Discussion

Explanation:

Average of 2 numbers is greater than 50 means that the sum should be greater than 100. 

Different pairs are as follows:
(1, 100) … (1 pair)
(2, 99), (2, 100) … (2 pairs)
(3, 98), (3, 99), (3, 100) … (3 pairs)

... so on

(49, 52), (49, 53) ... (49, 100) ... (49 pairs)
(50, 51), (50, 52 … (50, 100) ... (50 pairs)

So, 1 + 2 + 3 + 4 + ... + 50 = 1275

Again
(51, 51), (51, 52), (51, 53), ... (51, 100) ... (50 pairs)
(52, 52), (52, 53), (52, 54), ... (52, 100) ... (49 pairs)
(53, 53), (53, 54), (53, 55), ... (53, 100) ... (48 pairs)

... so on

(99, 99), (99, 100) ... (2 pairs)
(100, 100) ... (1 pair)

So, 1 + 2 + 3 + 4 + ... + 50 = 1275

Hence, total = 1275 + 1275 = 2550 pairs

Hence, option (c).

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