There are 3 overlapping sets A,B, and C inside the big rectangle,
making 8 regions to consider.
Circle A contains all the backpacks that had at least a black pen.
Circle B contains all the backpacks that had at least a blue pen.
Circle C contains all the backpacks that had at least a pencil.
We want to know how many are in
region k, which is the region outside all three circles.
Let's reverse the order the clues
are listed in:
10 contained all three items.
So we put 10 in region f
18 contained both a blue pen and a pencil,
We have accounted for 10 of these among the 18, so the remaining
8 are in region i. So we put 8 in i
12 contained both a black pen and a pencil,
We have accounted for 10 of these among the 12, so the remaining
2 are in region g. So we put 2 in g
15 contained both a black pen and a blue pen,
We have accounted for 10 of these among the 15, so the remaining
5 are in region e. So we put 5 in region e:
21 contained a pencil,
We have filled in 3 of the regions of the bottom circle
representing all the backpacks which had at least a pencil.
2+10+8=20, so the remaining 1 of the 21 is in region j.
So we put 1 in region j.
27 contained a blue pen
We have filled in 3 of the regions of the right circle
representing all the backpacks which had at least a blue pen.
5+10+8=23, so the remaining 4 of the 27 is in region h. So
we put 4 in region h.
23 contained a black pen,
We have filled in 3 of the regions of the left circle
representing all the backpacks which had at least a black pen.
5+10+2=17, so the remaining 6 of the 23 is in region h. So
we put 6 in region d.
Now we come to the question:
How many backpacks contained none of the three writing instruments?
Now we have the number in every region but k. We are told
there are 38 backpacks. The other 7 regions contain
10+8+2+5+1+4+6 = 36
So the remining 2 are in the outside region k. So we
put 2 in region k:
Answer: 2
Edwin
