Is k^2 odd? : GMAT Data Sufficiency (DS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 05 Dec 2016, 21:50
GMAT Club Tests

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is k^2 odd?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Manager
Manager
avatar
Joined: 07 Dec 2010
Posts: 116
Concentration: Marketing, General Management
Followers: 0

Kudos [?]: 30 [1] , given: 12

Is k^2 odd? [#permalink]

Show Tags

New post 08 Aug 2011, 19:24
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

67% (01:51) correct 33% (01:01) wrong based on 145 sessions

HideShow timer Statistics

Is k^2 odd?

(1) k - 1 is divisible by 2.
(2) The sum of k consecutive integers is divisible by k.
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Aug 2013, 06:13, edited 1 time in total.
Renamed the topic and edited the question.
Intern
Intern
avatar
Joined: 17 Jul 2010
Posts: 15
Location: United States (AL)
GMAT 1: 720 Q49 V39
Followers: 2

Kudos [?]: 8 [0], given: 4

Re: MGmat DS [#permalink]

Show Tags

New post 08 Aug 2011, 20:01
How's this.

(2) The sum of k consecutive integers is divisible by k.

This can be expressed as a + (a+1) + (a+2) ... (k-1).
Group the a's together and group the numbers together to get: ka + k(k-1)/2

Given that this sum is divisible by k, the k(k-1)/2 term must be an integer.
For that to be true, k must be odd - essentially what 1) is saying.

Great question.
Manager
Manager
avatar
Joined: 07 Dec 2010
Posts: 116
Concentration: Marketing, General Management
Followers: 0

Kudos [?]: 30 [0], given: 12

Re: MGmat DS [#permalink]

Show Tags

New post 08 Aug 2011, 20:05
cellydan wrote:
How's this.

(2) The sum of k consecutive integers is divisible by k.

This can be expressed as a + (a+1) + (a+2) ... (k-1).
Group the a's together and group the numbers together to get: ka + k(k-1)/2

Given that this sum is divisible by k, the k(k-1)/2 term must be an integer.
For that to be true, k must be odd - essentially what 1) is saying.

Great question.



How can u say K must be odd...even if its even k(k-1)/2 is an integer.
Intern
Intern
avatar
Joined: 17 Jul 2010
Posts: 15
Location: United States (AL)
GMAT 1: 720 Q49 V39
Followers: 2

Kudos [?]: 8 [0], given: 4

Re: MGmat DS [#permalink]

Show Tags

New post 08 Aug 2011, 20:25
Ah, you are right. I have omitted one additional step.

Group the a's together and group the numbers together to get: ka + k(k-1)/2
Factor out a k.
k(a+ (k-1)/2)
For this to be divisible by k, (a + (k-1)/2) must be a integer. So therefore k must be odd, otherwise the (k-1)/2) term would be a fraction...
Manager
Manager
avatar
Joined: 07 Dec 2010
Posts: 116
Concentration: Marketing, General Management
Followers: 0

Kudos [?]: 30 [0], given: 12

Re: MGmat DS [#permalink]

Show Tags

New post 08 Aug 2011, 20:27
hey cellydan thanks alot for the explanation....btw when is your GMAT?
Senior Manager
Senior Manager
User avatar
Joined: 03 Mar 2010
Posts: 440
Schools: Simon '16 (M)
Followers: 5

Kudos [?]: 261 [0], given: 22

Re: MGmat DS [#permalink]

Show Tags

New post 08 Aug 2011, 23:06
ruturaj wrote:
Is k2 odd?
(1) k - 1 is divisible by 2.
(2) The sum of k consecutive integers is divisible by k.


Question Is k^2 odd?

Stmt1: k-1 is divisible by 2.

(k-1)/2 = m where m is some integer
k-1 = 2m
k = 2m+1. Now this is the equation of any odd number

Hence k is odd. Therefore k^2 is odd.
Sufficient.

Stmt2: The sum of k consecutive integers is divisible by k
sum = k(k+1)/2
Sum/k = m where m is some integer
k(k+1)/2k = m
(k+1)/2 = m
k=2m-1. This again represents odd number.

Hence k is odd. Therefore k^2 is odd.
Sufficient.

OA D
_________________

My dad once said to me: Son, nothing succeeds like success.

VP
VP
User avatar
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1122
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 120

Kudos [?]: 526 [0], given: 19

Re: MGmat DS [#permalink]

Show Tags

New post 09 Aug 2011, 02:56
jamifahad,

I would like to point out a small possible improvement in your analysis, which is otherwise on track.

The sum of k consecutive integers is not k(k+1)/2. This is the expression for the sum of the first k natural numbers.
Example: The sum of three consecutive integers 50,51,and 52 is not 3(3+1)/2.

The expression for the sum of k consecutive integers is ak + k(k-1)/2, where a is the first number and k is the number of terms. In this question, you may have assumed that k consecutive integers can also be n consecutive natural numbers and so used the expression k(k+1)/2.

The OA is (D) as explained by cellydan
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Top MBA Admissions Consulting | Top MiM Admissions Consulting

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Intern
Intern
avatar
Joined: 15 Jul 2012
Posts: 20
Location: India
Concentration: International Business, General Management
GMAT Date: 09-27-2013
GPA: 3.04
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 9 [0], given: 66

Re: MGmat DS [#permalink]

Show Tags

New post 21 Aug 2013, 05:55
Hi, What if I assume K is a fraction/decimal?

jamifahad wrote:
ruturaj wrote:
Is k2 odd?
(1) k - 1 is divisible by 2.
(2) The sum of k consecutive integers is divisible by k.


Question Is k^2 odd?

Stmt1: k-1 is divisible by 2.

(k-1)/2 = m where m is some integer
k-1 = 2m
k = 2m+1. Now this is the equation of any odd number

Hence k is odd. Therefore k^2 is odd.
Sufficient.

Stmt2: The sum of k consecutive integers is divisible by k
sum = k(k+1)/2
Sum/k = m where m is some integer
k(k+1)/2k = m
(k+1)/2 = m
k=2m-1. This again represents odd number.

Hence k is odd. Therefore k^2 is odd.
Sufficient.

OA D
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35867
Followers: 6841

Kudos [?]: 89965 [3] , given: 10393

Re: MGmat DS [#permalink]

Show Tags

New post 21 Aug 2013, 06:22
3
This post received
KUDOS
Expert's post
ganesamurthy wrote:
Hi, What if I assume K is a fraction/decimal?

jamifahad wrote:
ruturaj wrote:
Is k2 odd?
(1) k - 1 is divisible by 2.
(2) The sum of k consecutive integers is divisible by k.


Question Is k^2 odd?

Stmt1: k-1 is divisible by 2.

(k-1)/2 = m where m is some integer
k-1 = 2m
k = 2m+1. Now this is the equation of any odd number

Hence k is odd. Therefore k^2 is odd.
Sufficient.

Stmt2: The sum of k consecutive integers is divisible by k
sum = k(k+1)/2
Sum/k = m where m is some integer
k(k+1)/2k = m
(k+1)/2 = m
k=2m-1. This again represents odd number.

Hence k is odd. Therefore k^2 is odd.
Sufficient.

OA D

Both statements imply that k is an integer.

Is k^2 odd?

(1) k - 1 is divisible by 2 --> \(k-1=even\) --> \(k=even+1=odd=integer\) --> \(k^2=odd^2=odd\). Sufficient.

(2) The sum of k consecutive integers is divisible by k. Here k must be a positive integer because otherwise the statement does not make sense.

Properties of consecutive integers:
• If n is odd, the sum of n consecutive integers is always divisible by n. Given \(\{9,10,11\}\), we have \(n=3=odd\) consecutive integers. The sum is 9+10+11=30, which is divisible by 3.
• If n is even, the sum of n consecutive integers is never divisible by n. Given \(\{9,10,11,12\}\), we have \(n=4=even\) consecutive integers. The sum is 9+10+11+12=42, which is NOT divisible by 4.

The statement says that the sum of k consecutive integers is divisible by k, which, according to the above means that k is odd, therefore \(k^2=odd^2=odd\). Sufficient.

Answer: D.

For more check Number Theory chapter of our Math Book: math-number-theory-88376.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12877
Followers: 559

Kudos [?]: 158 [0], given: 0

Premium Member
Re: Is k^2 odd? [#permalink]

Show Tags

New post 28 Oct 2014, 04:35
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12877
Followers: 559

Kudos [?]: 158 [0], given: 0

Premium Member
Re: Is k^2 odd? [#permalink]

Show Tags

New post 25 Sep 2016, 10:27
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 17 Mar 2016
Posts: 22
Location: Singapore
GPA: 3.5
WE: Business Development (Energy and Utilities)
Followers: 0

Kudos [?]: 10 [0], given: 30

GMAT ToolKit User
Re: Is k^2 odd? [#permalink]

Show Tags

New post 26 Sep 2016, 02:24
Question asks is k odd?

1. Clearly Suff, k-1 --> even so k is odd
2. Choose a case or two to test. 3,4,5 yes div by 3
3,4 not div by 2
1,2,3,4,5 - yes div by 5

So, click on D & move on
BSchool Forum Moderator
User avatar
Joined: 12 Aug 2015
Posts: 1492
Followers: 32

Kudos [?]: 269 [0], given: 361

GMAT ToolKit User CAT Tests
Re: Is k^2 odd? [#permalink]

Show Tags

New post 21 Nov 2016, 07:45
Here we need to get i k is even/odd
Statement 1
(k-1)/2=integer
hence k-1=2m for some integer m
k=2m+1=> odd
hence sufficient
Statement 2
Here we can use a simple Rule =>

SUM OF N CONSECUTIVES IS DIVISIBLE BY N FOR N BEING ODD AND NEVER DIVISIBLE BY N FOR N BEING EVEN

Hence K must be odd
Alternatively,
Since consecutives inters form an AP
mean = median
It is given that mean = integer
so median => integer too
hence number of terms must be odd
hence K is odd

Thus sufficient

Hence D
_________________

Give me a hell yeah ...!!!!!

Math Forum Moderator
User avatar
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 2074
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Followers: 81

Kudos [?]: 552 [0], given: 309

GMAT ToolKit User Premium Member CAT Tests
Re: Is k^2 odd? [#permalink]

Show Tags

New post 21 Nov 2016, 10:40
ruturaj wrote:
Is k^2 odd?

(1) k - 1 is divisible by 2.
(2) The sum of k consecutive integers is divisible by k.


FROM STATEMENT - I ( SUFFICIENT )

Since, k - 1 is divisible by 2 ; k must be Odd because -

Odd - 1 = Even ( Which is divisible by 2 )

FROM STATEMENT - II ( SUFFICIENT )

Test using numebrs...

Sum of 2 consecutive integers is 3 ( which is not divisible by 2 )
Sum of 3 consecutive integers is 6 ( which is divisible by 3 )
Sum of 4 consecutive integers is 10 ( which is not divisible by 4 )
Sum of 5 consecutive integers is 15 ( which is divisible by 5 )

So, we can safely conclude k = Odd...

And \(Odd^2\) = Odd

Thus, EACH statement ALONE is sufficient to answer the question asked, answer will be (D)....

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Re: Is k^2 odd?   [#permalink] 21 Nov 2016, 10:40
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic What is the value of k^2 - k? Bunuel 10 12 Dec 2014, 06:07
1 Experts publish their posts in the topic Is K^2 odd? 1) K-1 is divisable by 2 2) The sum of K amitjash 5 11 Jun 2010, 03:43
1 Experts publish their posts in the topic Is |k| = 2? zz0vlb 9 28 Apr 2010, 11:30
8 Experts publish their posts in the topic For positive integer k, is the expression (k + 2)(k2 + 4k + amitgovin 10 30 Sep 2009, 10:53
28 Experts publish their posts in the topic For positive integer k, is the expression (k + 2)(k^2 + 4k + kishankolli 19 22 Sep 2009, 02:51
Display posts from previous: Sort by

Is k^2 odd?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| 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®.