Bob is training for a fitness competition. In order to. . .

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

Bob is training for a fitness competition. In order to. . .

by M7MBA » Mon Nov 06, 2017 6:21 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 is C.

I can do it making the whole sum: 25+24+23+22+...+11, but, is there another way (faster or easier) to make it?

Experts, can you give me a hand here?

Quote

Source: Beat The GMAT — Problem Solving | Mon Nov 06, 2017 6:21 am

GMAT/MBA Expert

ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 am; Thanked: 86 times; Followed by:15 members; GMAT Score:770

by ErikaPrepScholar » Mon Nov 06, 2017 9:11 am

Great question - there is a faster way! When we have any group of terms, we can find the sum of all of those terms with:

$$mean\ \cdot\ number\ of\ terms$$

When we have a group of consecutive terms, we can find the mean of those terms with:

$$\frac{first\ term+last\ term}{2}$$

Combining those two equations, we can find the sum of a group of consecutive terms with:

$$\frac{first\ term+last\ term}{2}\cdot\ number\ of\ terms$$

Here, this gives:

$$\frac{25\ +\ 11}{2}\ \cdot\ 15\ =\ 270$$

Erika John - Content Manager/Lead Instructor
https://gmat.prepscholar.com/gmat/s/

Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/

Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial

Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Oct 29, 2019 6:00 am

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 OA is C.

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

I can do it making the whole sum: 25+24+23+22+...+11, but, is there another way (faster or easier) to make it?

Experts, can you give me a hand here?