Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43893

Is the average of X consecutive integers odd? [#permalink]
Show Tags
20 Jul 2016, 10:43
Question Stats:
62% (01:14) correct 38% (01:13) wrong based on 110 sessions
HideShow timer Statistics



SC Moderator
Joined: 13 Apr 2015
Posts: 1584
Location: India
Concentration: Strategy, General Management
WE: Analyst (Retail)

Re: Is the average of X consecutive integers odd? [#permalink]
Show Tags
20 Jul 2016, 18:24
2
This post was BOOKMARKED
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
Joined: 29 May 2016
Posts: 130

Re: Is the average of X consecutive integers odd? [#permalink]
Show Tags
20 Jul 2016, 22:25
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
Joined: 27 Aug 2015
Posts: 97

Re: Is the average of X consecutive integers odd? [#permalink]
Show Tags
04 Sep 2016, 12:49
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.



Manager
Joined: 17 Jun 2016
Posts: 62

Re: Is the average of X consecutive integers odd? [#permalink]
Show Tags
04 Sep 2016, 23:23
How is B the correct answer ? I got E



Manager
Joined: 03 Jan 2016
Posts: 92
WE: Operations (Manufacturing)

Re: Is the average of X consecutive integers odd? [#permalink]
Show Tags
05 Sep 2016, 00:51
1
This post was BOOKMARKED
shonakshi wrote: How is B the correct answer ? I got E 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
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3082

Re: Is the average of X consecutive integers odd? [#permalink]
Show Tags
09 Sep 2016, 05:18
prakhar39 wrote: shonakshi wrote: How is B the correct answer ? I got E 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.
_________________
How I improved from V21 to V40! ? How to use this forum in THE BEST way?



Board of Directors
Joined: 17 Jul 2014
Posts: 2734
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: Is the average of X consecutive integers odd? [#permalink]
Show Tags
22 Sep 2016, 06:09
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 noninteger. NO. 3+4+5+6+7 = 25. 25/5 = 5. yes. since 1+2 yields different outcomes, E is the answer.



Intern
Joined: 02 Apr 2016
Posts: 11

Re: Is the average of X consecutive integers odd? [#permalink]
Show Tags
22 Sep 2016, 11:30
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
Joined: 02 Apr 2016
Posts: 11

Re: Is the average of X consecutive integers odd? [#permalink]
Show Tags
22 Sep 2016, 11:40
I think I found my mistake. I go with E. Sent from my Nexus 4 using GMAT Club Forum mobile app



Senior Manager
Joined: 05 Jan 2017
Posts: 434
Location: India

Re: Is the average of X consecutive integers odd? [#permalink]
Show Tags
23 Feb 2017, 23:42
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




Re: Is the average of X consecutive integers odd?
[#permalink]
23 Feb 2017, 23:42






