Logical Reasoning Discussion

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. |

**Solution:**

Option(**C**) is correct

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*)* *+ 3*w *=* *90 -------- (4)

From the figure:

(*a* + *b* + *c*) + 2(*x* + *y* +* z*) + 3*w* = 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.