There are 24 children on a school outing. At lunch-time 11 of them ate sandwich, 9 ate banana, n of them ate neither a sandwich nor banana. By...

Out of the 24 students on the school outing
:

11 ate sandwich, so 24 - 11 = 13 did not eat a
sandwich.

9 ate a banana, so 24 - 9 = 15 did not eat eat a
banana.

Now the n of them ate neither a sandwich nor a
banana.

If the set of those ate a banana lies within those
who ate sandwich, those who ate neither is 24 - 11 = 13.

If
there are no common elements in the set who ate sandwich and those who ate banana the
number who ate neither is 24 - 11- 9 =
4.

Therefore the smallest possible value of n
is 4 and the largest value of n is 13.