SAT Math Question of the Day

Math Category: Algebraic Sets:

Q: In a group of 12 Seniors, 9 are in Key Club, 7 on the Tennis Team, and 5 are in both Key Club and the Tennis Team. How many are not in either group?

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

UNANSWERED.

The correct answer is A.

A: 1 is the right answer.

Let's make a chart to figure out this set problem. There are 12 Seniors, so make the chart 12 columns wide:

1 2  3 4  5 6  7 8  9 10  11 12 
                 
                 

Next fill in the 9 from Key Club:
1 2  3 4  5 6  7 8  9 10  11 12 
KCKC KCKC KCKC KCKC KC    
                 

Next fill in the 7 from the Tennis Team. Remember that 5 are in both Key Club and the Tennis Team, so let's say it's Seniors #1, #2, #3, #4, and #5:
1 2  3 4  5 6  7 8  9 10  11 12 
KCKC KCKC KCKC KCKC KC    
TTTT TTTT TT      TT TT 

Now we have filled out the chart with all the information we know. Looking at the chart we see that only Senior #12 is in neither group, so the answer is 1.