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Bob is training for a fitness competition. In order to

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by M7MBA » Thu Jun 14, 2018 11:31 pm

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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 OA is the option C.

Could someone explain how to solve this PS question to me? I don't know which equation helps me. <i class="em em-anguished"></i>
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by GMATGuruNY » Fri Jun 15, 2018 2:01 am
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.
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by Jeff@TargetTestPrep » Sun Jun 24, 2018 5:04 pm
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

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