that, in order for n^2 + (n + 1)^2 + (n + 2)^2 to be even,then n must be odd. Statement one alone is sufficient.

Statement Two Alone:

If n is odd, then n^2 is odd, (n + 1)^2 is even, and (n + 2)^2 is odd and n^2 - (n + 1)^2 - (n + 2)^2 = odd - even - odd = even.

If n is even, then n^2 is even, (n + 1)^2 is odd, and (n + 2)^2 is even and n^2 - (n + 1)^2 - (n + 2)^2 = even - odd - even = odd.

From the above, we see that in order for n^2 - (n + 1)^2 - (n + 2)^2 to be even, then n must be odd. Statement two alone is sufficient.

Answer: D
Non-Human User
Joined: 09 Sep 2013
Posts: 34816
Own Kudos [?]: 877 [0]
Given Kudos: 0
Re: Is the positive integer n odd? [#permalink]
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.
Re: Is the positive integer n odd? [#permalink]
Moderator:
Math Expert
95457 posts