Carcass wrote:
In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 560. What is the sum of the last 5 integers in the sequence?
(A) 585
(B) 580
(C) 575
(D) 570
(E) 565
Here's one approach:
Let a, b, c, d, and e be the first 5 consecutive integers, which means
a + b + c + d + e = 560 Here's a unique way to list all 10 consecutive integers:
a, b, c, d, e, a+5, b+5, c+5, d+5, e+5 [We can see that e is 4 greater than a, which means the number after e must be 5 greater than a, and so on]So, the sum of the last 5 integers
= (a+5) + (b+5) + (c+5) + (d+5) + (e+5)= a + b + c + d + e + 25= 560 + 25= 585Answer: A