question wrong? people problem

madhan_dc wrote:there are 7 ppl on commitee A 8 ppl on commitee B. If 3 ppl server on both committee, how many people serve on only one committe.

answer is 9

my answer is 15 - 3 = 12 ppl.

it doesnt state 3 ppl per committe serve on both committees.

Kaplan math workbook pg 281 pb #34.

P:S - working on this one book for the third week. Am i being really slow?

The correct answer is 9.

If A=7, and 3 of these 7 people also serve on B, then the number who serve only on A = 7-3 = 4.

If B=8, and 3 of these 8 people also serve on A, then the number who serve only on B = 8-3 = 5.

Only A + Only B = 4+5 = 9.

Please see the following Venn diagram for a visual representation of the problem:

The problem states 3 ppl work on both committees. Can it not be 2 ppl from team A and 1 person from team B?

why does it have to be 3 from A and 3 from B?

madhan_dc wrote:The problem states 3 ppl work on both committees. Can it not be 2 ppl from team A and 1 person from team B?

why does it have to be 3 from A and 3 from B?

If a person works on both committees, he can't come from one committee and not from the other; by definition, that person comes from both committees.

If 2 people from A work on both committees, then those 2 people from A also work on B. So those 2 people come both from A and from B, because they work on both committees.

If 1 person from B works on both committees, then that 1 person from B also works on A. So that 1 person comes from both B and from A, because he works on both committees.

So the result is the same: in total 2+1 = 3 people work on both committees.