SAT Math Question of the Day

Math Category: Algebraic Sets:

Q: In a group of 6 Freshmen Gleeks chatting about the TV show Glee, 3 think that Rachel Berry is a great singer, 3 think that Mercedes Jones is a great singer, but only 2 believe Rachel and Mercedes are both great singers. How many of these Freshmen think that neither Rachel or Mercedes is a great singer?

  1. 0
  2. 1
  3. 2
  4. 3
  5. 4

UNANSWERED.

The correct answer is C.

A: 2 is the right answer.

Let's make a chart to figure out this set problem. There are 6 Freshmen, so make the chart 6 columns wide:

1 2  3 4  5 6 
        
        

Next fill in the 3 Rachel Berry fans:
1 2  3 4  5 6 
RR R    
        

Next fill in the 3 Mercedes Jones fans. Remember that 2 are fans of both Glee characters, so let's say it's Freshmen #2, #3, and #4:
1 2  3 4  5 6 
RR R    
 M MM   

Now we have filled out the chart with all the information we know. Looking at the chart we see that only Freshmen #5 and #6 are in neither group, so the answer is 2.