Problem Solving

At a certain university, the ratio of the number of teaching assistants to the number of students in a course must always be greater than 3:80. At this university, what is the maximum number of students possible in a course that has 5 teaching assistants.

130, 131, 132, 133, 134

My reasoning is that the ratio should be atleast 3:80 (always greater than). If instead of 3 we have 5 assiatant then the exact value is 133.33, however since we have to find the maximum number of students per teacher, where the ratio should be atleast 3:80 the answer has to be more than 133.33, the given max is 134, so i selectd E.

The answer is d. Can someone tell me the flaw in my reasoning.

given,
the number of students in a course must always be greater than 3:80
i.e....
t/s=3/80
this means for 80 students there must be at least 3 teaching assistants.
or 3 teaching assistant can only teach at most 80 students..
1 teaching assistant can only teach at most 80/3 students
5 teaching assistants can only teach at most 80/3 x 5 students = 133.3..
so, as per the question the number of students that the 5 teaching asst can teach must be below 133.33 but not more than 133.33...
So 133 is the answer...
(D)
Hope this helps

As the denominator value increases the value of the ratio decreases.So once should choose the value in the lower range.So the answer is 133.

As the denominator value increases the value of the ratio decreases.So once should choose the value in the lower range.So the answer is 133.

For 134 students you should have
134*3/80 = 5.025 TAs (i.e. more than 5)

so 5 TAs can take care of 133 students

Thanks for the responses guys, I understand all you say but please explain the following part of the Q

"the ratio of the number of teaching assistants to the number of students in a course must always be greater than 3:80"

the bold part says that ratio should always be greater than 3:80, so it can be greater than 3:80 but not less, if we take 133 then the ratio is less than 3:80, it will be 3:79.8. this is the part that I do not really understand.

vineetbatra wrote:Thanks for the responses guys, I understand all you say but please explain the following part of the Q

"the ratio of the number of teaching assistants to the number of students in a course must always be greater than 3:80"

the bold part says that ratio should always be greater than 3:80, so it can be greater than 3:80 but not less, if we take 133 then the ratio is less than 3:80, it will be 3:79.8. this is the part that I do not really understand.

Yes, look at the following:
3/80 = 0.0375
3/79.8 = 0.03759

0.03759 > 0.0375, therefore 3/79.8 is GREATER that 3/80, thus satisfying the original question!