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At a certain university

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by BTGmoderatorDC » Sun Feb 04, 2018 9:43 pm
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

Can some experts show me the simplest solution?

OA D
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by GMATGuruNY » Mon Feb 05, 2018 4:03 am
lheiannie07 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
Let a = the number of advisers.

Since there are 3500 residents -- and the ratio of advisers to residents must be at least 7/200 -- we get:
a/3500 ≥ 7/200
200a ≥ 3500*7
2a ≥ 35*7
2a ≥ 245
a ≥ 122.5.

Since the value of a must be an INTEGER, the least possible value for a is 123.

The correct answer is D.
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by Scott@TargetTestPrep » Tue Feb 06, 2018 5:13 pm
lheiannie07 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 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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