Solving by Venn diagrams.

All professors are researchers

Now, some scientists are professors

So, from Venn diagram it is true that some researchers are scientists. No other conclusions follow.

I + G = 49 + 2401 = 2450

From the given table, we can formulate the below table.

From the above table, it is clear that the player Q got the 10 and 5 points, the greatest number of times compared to others. Therefore, the player Q is most accurate.

The player R hit outside circle 5 times out of 7 rounds. Therefore, the plater R is most consistent.

Given that the total number of runs scored by the batsman is 306.

From the given pie chart, the total number of runs scored by hitting only 4’s is:

43.24% of 306.

$=\frac{43.14}{100}\times 306$

= 132 runs

The number of 4’s hit will be:

n(fours) $=\frac{132}{4}=33$

Similarly, the total number runs scored by 6’s will be:

3.92% of 306

$=\frac{3.92}{100}\times 306$

= 12

∴ The number of 6’s hit will be:

n(sixes) $=\frac{12}{6}=2$

∴ 33 fours and 2 sixes were hit by the batman.

From the revenue numbers it is clear that the maximum revenue is by sale of executive type razor.

A prime number on division by 4 gives a remainder of 1

Let the prime number is x.

Now, we can express the number as

x = 4n + 1

Let us consider the prime numbers that satisfies the above equation i.e. x = 5, 13, 17, 29, 37, 41, 53, …

x = 5 = 1² + 2²

x = 13 = 2² + 3²

x = 17 = 1² + 4²

x = 29 = 2² + 5²

x = 37 = 1² + 6²

x = 41 = 4² + 5²

x = 53 = 2² + 7²

In a school, 60% of students play cricket.

A student who does not play cricket, plays football.

Every football player has got a two-wheeler.

1. 60% of the students do not have two-wheelers: Every football player has got a two-wheeler. It doesn’t mean that the students who play cricket don’t have two-wheelers. So, it is not definitely true.

2. No cricketer has a two-wheeler: Every football player has got a two-wheeler. It doesn’t mean that the students who play cricket don’t have two-wheelers. So, it is not definitely true.

3. Cricket players do not play football: In a school, 60 % of students play cricket. A student who does not play cricket, plays football. But there is no information about whether the students playing cricket plays football or not. So, it is not definitely true.

Given that only one among A, B and C is truthful.

Case 1: A is truthful

A: turn left → it means we need to turn left

B: do not turn left → it means we need to turn left

C: go straight → it means we need to turn left or right

Conclusion: A is truthful, and we need to turn left

Case 2: B is truthful

A: turn left → it means we need to turn right or go straight

B: do not turn left → it means we need to turn right or go straight

C: go straight → it means we need to turn left or right

Conclusion: B is truthful, and we need to turn right

Case 3: C is truthful

A: turn left → it means we need to turn right or go straight

B: do not turn left → it means we need to turn left

C: go straight → it means we need to go straight

Conclusion: The statements are contradicting each other and hence the C is not truthful.

Overall quality score = 4.8 + 2.0 + 4.2 + 3.6 + 2.4 + 3.0 = 20

From the above table, the lowest contribution is from tangibles among all the above factors to the overall quality of services.

Now, the lowest contribution among all the above factors to the overall quality of services delivered by the company is $=\frac{2}{20}\times 100=10\mathrm{\%}$

Female in IT industry = $60000\times \frac{20}{100}\times \frac{12}{100}=1440$

Female in Gaming Industry = $60000\times \frac{20}{100}\times \frac{18}{100}=2160$

Female in Call Centre Industry = $60000\times \frac{45}{100}\times \frac{32}{100}=8640$

Female in Sales Industry = $60000\times \frac{60}{100}\times \frac{8}{100}=2880$

Female in Banking Industry = $60000\times \frac{40}{100}\times \frac{14}{100}=3360$

Female in Chemical Industry = $60000\times \frac{15}{100}\times \frac{16}{100}=1440$