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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 [#permalink]

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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

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: At a certain university, the dormitory policy is that each dormitory m [#permalink]

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New post 05 May 2015, 02:52
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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
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Re: At a certain university, the dormitory policy is that each dormitory m [#permalink]

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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.
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Re: At a certain university, the dormitory policy is that each dormitory m [#permalink]

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New post 05 May 2015, 08:41
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7/200=x/3500

x=122.5 i.e. ~ 123

So answer is D
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Re: At a certain university, the dormitory policy is that each dormitory m [#permalink]

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New post 05 May 2015, 18:26
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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
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Re: At a certain university, the dormitory policy is that each dormitory m [#permalink]

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New post 11 May 2015, 04:14
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Bunuel 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

Kudos for a correct solution.


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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: At a certain university, the dormitory policy is that each dormitory m [#permalink]

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New post 06 Feb 2018, 17:37
Bunuel 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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Re: At a certain university, the dormitory policy is that each dormitory m   [#permalink] 06 Feb 2018, 17:37
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