What is the average height of the class?
(I) Average height of the class decreases by 1 cm if we exclude the tallest person of the class whose height is 56 cm.
(II) Average height of the class increases by 1 cm if we exclude the shortest person of the class whose height is 42 cm.

Let x be the average height of the class and n be the number of students in the class.
Consider statements I alone
xn - 56 = (x -1)(n -1)
⇒ x + n = 57        (1)
Hence, the value of x cannot be found. So, I alone is not sufficient.
Consider statement I alone:
xn - 42 = (x + 1)(n - 1)
⇒ x - n = 41           (2)
Hence, the value of x cannot be found. So, II alone is not sufficient.
Both the statements together are sufficient as the value of x can be found by solving (1) and (2)