Carcass wrote:
If x denotes the sum of the integers from 1 to 40 inclusive, what is the sum of the integers from 41 to 80 inclusive, in terms of x?
Aside: Please recognize that this could never be an official GRE numeric entry (NE) question, since NE questions only have numeric answers. Okay, here's my solution,
We're told that
x = 1 + 2 + 3 + . . . + 39 + 40We want to find the sum: 41 + 42 + 43 + . . . + 79 + 80
We can rewrite the sum as: (40 +
1) + (40 +
2) + (40 +
3) + . . . + (40 +
39) + (40 +
40)
Rewrite as follows:
1 + 2 + 3 + . . . + 39 + 40 + 40 + 40 + 40 + 40 .....+ 40 + 40
Rewrite as:
1 + 2 + 3 + . . . + 39 + 40 + (40)(40)
Rewrite as:
x + 1600
Answer: x + 1600