Is the average of X consecutive integers odd?

Question

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

Kurtosis · Answer

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

mbaprep2016 · Answer

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.

rakaisraka · Answer

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.

shonakshi · Answer

How is B the correct answer ? I got E :shock:

sweetkriti · Answer

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

abhimahna · Answer

Dude, the correct answer is E, not B.

mvictor · Answer

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.

GMATonMind · Answer

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.

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GMATonMind · Answer

I think I found my mistake.

I go with E.

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KrishnakumarKA1 · Answer

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

Jailer1284 · Answer

I got B but may be missing something
If sum is odd then half of digits need to be even half need to be odd (as even + odd) = odd
For half to be odd or even the total digits need to be even
Odd / Even is not an integer, so B is correct since it is always no.

Thoughts?

Bunuel · Answer

Check the following cases:

{2, 3}. The sum is odd (5), the averrage is NOT odd (2.5).

{2, 3, 4}. The sum is odd (9), the averrage IS odd (3).

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Is the average of X consecutive integers odd?

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Is the average of X consecutive integers odd?

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