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September 20th, 2015, 07:11 PM  #1 
Newbie Joined: Oct 2012 Posts: 29 Thanks: 0  Students taking class, and intersections
Attached is the problem. The teacher had an approach but it didnt seem to work, attachment will be posted in the replies.

September 20th, 2015, 07:17 PM  #2 
Newbie Joined: Oct 2012 Posts: 29 Thanks: 0  Teachers approach
This is the teachers approach. She wadnt the one who gave the problem so she isnt sure about her approach either
Last edited by Volle; September 20th, 2015 at 07:27 PM. Reason: Attachment unsuccessfully uploaded 
September 21st, 2015, 05:38 PM  #3 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 645 Thanks: 85 
The question is wrong. 34 took English and Math + 20 took Math and Chemistry + 6 took all three = at least 60 students who took Math, but the question says 56 took Math.

September 21st, 2015, 05:55 PM  #4 
Newbie Joined: Oct 2012 Posts: 29 Thanks: 0 
The students who took all thhree subjects are counted into the students who took at least two subjects. English and math denotes the number of students who took at least english and math, not english only and math only but not chemistry. Similarly, english denotes the number of students who took at least the english class, so english and chem, english and math, and took all subjects, are included under that. 
September 22nd, 2015, 07:35 AM  #5 
Senior Member Joined: Feb 2010 Posts: 706 Thanks: 141 
The problem is correct as stated. The answers are a) 26 b) 8 c) 28 The best way to solve these is to use a Venn diagram. 
September 24th, 2015, 07:41 AM  #6 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 645 Thanks: 85  
September 24th, 2015, 11:43 AM  #7 
Senior Member Joined: Feb 2010 Posts: 706 Thanks: 141 
Here is a Venn diagram of this problem (except there is a typo ... the 6 that is outside all three circles but inside the box should be a 26).


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class, intersections, students, taking 
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