Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27
Contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12
Contained both a black pen and a pencil, 18 contained both a blue pen and a pencil, and 10 contained
All three items. How many backpacks contained exactly two of the three writing instruments?
A)11
B)2
C)15
D)3

Question

Quizplus · Accepted Answer

To find the number of backpacks that contained exactly two of the three writing instruments, we need to subtract the backpacks that contained only one writing instrument and those that contained all three from the total number of backpacks. 
Total number of backpacks = 38
Number of backpacks with only a black pen = 23 - 15 - 12 + 10 = 6
Number of backpacks with only a blue pen = 27 - 15 - 18 + 10 = 4
Number of backpacks with only a pencil = 21 - 12 - 18 + 10 = 1
Therefore, the number of backpacks that contained exactly two of the three writing instruments = 38 - 6 - 4 - 1 - 10 = 15. Answer: C

Upon Examining the Contents of 38 Backpacks, It Was Found