Question

Given that 1 + 2 + 3 + 4 + 5 + 6 = 21, the sum of 61 + 62 + 63 + 64 + 65 + 66 is .

• A. 351
• B. 341
• C. 361
• D. 381

Answer 1

The correct option is D 381

We can use the method of smart addition to easily find out the sum.
We can splt up the numbers in the sum of 61 + 62 + 63 + 64 + 65 + 66 as (60 + 1), (60 + 2), ... , (60 + 6).

Then grouping the 60 together,
61 + 62 + 63 + 64 + 65 + 66 becomes 60 $\times$ 6 + (1 + 2 + 3 + 4 + 5 + 6)
Since it's already given that
1 + 2 + 3 + 4 + 5 + 6 = 21,

Sum = 60 $\times$ 6 + 21 = 360 + 21 = 381