Problem Solving

A survey asked 210 college students if they preferred either windows or mac brand computers. 60 students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the preferred Windows to Mac Brand?


I tried to solve this by overlapping set table but im not translating the statements correctly.. can someone tell me where i went wrong? below is my table followed by translation logic..

Sorry had to remove the table it would not show properly (edited by HP engineer)..


the first statement 60 students claimed to prefer Mac i put as the total in the Prefer Mac Row.

Second statement says 1/3rd as many students who prefer Mac (i assume this to be 60) equally prefer both brands.. So i put 20 in the Yes Yes box.

Lastly they say 90 students no preference so i put that in the No No box.

Prefer windows in my Table = 80 and Prefer Mac = 60 which makes a difference of twenty which is incorrect..

HPengineer wrote:A survey asked 210 college students if they preferred either windows or mac brand computers. 60 students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the preferred Windows to Mac Brand?


I tried to solve this by overlapping set table but im not translating the statements correctly.. can someone tell me where i went wrong? below is my table followed by translation logic..

Sorry had to remove the table it would not show properly (edited by HP engineer)..


the first statement 60 students claimed to prefer Mac i put as the total in the Prefer Mac Row.

Second statement says 1/3rd as many students who prefer Mac (i assume this to be 60) equally prefer both brands.. So i put 20 in the Yes Yes box.

Lastly they say 90 students no preference so i put that in the No No box.

Prefer windows in my Table = 80 and Prefer Mac = 60 which makes a difference of twenty which is incorrect..

All = Mac Only + Windows Only + both + Neither
=> 210 = 60 + x + (60/3) + 90
=> x = 40

Let me try to put that in a table :

---------M-------------M'--------------

W------20------------x---------------

W'-----60-------------90------------

sorry still not seeing where u get 40 from the table... Question ask for Prefer Windows - Prefer Macs Dont we need the total for each of those rows to calculate the difference?

For this problem i feel i should have used venn diagram... it can be done in less then 1 minute that way... However now im fixated as to why i cant solve this by Overlapping sets table

HPengineer wrote:sorry still not seeing where u get 40 from the table... Question ask for Prefer Windows - Prefer Macs Dont we need the total for each of those rows to calculate the difference?

For this problem i feel i should have used venn diagram... it can be done in less then 1 minute that way... However now im fixated as to why i cant solve this by Overlapping sets table

Both approaches work.

Please note in the diagram above :

Intersection of M,W => 20 => students who prefer both Mac and windows
Intersection of M,W' => 60 => students who prefer Mac but not windows
Intersection of M',W' => 20 => students who neither prefer Mac nor windows
Intersection of M',W => x => students who prefer windows but not mac (This is what the question asks for).

As you can see these four cover all the possible sets of students, so their sum = 210
=> 20+x+60+90 = 210
=> x = 40.

that clears my confusion friend.... I was thinking i need to subtract the totals but really the problem was looking for a specific intersection.

Good problem. I too was thrown off by "prefer Mac TO windows" - Should've interpreted it as "Likes MAC NOT WINDOWS!".
Must brush up my Idioms!!!

210 total students
60 for Mac
20 both
90 none
x Windows

so,
210-90=120-60=60-20=40