For any set of consecutive integers:
count = biggest - smallest + 1.
average = (biggest + smallest)/2.
sum = (count)(median).

M7MBA wrote:Bob is training for a fitness competition. In order to increase his maximum number of pull-ups, he follows the following routine: he begins with 25 pull-ups, rests for thirty seconds, and then does 24 pull-ups and rests, dropping one pull-up each time (25, 24, 23, etc.) until his final set of 11 pull-ups. How many total pull-ups does Bob do?

(A) 55
(B) 150
(C) 270
(D) 275
(E) 325

Since Bob starts with 25 pull-ups and drops 1 pull-up each round until his final set of 11 pull-ups, the pull-ups are composed of the consecutive integers between 11 and 25, inclusive.
Thus:
count = 25 - 11+ 1 = 15.
average = (25+11)/2 = 18.
sum = 15*18 = 270.

The correct answer is C.

M7MBA wrote:Bob is training for a fitness competition. In order to increase his maximum number of pull-ups, he follows the following routine: he begins with 25 pull-ups, rests for thirty seconds, and then does 24 pull-ups and rests, dropping one pull-up each time (25, 24, 23, etc.) until his final set of 11 pull-ups. How many total pull-ups does Bob do?

(A) 55
(B) 150
(C) 270
(D) 275
(E) 325

The number of pull-ups Bob does is the sum of integers from 11 to 25 inclusive. Thus, the total number of pull-ups he does is

15(11 + 25)/2 = 15 x 18 = 270

Alternate Solution:

We need to calculate the sum of the consecutive integers from 11 to 25, inclusive. Rather than calculate 11 + 12 + 13 + ... + 24 + 25, we can calculate the average of the integers and then multiply the average by the number of integers to get the sum.

We know that there are (25 - 11) + 1 = 14 + 1 = 15 integers.

To calculate the average of the 15 integers, we use (smallest + largest)/2 = (11 + 25)/2 = 18.

The average is 18. Thus, the sum is 18 x 15 = 270.

Answer: C