SAT Math Question of the Day

Math Category: Algebraic Sets:

Q: Everyone in Mr. Anderson's class of 15 students is involved with student government, sports, or both. If 9 students are active in student government and 10 are in sports, how many are in sports but not student government?

UNANSWERED.

The correct answer is A.

A: The answer is 6 students.

Let's make a chart to figure out this set problem. There are 15 students, so make the chart 15 columns wide:

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15

Next fill in the 9 in student government:

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
G	G	G	G	G	G	G	G	G

Next fill in the 10 involved in sports. Remember, every student is active in student government, sports, 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	11	12	13	14	15
G	G	G	G	G	G	G	G	G
					S	S	S	S	S	S	S	S	S	S

Now we have filled out the chart with all the information we know. Looking at the chart we see that Students #10, #11, #12, #13, #14, and #15 play sports, but are not in student government, so the answer is 6 students.