Bob is training for a fitness competition. In order to increase his maximum number of pull-ups, he follows...

BTGmoderatorLU wrote: ↑

Fri Jun 12, 2020 4:23 am

Source: Magoosh

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 C

So, the no. of pull-ups are in descending order, starting from 25, 24, 23, ...., 11. So, there are a total of (25 – 11) + 1 = 15 sets.

Since the no. of pull-ups are evenly spaced, we can find out their average (arithmetic mean) by taking the average of the first and the last set, i.e., 25 and 11. So, the average = (25 + 11)/2 = 18

So, the total no. of pull-ups in 15 sets = 15*18 = 270

Correct answer: C

Hope this helps!

-Jay
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BTGmoderatorLU wrote: ↑

Fri Jun 12, 2020 4:23 am

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 C

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