At a certain university, the dormitory policy is that each dormitory m

Question

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

Kudos for a correct solution.

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

maxville23 · Accepted Answer

3500 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

D

noTh1ng · Answer

Ratio of advisers to students is at least 7 / 200.

3.500 * (7/200) = 122,5. As there can not be half a adviser, round up to 123, which is the minimum amount of advisers. Answer D.

RAHULSAINI · Answer

7/200=x/3500

x=122.5 i.e. ~ 123

So answer is D

akhilbajaj · Answer

Min No of advisors per student = 7/200
Min No of advisors for 3500 students = 3500 * 7/200 =122.5

Since this is the min no of advisors, round it up to 123.

Answer D

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

If the minimum ratio of resident advisers to residents is 7:200, and the dormitory has 3500 advisers, then you can set up an equation using the idea that:

The ratio of x:3500 must be greater than or equal to 7:200.

Which, mathematically, translates to:

x/3500≥7/200

Then you can cross-multiply and solve for x:

200x≥7(3500) (Note: don't actually do the multiplication when you know you'll be able to divide both sides by 100)

That reduces to:

2x≥7(35)

Which then becomes:

x≥7(35)/2

From this point you can crunch the numbers however you like. One method is to divide the 35 by 2 so that you're multiplying 7 by 17.5, which breaks out somewhat conveniently to:

7 times 10, which you know is 70.

Plus 7 times 7, which you know is 49.

Plus 7 times .5, which is 3.5.

Add those up and x must be greater than (or equal to) 122.5, but since resident advisers must be integers the answer is then 123.

JeffTargetTestPrep · Answer

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

djangobackend · Answer

Bunuel   KarishmaB  why did we round up 3.5 to 4 and not round down to 3?

Bunuel · Answer

Because the condition is x ≥ 122.5, we need the smallest integer that satisfies it, which is 123. Rounding down to 122 would not meet the requirement.

At a certain university, the dormitory policy is that each dormitory m

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At a certain university, the dormitory policy is that each dormitory m

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