In a 100 page book, pages 2 and 3 face each other. Similarly, pages 4 and 5 and 6 and 7 face each other. This pattern is repeated to the end of the book. The sum of two facing pages could be [a] 95 [b] 97 [c] 99 [d] 90

Let the left side page = x (even)
The right side page =x+1 (odd)
Sum = 2x+1 (odd)

Now, consider the option 97.

If the sum is 97, then, 

97=2x+1
2x=96
x= 48
Then pages are 48 and 49.

 

You will observe that for all the other three options, we will get contradiction.