2013-09-23 09:00:25

The sum of 5 consecutive integers is 20n + 5. What is the largest of the integers in terms of n?

(A) 4n + 1
(B) 4n + 2
(C) 4n + 3
(D) 5n + 1
(E) 5n + 3


The correct answer is C
Explanation: In a set of consecutive integers, the middle number will be their average. Thus, if the five integers in question sum to 20n + 5, then the middle number will be 4n + 1, as 4n + 1 is the average of five numbers that sum to 20n + 5 (put differently: 20n + 5 ÷ 5 = 4n + 1).

Thus, 4n + 1 is the middle number. That means two numbers will be less than that and two numbers will be greater than it. The numbers would, as such, be

4n – 1, 4n, 4n + 1, 4n + 2, and 4n + 3

The question asks for the greatest integer, so it is 4n + 3, which is choice C