SAT math question please?

Question

I know I already asked this question, but nobody explained to me how to get the right answer. I don't even know where to begin on this one.

At Central High School, the math club has 15 members and the chess club has 12 members. If a total of 13 students belong to only one of the two clubs, how many students belong to both clubs?

PS: The answer is 7, not 14.

Answer 1

Draw a Venn diagram:

Let the number of members of BOTH clubs be x

Number of members of ONLY the math club = 15-x

Number of members of ONLY the chess club = 12-x

Number of members of ONLY one club = 15-x + 12-x = 27-2x = 13

27 - 2x = 13

2x = 14

x = 7

The number of members of both clubs is 7

Answer 2

Ok, in total there's 27 members of both groups. 13 students are just in one of them. So now we can take that away from the total, which leaves us with 14 members that are in two groups each. So we just divide by 2, which is 7.

(I explained that absolutely horribly but I don't know how else to explain it. Sorry.)

Answer 3

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Answer 4

You add the number of members for both clubs together, which is 15 + 12 = 27.

This 27 = Number of people in the math club only + number of people in chess club only + 2 times of the people in both clubs.

The 2 times is due to the fact that they are counted twice, as they are included in the attendance for both clubs.

From here we subtract 13 from 27 and get 14.

Lastly, due to the double counting, we divide 14 by 2 to get 7.

Answer 5

ok draw 2 circles that overlap

label the left circle x

the overlap y

and the right z

so we know that x+Z = 13

x+y=13

and y+z = 12

we need to find y

Answer 6

ok if you know 13 belongs to only one you have to find out how many belongs to both clubs...so when you subtract 13 from the 27 members in all you get 14...but you have to think about it like this...the 14 belongs to both clubs so divide it by 2 to see how many there are which is 7