by: pintukr
27 mins
Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 0201:00 PM EDT
-11:59 PM EDT
Take 30% off all study plans with code COURSEWORK - Expires on Monday 9/7
Sep 0410:00 AM EDT
-11:59 PM EDT
We’ve worked incredibly hard to build TTP into the best test prep experience possible, and it would mean a lot to us to win Newsweek’s 2026 Readers’ Choice Award for Best Test Prep. If TTP has helped you, we’d be incredibly grateful for your vote.
Sep 0609:30 AM EDT
-12:30 PM EST
Top scores are possible when you enroll in a powerful EA course, taught live online + 6 months access to TTP OnDemand video courses included! Perfect class schedule and easy course access for working professionals. Class starts Sundays Sept. 6, 2026.
Sep 0712:01 AM PDT
-11:59 PM PDT
On the 7th, GMAT Club Tests will be Free! Including all the Quizzes, Questions, and Tests. 12 AM - 11:59 PM PDT- Sep 07
10:00 AM PDT
-11:00 AM PDT
A complete walkthrough of GMAT Club’s free 12-week GMAT study plan: what you study each week, how progress and goals are tracked, how the error log works, and how your practice unlocks paid tools at no cost. - Sep 09
07:00 AM PDT
-10:00 AM PDT
Meet AdComs and explore top Master’s programs - MiM, MiF, MSc, MSBA and more. - Application Fee Waivers - Free 1-Week of GMAT Club Tests: - Master's Application Toolkit - Grand Prize Giveaway - Sep 09
10:00 AM PDT
-11:00 AM PDT
Three MBA applications. Three rejections. No interview invites. A year later, Aman was admitted to Cambridge Judge, SMU, and IMD. In this episode of MBA Admit Stories, Aman shares how he rebuilt his MBA application... 
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 2108:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST
AbdurRakib
Joined: 11 May 2014
Last visit: 03 Mar 2026
Posts: 464
Status:I don't stop when I'm Tired,I stop when I'm done
Location: Bangladesh
Concentration: Finance, Leadership
Schools: Wharton '20 Yale '20 Tepper '20
GPA: 2.81
WE:Business Development (Real Estate)
Schools: Wharton '20 Yale '20 Tepper '20
Posts: 464
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
85% (01:49) correct
15%
(02:01)
wrong
based on 1784
sessions
History
Date
Time
Result
Not Attempted Yet
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)
(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)
Solving this question helps.
Taking a timed set of similar questions in
GMAT Club Forum Quiz →
is even better.
guenthermat
Hi
Here is what i would do in this question =>
Lets start from scratch -->
Given data => n is a positive integer.
We are asked if it is odd or not.Hence we just need the even/odd nature of n.
Lets roll =>
Statement 1 =>
n^2+(n+1)^2+(n+2)^2 is odd.
There are three ways to tackle this one.
First way => Open the brackets using (a+b)^2=a^2+b^2+2ab
n^2+(n+1)^2+(n+2)^2=> n^2+(n^2+1+2n)+(n^2+4+4n)=> 3n^2+6n+5
So 3n^2+6n+5 =even
3n^2 +even +odd =even
3n^2+odd=even
3n^2=odd-even
3n^2=odd
As 3 is odd =>Hence n must be also to make 3n^2 even.
Thus n is even
Hence this statement is sufficient.
Second way(The more reasonably very quick) => Use hit and trial.
Since n is an integer => It can be either even or odd.
If n is odd => n^2+(n+1)^2+(n+2)^2 => odd+(odd+odd)^2 +(odd+even)^2 => odd+even+odd => even
Hence n can be odd
If n is even => n^2+(n+1)^2+(n+2)^2 => even+odd+even => odd
REJECTED.
Hence n must be always odd.
Sufficient
Third way=> Power does not affect the even/odd nature of any number.
So if n is odd => n^2 is odd
if n is even => n^2 is even too.
n^2+(n+1)^2+(n+2)^2 = even
n+n+1+n+2=> even
3n+3=even
3n => even-odd=> odd
Hence n must be odd.
The same way we can get Statement 2 => Sufficient.
Does this make sense ?
Regards
Stone Cold
Is the positive integer n odd?
(1) \(n^2+(n+1)^2+(n+2)^2\) is even.
In n = odd, then \(n^2+(n+1)^2+(n+2)^2\) would be:
\(odd^2 + (odd+1)^2 + (odd+2)^2=odd + even^2 + odd^2=odd+even+odd=even\). Matches with the info given in the statement.
In n = even, then \(n^2+(n+1)^2+(n+2)^2\) would be:
\(even^2 + (even+1)^2 + (even+2)^2=even + odd^2 + even^2=even+odd+even=odd\). Does not match with the info given in the statement.
So, n = odd.
Sufficient.
(2) \(n^2-(n+1)^2-(n+2)^2\) is even
In n = odd, then \(n^2-(n+1)^2-(n+2)^2\) would be:
\(odd^2 - (odd+1)^2 - (odd+2)^2=odd - even^2 - odd^2=odd-even-odd=even\). Matches with the info given in the statement.
In n = even, then \(n^2-(n+1)^2-(n+2)^2\) would be:
\(even^2 - (even+1)^2 - (even+2)^2=even - odd^2 - even^2=even-odd-even=odd\). Does not match with the info given in the statement.
So, n = odd.
Sufficient.
Notice that (2) (n^2 - (n + 1)^2 - (n + 2)^2) is different from (1) (n^2 + (n + 1)^2 + (n + 2)^2) only by signs in two places, which won't affect the even/odd nature. Therefore, since (1) was sufficient, then (2) would also be sufficient and you could skip analyzing (2) altogether and say that it's sufficient as well.
Answer: D.
_________________
(1) \(n^2+(n+1)^2+(n+2)^2\) is even.
In n = odd, then \(n^2+(n+1)^2+(n+2)^2\) would be:
\(odd^2 + (odd+1)^2 + (odd+2)^2=odd + even^2 + odd^2=odd+even+odd=even\). Matches with the info given in the statement.
In n = even, then \(n^2+(n+1)^2+(n+2)^2\) would be:
\(even^2 + (even+1)^2 + (even+2)^2=even + odd^2 + even^2=even+odd+even=odd\). Does not match with the info given in the statement.
So, n = odd.
Sufficient.
(2) \(n^2-(n+1)^2-(n+2)^2\) is even
In n = odd, then \(n^2-(n+1)^2-(n+2)^2\) would be:
\(odd^2 - (odd+1)^2 - (odd+2)^2=odd - even^2 - odd^2=odd-even-odd=even\). Matches with the info given in the statement.
In n = even, then \(n^2-(n+1)^2-(n+2)^2\) would be:
\(even^2 - (even+1)^2 - (even+2)^2=even - odd^2 - even^2=even-odd-even=odd\). Does not match with the info given in the statement.
So, n = odd.
Sufficient.
Notice that (2) (n^2 - (n + 1)^2 - (n + 2)^2) is different from (1) (n^2 + (n + 1)^2 + (n + 2)^2) only by signs in two places, which won't affect the even/odd nature. Therefore, since (1) was sufficient, then (2) would also be sufficient and you could skip analyzing (2) altogether and say that it's sufficient as well.
Answer: D.
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
General Discussion
Schools: Schulich '16
Posts: 190
D
given x is positive integer
only odd integer(n) satisfy both equations
given x is positive integer
only odd integer(n) satisfy both equations
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
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
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.
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.
Posts: 33
stonecold
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
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
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
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.
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.
Salsanousi
Joined: 19 Oct 2013
Last visit: 29 Dec 2020
Posts: 390
Location: Kuwait
GPA: 3.2
WE:Engineering (Real Estate)
Posts: 390
AbdurRakib
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
blitzkriegxX
Joined: 28 Jun 2018
Last visit: 28 May 2019
Posts: 89
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
GMAT 4: 490 Q39 V18
Posts: 89
adkikani
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.
AbdurRakib
(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.
ScottTargetTestPrep
Expert
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 04 Sep 2026
Posts: 22,729
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Posts: 22,729
AbdurRakib
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
_________________
Scott Woodbury-Stewart | Founder and
CEO |
[email protected]
See why Target Test Prep is the top rated GMAT course on GMAT Club. Read Our Reviews
GMAT 1: 750 Q49 V42
Posts: 469
Moderators:
Announcements
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.