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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At a certain university, the dormitory policy is that each
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BTGmoderatorDC
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One approach is to use equivalent ratiosBTGmoderatorDC 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
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
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Scott@TargetTestPrep
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We can create the following proportion, where n is the required number of resident advisers: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
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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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.
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.
