1. Let's say that we're looking at the first 26 numbers, including 0. If we consider x = 0 and y = 26, then indeed we have 12 even integers between these two values. We will also have 13 odd numbers between 0 and 26. But if we consider x = 1 and y = 26, again, we have 12 even numbers between the two, but now we only have 12 odd numbers that fit the description.

2. In this case, one of the numbers has to be odd and one has to be even. Let's consider our numeric example again: if x = 0, then y has to be 25. Between the two there are exactly 12 odd numbers. If x = 1, then y = 26 and again we have 12 odd integers between the two. No matter how we "shift" x and y (meaning adding n to both of them) up the number scale, we will always get the same answer.

So B is sufficient

Very clear, thanks.

awilhelm wrote:Very clear, thanks.

Though it has been well explained by DanaJ, I would like to remind of one high school math rule which will help us tackling such problems on numbers without the need of assuming values.

1) it a and b are two integers and (b-a) = even no then no of odd integer b/w a and b = no of even integer b/w a and b

2) if (b-a)= not an odd integer then we should consider (b-1 -a) which will obviously be even then if b is odd then no of odd= 1+ no of even and if b is even then no of odd = no of even - 1

now coming back to question,

from 1st stmt since we dont know about total no of integers we also dont know about total no of odd nos.

from 2nd stmt clearly no of odd= no of even = 24/2 = 12

Hence B is the ans