If the population of a certain country increases...

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swerve: Legendary Member; Posts: 2548; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Mon Jan 08, 2018 6:47 am

If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 20 minutes?

A. 80
B. 100
C. 150
D. 240
E. 300

The OA is A.

Please, can any expert explain this PS question for me? I tried to solve it of the following way,

I know that every 15 seconds the population increases at a rate of one person, that's mean 4 persons per minute, then in 20 minutes will be 20 x 4 = 80, right? That's it? Thanks.

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Source: Beat The GMAT — Problem Solving | Mon Jan 08, 2018 6:47 am

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

by ErikaPrepScholar » Mon Jan 08, 2018 6:54 am

You nailed it! This problem is deceptively simple. We can also do this a more traditional way by cancelling units using conversion factors:
$$20\ \min\ \cdot\ \left(\frac{60\ \sec}{1\ \min}\right)\cdot\left(\frac{1\ person}{15\ \sec}\right)$$ Then cancel units $$20\ \ \cdot\ \left(\frac{60\ }{1\ }\right)\cdot\left(\frac{1\ person}{15\ }\right)$$ Cancel 15 from the numerator and denominator and solve $$20\ \ \cdot\ \left(\frac{4}{1\ }\right)\cdot\left(\frac{1\ person}{1\ }\right) = 80\ people$$

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8157; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Aug 12, 2019 10:42 am

swerve wrote:If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 20 minutes?

A. 80
B. 100
C. 150
D. 240
E. 300

We are given that a population increases by 1 person every 15 seconds, and we need to determine how many people it will increase by in 20 minutes, which is 20 x 60 = 1200 seconds. We can let x = the number of people being added to the population in 20 minutes and create the following proportion:

1/15 = x/1200

15x = 1200

x = 80

Alternate Solution:

A rate of one person every 15 seconds equals a rate of 4 people per minute. Thus, in 20 minutes, the population is increased by 4 x 20 = 80 people.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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