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

It is currently 16 Oct 2018, 03:10

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

Is the average of X consecutive integers odd?

  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: 49892
Is the average of X consecutive integers odd?  [#permalink]

Show Tags

New post 20 Jul 2016, 11:43
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

58% (01:59) correct 42% (01:59) wrong based on 119 sessions

HideShow timer Statistics

SC Moderator
User avatar
D
Joined: 13 Apr 2015
Posts: 1694
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
GMAT ToolKit User Premium Member
Re: Is the average of X consecutive integers odd?  [#permalink]

Show Tags

New post 20 Jul 2016, 19:24
2
If the number of consecutive integers is even the average will be a fraction.
If the number of consecutive integers is odd the average will be an integer.

St1: First number is odd --> We do not know about the number of terms. Insufficient

St2: Sum of the numbers is odd --> Let n be the number of even integers and n' be the number of odd integers
n(Even) + n'(Odd) = Odd
Possible cases: n is even and n' is odd --> Number of terms = n + n' = odd --> Average is an integer. --> Average may be odd or even
n is odd and n' is odd --> n + n' = even --> Average is not an integer --> Average is not odd
Not Sufficient

Combining St1 and St2: First number is odd and sum is odd --> Odd + Even + Odd + Even + Odd --> Sum is odd and average is odd
Odd + Even --> Sum is odd, but average is not odd.
Not Sufficient

Answer: E
Manager
Manager
avatar
S
Joined: 29 May 2016
Posts: 106
Re: Is the average of X consecutive integers odd?  [#permalink]

Show Tags

New post 20 Jul 2016, 23:25
1)
consider 1 and 2 ; average is 1.5 answer is NO
consider 1,2,3,4,5; average is 3 answer is Yes

2) consider same numbers sum of number in both set will be odd answer again Yes and NO
combine Answer is E.
Manager
Manager
avatar
B
Joined: 27 Aug 2015
Posts: 86
Re: Is the average of X consecutive integers odd?  [#permalink]

Show Tags

New post 04 Sep 2016, 13:49
Hi Bunuel , Can you explain how B is correct answer.

I did as -

1+ 2 = 3 > odd and avg 1.5 so answer is No
1+2+3+4+5 = 15 > odd , avg = 3 , so Y
This makes it insuf.
Intern
Intern
User avatar
B
Joined: 17 Jun 2016
Posts: 45
Re: Is the average of X consecutive integers odd?  [#permalink]

Show Tags

New post 05 Sep 2016, 00:23
How is B the correct answer ? I got E :shock:
Manager
Manager
avatar
B
Joined: 03 Jan 2016
Posts: 80
WE: Operations (Manufacturing)
GMAT ToolKit User Reviews Badge
Re: Is the average of X consecutive integers odd?  [#permalink]

Show Tags

New post 05 Sep 2016, 01:51
1
shonakshi wrote:
How is B the correct answer ? I got E :shock:


Here is what I can think of:
taking 4 cases
first start with odd number, and take number of terms as even and odd:
3,4,5,6 => sum 18
3,4,5 => sum 12

first start with even number, and take number of terms as even and odd:
4,5,6,7 => sum 22
4,5,6 => sum 15

only one case, when I start with even and take odd number of terms I get odd sum.
and therefore average will also be odd.

Statement B
Board of Directors
User avatar
V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3627
Premium Member Reviews Badge
Re: Is the average of X consecutive integers odd?  [#permalink]

Show Tags

New post 09 Sep 2016, 06:18
prakhar39 wrote:
shonakshi wrote:
How is B the correct answer ? I got E :shock:


Here is what I can think of:
taking 4 cases
first start with odd number, and take number of terms as even and odd:
3,4,5,6 => sum 18
3,4,5 => sum 12

first start with even number, and take number of terms as even and odd:
4,5,6,7 => sum 22
4,5,6 => sum 15

only one case, when I start with even and take odd number of terms I get odd sum.
and therefore average will also be odd.

Statement B


Dude, the correct answer is E, not B.
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place
Blog: Subscribe to Question of the Day Blog

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.

New! Best Reply Functionality on GMAT Club!



Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free

Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2654
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: Is the average of X consecutive integers odd?  [#permalink]

Show Tags

New post 22 Sep 2016, 07:09
Bunuel wrote:
Is the average of X consecutive integers odd?

(1) The first number in the sequence is odd.
(2) The sum of the numbers is odd.


damn, took ~2 mins to test all the options...
1. (1+2+3)/3 = 2 no and (1+2+3+4+5)/5=3 yes
A and D are out.

2. 2+3+4 = 9. 9/3 =3 odd yes.
3+4+5 = 12. 12/3 = 4 even no

B is out.
so it's either D or E. at least 50% probability of getting the right answer is better than 20% :)

1+2
first number is odd, and sum is odd.
1+2 = 3. 3/2 = 1.5 non-integer. NO.
3+4+5+6+7 = 25. 25/5 = 5. yes.

since 1+2 yields different outcomes, E is the answer.
Intern
Intern
avatar
Joined: 02 Apr 2016
Posts: 10
GMAT ToolKit User
Re: Is the average of X consecutive integers odd?  [#permalink]

Show Tags

New post 22 Sep 2016, 12:30
The sum of consecutive integers is odd.

Given, sum is odd. Thus the number of terms is odd. So first + last = even + even = even

Or odd + odd = even.

Thus even/ 2 can be either even or odd.


So B cannot give the answer.

Now A states first term is odd . So last term is odd as well from B.

So odd + odd divided by 2 is odd. So the average is odd.
C.

Sent from my Nexus 4 using GMAT Club Forum mobile app
Intern
Intern
avatar
Joined: 02 Apr 2016
Posts: 10
GMAT ToolKit User
Re: Is the average of X consecutive integers odd?  [#permalink]

Show Tags

New post 22 Sep 2016, 12:40
I think I found my mistake.

I go with E.

Sent from my Nexus 4 using GMAT Club Forum mobile app
Senior Manager
Senior Manager
User avatar
B
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 468
Location: India
Premium Member
Re: Is the average of X consecutive integers odd?  [#permalink]

Show Tags

New post 24 Feb 2017, 00:42
Superset
The answer will be either yes or no

Translation
In order to find the answer, we need
1# exact value of average
2# sum of the numbers as well as number of numbers
3# all the numbers in the set

Statement analysis
St 1: we take 2 set.(3,4,5) and (3,9,15). The average for 1st is 4 and second is 9. INSUFFICIENT
St 2: sum is odd. If sum is divided by odd integer it might yield an odd integer or a fraction and if it is divided by even integer, it will yield a fraction. INSUFFICIENT

St 1 & St2: take (3,9,15) and (3,9,13). The average will be 9 and 8.33. INSUFFICIENT

OPtion E
_________________

GMAT Mentors
Image

GMAT Club Bot
Re: Is the average of X consecutive integers odd? &nbs [#permalink] 24 Feb 2017, 00:42
Display posts from previous: Sort by

Is the average of X consecutive integers odd?

  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®.