Venn Diagrams
Logical Reasoning

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Q.

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, then which of the below statement is true:

 A.

The person is telling the truth.

 B.

Students who do all three activities are more than 20%.

 C.

Students who do all three activities are less than 20%.

 D.

There are no students who do all three activities.

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Solution:
Option(C) is correct

Assume the strength of the university to be 100.

Then we have the following Venn diagram representation:

Answer image for Venn Diagrams, Logical Reasoning:2316-1

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 in option(C) states that students who do all three activities are less than 20%, is right as w = 10 = 10%.

Hence, option C is the correct choice.


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