OG12, Q 178, Problem solving

liuyongmei

The table above shows the number of students in
three clubs at McAuliffe School. Although no student is
in all three clubs, 10 students are in both Chess and
Drama, 5 students are in both Chess and Math, and
6 students are in both Drama and Math. How many
different students are in the three clubs?
(A) 68
(B) 69
(C) 74
(D) 79
(E) 84
Arithmetic Interpretation of graphs and tables
A good way to solve this problem is to create a
Venn diagram. To determine how many students
to put in each section, begin by putting the given
shared-student data in the overlapping sections.
Put 0 in the intersection of all three clubs, 10 in the
Chess and Drama intersection, 5 in the Chess and
Math intersection, and 6 in the Drama and Math
intersection, as shown in the Venn diagram below.

Math intersection, and 6 in the Drama and Math
intersection, as shown in the Venn diagram below.
Subtracting the shared students from the totals in
each club that are listed in the table establishes the
members who belong only to that club. Th rough
this process, it can be determined that the Chess
club has 25 such members (40 – 10 – 5 = 25), the
Drama club has 14 such members (30 – 10 – 6 =
14), and the Math club has 14 such members
(25 – 5 – 6 = 14). Putting the number of unshared
club members into the Venn diagram and then
adding up all the sections of the diagram gives
25 + 14 + 14 + 10 + 5 + 6 = 74 students.
Th e correct answer is C.

问题我不理解的就是题目本身难道就没有考虑到Math, chess, drama都参加的同学们么？

sereinsun

“Although no student is in all three clubs”

anono2010

用这个图解
http://forum.chasedream.com/GMAT_Math/thread-406782-1-1.html?SearchText

然后中间的ABC部分＝0