CMI2013-A-08

Question

In the passing out batch, $54$ students know Java, $39$ know Python and $43$ know C++. Of these, $15$ know both Java and Python, $17$ know both Python and C++ and $23$ know both Java and C++ and $11$ know all three languages. If there are $100$ students in the class, how many know none of these three languages?

• A. $3$
• B. $8$
• C. $17$
• D. $19$

Answer 1

Let $J$ denote the set of of students knowing Java and similarly $P$ and $C$. Now,

$JPC = J + P + C - JP - PC - JC + JPC \\= 54 + 39 + 43 - 15 - 17 - 23 + 11 \\= 92.$

$JPC$ gives the no. of students knowing at least one of Java, Python or C++. So, no. of students not knowing any of these languages
$=100 - 92 = 8.$

Correct Answer: $B$

Answer 2