In a school, 60% students play cricket. A student who does not play cricket, plays football. Every football player has got a two-wheeler. Which of the following conclusions cannot be drawn from the above data ?

1. 60% of the students do not have two-wheelers.

2. No cricketer has a two-wheeler.

3. Cricket players do not play football.

Select the correct answer using the code given below:

The correct answer is 1, 2 and 3.

Let us analyze the given information step-by-step to understand why none of the three conclusions can be drawn from the data:

Given Premise 1: 60% of students play cricket.
This implies that the remaining 40% of students do not play cricket. If we assume the total number of students is 100%, we have:
Cricketers = 60%
Non-Cricketers = 40%

Given Premise 2: A student who does not play cricket, plays football.
This means that all non-cricketers (40% of the total students) play football. However, this statement does not restrict cricket players from playing football. A cricketer may or may not play football.

Given Premise 3: Every football player has got a two-wheeler.
This tells us that if a student plays football, they definitely own a two-wheeler. Since all non-cricketers (40%) play football, at least 40% of the school's students must own a two-wheeler.

Now, let us evaluate each of the given conclusions:

Conclusion 1: 60% of the students do not have two-wheelers.
We know that at least 40% of students (the non-cricketers who play football) have two-wheelers. The remaining 60% of students (cricketers) may or may not own two-wheelers. Since we do not have information about whether cricketers own two-wheelers or not, we cannot determine the exact percentage of students without two-wheelers. Thus, Conclusion 1 cannot be drawn.

Conclusion 2: No cricketer has a two-wheeler.
The premises state that every football player has a two-wheeler. They do not state that cricketers cannot own a two-wheeler. Furthermore, some cricketers might also play football, which would guarantee they have a two-wheeler. Therefore, we cannot conclude that no cricketer has a two-wheeler. Thus, Conclusion 2 cannot be drawn.

Conclusion 3: Cricket players do not play football.
The premise "A student who does not play cricket, plays football" defines a rule for non-cricketers. It does not state that playing cricket and playing football are mutually exclusive. It is entirely possible for a student to play both cricket and football. Thus, Conclusion 3 cannot be drawn.

Since all three conclusions (1, 2, and 3) cannot be drawn from the given data, the correct choice is 1, 2 and 3.