At a certain university, the dormitory policy is that each

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Fri Aug 10, 2018 5:22 pm

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At a certain university, the dormitory policy is that each dormitory must have at least 7 resident advisers for every 200 residents. If a dormitory is home to 3500 residents, what is the minimum number of resident advisers required?

A. 120
B. 121
C. 122
D. 123
E. 124

OA D
Source: Veritas Prep

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by Brent@GMATPrepNow » Sat Aug 11, 2018 6:30 am

BTGmoderatorDC wrote:At a certain university, the dormitory policy is that each dormitory must have at least 7 resident advisers for every 200 residents. If a dormitory is home to 3500 residents, what is the minimum number of resident advisers required?

A. 120
B. 121
C. 122
D. 123
E. 124

OA D
Source: Veritas Prep

One approach is to use equivalent ratios

Each dormitory must have at least 7 resident advisers for every 200 residents.
So, advisers/residents = 7/200

If a dormitory is home to 3500 residents, what is the minimum number of resident advisers required?
Let x = minimum number of advisers
We can write: 7/200 = x/3500
Cross multiply to get: (7)(3500) = 200x
Divide both sides by 200 to get: (7)(3500)/200 = x
Simplify: (7)(35)/2 = x
Evaluate: 245/2 = x
Solve: 122.5 = x
Since we can't have HALF A PERSON, we must round up to 123

Answer: D

Cheers,
Brent

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Aug 26, 2018 6:34 pm

BTGmoderatorDC wrote:At a certain university, the dormitory policy is that each dormitory must have at least 7 resident advisers for every 200 residents. If a dormitory is home to 3500 residents, what is the minimum number of resident advisers required?

A. 120
B. 121
C. 122
D. 123
E. 124

We can create the following proportion, where n is the required number of resident advisers:

n/3500 ≥ 7/200

200n ≥ 7 x 3500

2n ≥ 7 x 35

n ≥ 122.5

Thus, the minimum value of n is 123.

Answer: D

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swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Mon Aug 27, 2018 3:13 pm

3,500 residents -> 17*200 residents + 100 residents

For 3400, at least 17*7 = 119 resident advisors required.

As there are at least 7 for 200 residents required, for 100, there are 7/2 required -> has to be an integer -> round up -> at least 4 for 100.

For the remaining 100 residents: 4 resident advisors required

Adding them up: 119 + 4 = 123

Hence, D is the correct answer.

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