If x represents the product of the first 100 positive odd integers and

Normally choices help us even before we start..
we are looking at integers and it can be either odd or even, so answer has to be A or B..

\(x = 1*3*5.......*199\)... Product of odd integers will be ODD
\(y = 1+3+5.......+199\), there are 100 numbers of ONE type, so irrespective of all being ODD or all being even, the SUM will be EVEN
so x-y = Odd-Even = Odd..
B
But lets look at other choices..
A) even:
It cannot be EVEN
C) Negative :-
x is product and y sum so x >y, so x-y>0
D) divisible by 3..
product consists of multiple of 3, so x= 1*3*5..*199 will be div by 3
SUM.. sum of any three consecutive odd integers will be div by 3, so had there been 99 integers, it would have been div by 3, but there are 100 integers so SUM is NOT div by 3
so Multiple of 3-Non-multiple of 3 = Non-multiple of 3.. ans No
E) div by 6..
If not div by3, it will NOT be div by 6.. hence NO

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