SAT Math Question of the Day

Math Category: Algebraic Sets:

Q: Everyone in Ms. Gillespie's class of 10 students likes Frosted Flakes cereal, Peanut Butter Captain Crunch, or both. 7 students like Frosted Flakes, 8 like Peanut Butter Captain Crunch. How many like both?

  1. 3
  2. 4
  3. 5
  4. 6
  5. 7

UNANSWERED.

The correct answer is C.

A: 5 is the right answer.

Let's make a chart to figure out this set problem. There are 10 students, so make the chart 10 columns wide:

1 2  3 4  5 6  7 8  9 10 
              
              

Next fill in the 7 who like Frosted Flakes cereal:
1 2  3 4  5 6  7 8  9 10 
FF FF FF F    
              

Next fill in the 8 who like Peanut Butter Captain Crunch. Remember, in this problem, everyone likes Frosted Flakes, Peanut Butter Captain Crunch, or both. This means we have to fill out the blank squares on the right first, so that every student is assigned something.
1 2  3 4  5 6  7 8  9 10 
FF FF FF F    
   PP PP PP PP

Now we have filled out the chart with all the information we know. Looking at the chart we see that students #3, #4, #5, #6, and #7 like both cereals, so the answer is 5 students.