Given ratio between assistant and students > 3:80pratyoosh wrote:Q. At a certain university, the ration of the number of teaching assistants to the number of students in any 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?
1. 130
2. 131
3. 132
4. 133
5. 134
Ans : D
shovan85 wrote:Given ratio between assistant and students > 3:80pratyoosh wrote:Q. At a certain university, the ration of the number of teaching assistants to the number of students in any 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?
1. 130
2. 131
3. 132
4. 133
5. 134
Ans : D
Asst/Stud > 3x/80x (x multiplied to both numerator and denominator)
This means students will be less than or equal to 80x .In other words, maximum possible students 80x (Denominator is the student and if student is more than 80x then Ratio will be less than 3:80. Thus, student will be always less than 80x)
As per question 3x = 5 i.e. x = 5/3
Thus, Number of students 80x = 400/3 = 133.33 . We have to round down here to maintain the inequality .
So Students = 133
gdk800 wrote:pratyoosh wrote:
I c. Had got 133.something as the answer, but I choose 134 as it said "maximum number of students" and presumed that since I had the decimals there, that 134 would be the safer bet!
Thanks for your help.
Pratyoosh, the answer as Shovan described should be 133 and not 134. You cannot round off 133.33 to 134 for following 2 reasons:
1) Number of people has to be whole number.
2) since 133.33 < 133.5, rounding off would lead to 133 and not 134.
Hope it clarifies.
The safest approach would be to plug in the answer choices, which represent the number of students. We should start with the largest answer choice, since the question asks for the maximum number of students possible. When we plug in the correct answer choice, assistants/students will be greater than 3/80.shovan85 wrote:Given ratio between assistant and students > 3:80pratyoosh wrote:Q. At a certain university, the ration of the number of teaching assistants to the number of students in any 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?
1. 130
2. 131
3. 132
4. 133
5. 134
Ans : D
Asst/Stud > 3x/80x (x multiplied to both numerator and denominator)
This means students will be less than or equal to 80x .In other words, maximum possible students 80x (Denominator is the student and if student is more than 80x then Ratio will be less than 3:80. Thus, student will be always less than 80x)
As per question 3x = 5 i.e. x = 5/3
Thus, Number of students 80x = 400/3 = 133.33 . We have to round down here to maintain the inequality .
So Students = 133
That's not entirely correct.... you're right on point 1 that the number of people has to be a whole number, but we know this because all of our answer choices are whole numbers. As for point two however, we're not "rounding down" because 133.33 < 133.5, but instead.... since the answer when doing the math came to 133.33 and the question states that the ratio "must ALWAYS be greater than 3:80" then it would have to be LESS than 133.33.... ALWAYS. Even if doing the math got you say 133.8... you WOULD NOT be able to round up to 134, the answer would still be 133, because the ratio MUST ALWAYS BE GREATER THAN.... make sense?gdk800 wrote: Pratyoosh, the answer as Shovan described should be 133 and not 134. You cannot round off 133.33 to 134 for following 2 reasons:
1) Number of people has to be whole number.
2) since 133.33 < 133.5, rounding off would lead to 133 and not 134.
Hope it clarifies.
Let S be the number of students. We need 3/80 < 5/S, therefore multiplying both sides by the positive value 80Spratyoosh wrote:Q. At a certain university, the ration of the number of teaching assistants to the number of students in any 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?
1. 130
2. 131
3. 132
4. 133
5. 134
fskilnik wrote:Let S be the number of students. We need 3/80 < 5/S, therefore multiplying both sides by the positive value 80SPratyoosh wrote:Q. At a certain university, the ration of the number of teaching assistants to the number of students in any 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?
1. 130
2. 131
3. 132
4. 133
5. 134
we get 3S < 5*80, that means S < 400/3 = (399+1)/3 = 133 + 1/3.
From the fact that S must be an integer, the maximum value it may achieve is 133.
Regards,
Fabio.
