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The average of consecutive numbers is nothing but middle number (if X is odd) or average of middle two numbers (if X is even)

Statement 1 : tells nothing about X, set could be, 1,2,3 - Avg = 2 OR just 1,2 - Avg = 1.5 Statement 2 : sum of X consecutive integers = X * Avg As per statement its Odd. Odd * Odd = Odd.

So we know both X and Avg should be Odd. Suff.

Answer B.

hi durgesh79, u said that sum of X consecutive integers = X * Avg correct

(2) The sum of the numbers is odd.

if x=2 i.e even+odd=odd average is in decimals its not a integer as a result it cannot be odd or even

1) clearly insuff, consider 3,4 result is fraction, then consider 1,2,3 average is even 2) for sum to be odd there should be odd number of odd numbers in the sequence. 2,3 OR 3,4 result is fraction, -1,0,1,2,3 average is odd. so insuff

together, insuff, consider sequences in 2 above (3,4)(-1,0,1,2,3)

The average of consecutive numbers is nothing but middle number (if X is odd) or average of middle two numbers (if X is even)

Statement 1 : tells nothing about X, set could be, 1,2,3 - Avg = 2 OR just 1,2 - Avg = 1.5 Statement 2 : sum of X consecutive integers = X * Avg As per statement its Odd. Odd * Odd = Odd.

Even set of terms results in a decimal= NO Odd set of terms results in an odd or even integer= YES & NO Therefore is insufficent

Statement 2

odd number of terms results in a odd integer using 1+2+3+4+5/2= ODD= YES maybe odd number of terms results in a odd integer using 1+2+3+4+5+6+7/2= EVEN= NO maybe Therefore is insufficent

When I combined them, Still not consistent 19:27=ODD/9=ODD=YES 1:6=ODD/6= decimal= NO

I did a quick chart with the simplest of choices. I will try to sum up the chart without one.

1: Take the odd start to be 1. X = 1 => odd X = 2 => (1 + 2)/2 => decimal Insufficient.

2: Though it may not be suggestible I decided to use above examples so both figuring out if it was B as well as if it was either C or E. X = 1 => odd X = 2 => (1 + 2)/2 => decimal B is Insufficient and because I used examples that started with an odd number both together are also insufficient.