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# The ratio of teachers to students must always be greater

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Intern
Joined: 10 Aug 2005
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The ratio of teachers to students must always be greater [#permalink]  10 Aug 2005, 18:21
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The ratio of teachers to students must always be greater than 3:80
If there are 5 teachers, what is the maximum number of students possible?

a)130
b)131
c)132
d)133
e)134
Manager
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[#permalink]  10 Aug 2005, 20:28
If I interpret the question correctly, here is my solution:

Let the number of students be x

3/80=5/x

3x=(5)(80)=400

x=133.33333

The question demands that the ratio needs to be greater than 3/80, so 132 will be the number that fits.

Check: 3/80=0.0375; 5/132=0.03788

Hope this helps.
SVP
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Re: PS - Maximum number based on a ratio [#permalink]  10 Aug 2005, 20:37
(d) 133.

if it is 134, the ratio would be 5/134, which is less than 3/80. so if it is 5/133, the ratio 5/133>3/80.
Director
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[#permalink]  11 Aug 2005, 03:24
5/x>3/80, 3X>400, X>400/3 or X=133
Manager
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[#permalink]  11 Aug 2005, 06:05
3/80=5/x

x=133.333 or greater.

hence, E.

Editing:

Has to be 133.33 or smaller for the ratio to be greater.
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Thanks!

Manager
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[#permalink]  11 Aug 2005, 10:02
I think the I will retract me answer. If it is 133, then 5/133=0.037594, which is greater than 3/80. The answer should be D 133.
SVP
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[#permalink]  11 Aug 2005, 13:33
BG wrote:
5/x>3/80, 3X>400, X > 400/3 or X=133

Right way to solve this, but you forget to flip the sign on your way of deriving.

T/S>3/80
S/T<80/3
S<80/3*T
S<80*5/3=400/3=133.3
S=133
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keep on seeking, and you will find;
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[#permalink] 11 Aug 2005, 13:33
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# The ratio of teachers to students must always be greater

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