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>
Bob is training for a fitness competition. In order to
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For any set of consecutive integers:
count = biggest - smallest + 1.
average = (biggest + smallest)/2.
sum = (count)(median).
Thus:
count = 25 - 11+ 1 = 15.
average = (25+11)/2 = 18.
sum = 15*18 = 270.
The correct answer is C.
count = biggest - smallest + 1.
average = (biggest + smallest)/2.
sum = (count)(median).
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.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
Thus:
count = 25 - 11+ 1 = 15.
average = (25+11)/2 = 18.
sum = 15*18 = 270.
The correct answer is C.
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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 isM7MBA 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
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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