Question

In an university, out of 120 students, 15 opted mathematics only, 16 opted statistics only, 9 opted for physics only and 45 opted physics and mathematics, 30 opted physics and statistics, 8 opted mathematics and statistics and 80 opted physics. Find the number of students who opted mathematics.

• A. 60
• B. 64
• C. 50
• D. None of These

Answer 1

The correct option is B 64


Let M, S, P be the students who opted for mathematics, statistics and physics.
Let x be the no of students who opted for all the subjects.
There are 80 students who opted physics.
45 - x + 30- x + x + 9 = 80
$\Rightarrow$84 – x = 80
$\Rightarrow$–x = 80 – 84
$\Rightarrow$ x = 4

Students who opted Mathematics =
x + 8 - x + 45 - x +15
= 68 -x
=68-4 = 64

So, option b is correct.