Using the pairing method 1+100, 2+99, ..., 50+51, which expression equals the total sum from 1 to 100?

• A. 50 × 101
• B. 101 × 60
• C. 250 × 20
• D. 70 × 70

Answer: (A)

Pairing the numbers from 1 to 100 uses symmetry: the smallest and largest add to the same total. Pair 1 with 100, 2 with 99, and so on, up to 50 with 51. Each pair sums to 101, and there are 50 such pairs, so the total is 50 × 101, which equals 5050. This matches the familiar result for the sum of the first 100 integers. The other expressions would yield different values, so they don’t represent the total.