It is known that at the university, 60% of the students play tennis, 50% of them play bridge, 70% jog, 20% play tennis and bridge, 30% play tennis and jog, and 40% play bridge and jog. If someone claimed that 20% students play bridge, jog and play tennis,
[JMET 2009]

(1)The person is telling the truth.
(2)Students who do all three activities are more than 20%.
(3)Students who do all three activities are less than 20%.
(4)There are no students who do all three activities.

Solution:
Assume the strength of the university to be 100.
Then we have the following Venn diagram representation:



Given that:
y + w = 20 … (1)
x + w = 30 … (2)
z + w = 40 … (3)
Adding the above three equations we get,
(x + y + z) + 3w = 90 … (4)
From the figure:
(a + b + c) + 2(x + y + z) + 3w = 180 … (5)
Subtracting (4) from (5) we get,
(a + b + c) +(x + y + z) = 90 … (6)
Also since the total strength is 100, we have:
(a + b + c) + (x + y + z) + w = 100 … (7)
Subtracting (6) from (7) we get:
w = 10 … (8)
Statement 3 states that students who do all three activities are less than 20%, is right as w = 10 = 10%.
Hence, option 3.