Question

Let $A = \sum_{i=1}^{10} \sum_{j=1}^{10} \min(i, j)$
and
$B = \sum_{i=1}^{10} \sum_{j=1}^{10} \max(i, j)$
Then A + B is equal to___________.

Answer 1

The correct answer is 1100
Each element of ordered pair {i, j} is either present in A or in B.
So, A + B =Sum of all elements of all ordered pairs {i, j} for $1 ≤ i ≤ 10 and 1 ≤j≤ 10$
= 20 (1 + 2 + 3+…. + 10)= 1100