Hi..
Thanks for the solution. just confused where you say 4x-17 is always ODD so we can cancel options with even denominator, but we are talking about the ratio here rather than actual values. for instance if 25x-80 is also odd then an ODD factor cancelling both the terms out could also have resulted in an even denominator as well?
Bunuel wrote:
The student-professor ratio at a certain university was 25:4, but when the university expelled eighty students for acts of civil disobedience, seventeen professors quit in protest. Which of the following could be the new student-professor ratio at the university?
A. 63:12
B. 95:17
C. 33:5
D. 55:6
E. 55:3
Hi...
Ratio is \(\frac{25}{4}\)...
If common factor is x, then the numbers become 25x and 4x...
If you take out 80 students and 17 instr, numbers become 25x-80 and 4x-17...
We can eliminate few choices straight way..
4x-17 will be always ODD, so choices with even ratio in denominator can be left out..
So A and D are out..
Let's check the remaining..
Start from centre as you would know if you have to move to a higher or lower ratio after checking the middle value.
So \(\frac{25x-80}{4x-17}=33/5..........(25x-80)*5=(4x-17)*33....125x-400=132x-561......7x=161....x=23\)
Since x is an integer value, this is our answer.
C
We can check for other values but x should not be integer value.
Let's check ONE
So \(\frac{25x-80}{4x-17}=\frac{55}{3}..........(25x-80)*3=(4x-17)*55....75x-240=220x-935......145x=695....\)
Since x is not an integer value, this is not our answer.