Directions(1 - 5): Study the following figure and answer the questions given below.
There are 450 students in a college. Each student has to choose one or more elective out of management, history and physics. Further following information is also known –

1) 75 students selected only management and physics.
2) 84 students selected only management and history.
3) 52 students selected only physics and history.
4) The number of students who selected only history is 137 less the number of students who selected only management.
5) In total 238 students selected management as an elective.
6) In total 240 students selected history as an elective.

1. How many students selected both management and physics as elective?

A. 84 B. 107 C. 75 D. 96

Answer - Option E
Explanation [1-5]- Let ‘x’ be the number of students who took all the three electives and ‘y’ be the number of students who took only management as an elective.
We get following venn diagram –

Considering students who took management as an elective we have,
y + x + 84 + 75 = 238
x + y = 79
Considering students who took history as an elective we have,
137 – y + x + 84 + 52 = 240
y – x = 33
Adding both the equation we get,
2y = 112
y = 56
So, x = 23
So, number of students who took all the three electives = 23
Number of students who took only management = 56
Number of students who took only history = 137 – 56 = 81
So, the number of students who took only physics = 450 – 240 – 56 – 75 = 79
Thus, we get following venn diagram –

Number of students who selected both management and physics as elective = 75 + 23 = 98
2. How many students selected only management as an elective?

A. 56 B. 45 C. 58 D. 62

Answer - Option A
3. How many students selected the only history as an elective?

A. 78 B. 91 C. 81 D. 93

Answer - Option C
4. How many students select all the three electives?

A. 16 B. 29 C. 37 D. 23

Answer - Option D
5. How many students selected only physics as an elective?

A. 134 B. 79 C. 67 D. 93

Answer - Option B

Directions(1-5): Study the following figure and answer the questions given below.
350 people are living in a particular village. There are three drinks Tea, Coffee and Hot chocolate available in the village. Each citizen has to vote for one or more of the three drinks which he/she like. It is known that:

1) In total 120 people like Tea and 160 people like Coffee.
2) 46 people like all the three drinks.
3) 62 people like both Tea and Hot chocolate.
4) 53 people like both Hot chocolate and Coffee.
5) 89 people like both Tea and Coffee.

1. How many people like only Tea?

A. 14 B. 17 C. 9 D. 15

Answer - Option D
Explanation [1-5]- 46 people like all the three drinks. We make following venn diagram –

Since 62 people like both Tea and Hot chocolate
62 – 46 = 16 people like only Tea and Hot chocolate
Since 53 people like both Hot chocolate and Coffee
53 – 46 = 7 people like only Hot chocolate and Coffee
Since 89 people like both Tea and Coffee
89 – 46 = 43 people like only Tea and Coffee.
Thus, number of people who like only Tea = 120 – 46 – 16 – 43 = 15
Thus, number of people who like only Coffee= 160 – 43 – 46 – 7 = 64
Number of people who like only Hot chocolate = 350 – 160 – 16 – 15 = 159
We get following venn diagram –

2. How many people like only Tea and Coffee?

A. 43 B. 35 C. 47 D. 39

Answer - Option A
3. How many people like only Coffee and Hot chocolate?

A. 8 B. 11 C. 7 D. 13

Answer - Option C
4. How many people like only Coffee?

A. 56 B. 59 C. 70 D. 64

Answer - Option D
5. How many people like only Hot chocolate?

A. 124 B. 159 C. 47 D. 163

Answer - Option B

Directions(1-5): Study the following figure and answer the questions given below.
The results of annual health inspection of 100 schoolchildren is given in the following venn diagrams. It was discovered that 55% of the children were malnourished while 60% were underweight.

1. How many students are vaccinated?

A. 40 B. 45 C. 50 D. 60

Answer - Option C
Explanation [1-5]- We can make a table of the given values as follows:
As 60% are underweight, 60 students are underweight and 40 adequate weight. Similarly, 55 are malnourished and 45 are adequately nourished.
Let’s fill in the values given in the two venn diagrams
Hence, vaccinated, adeq wgt and malnourished = 55 – 5 – 25 – 0 = 25
Hence, vaccinated, adeq wgt and adeq nourished = 40 – 25- 5 – 0 = 10
Hence, not vaccinate, underweight and adeq nourished = 60 – 5 – 25 – 10 = 20

Hence, total number of students who are vaccinated = 5 + 10 + 25 + 10 = 50
2. Among students who are not vaccinated and underweight, what proportion are malnourished?

A. [latex]\frac {1}{3}[/latex] B. [latex]\frac {1}{4}[/latex] C. [latex]\frac {4}{9}[/latex] D. [latex]\frac {5}{9}[/latex]

Answer - Option D
Explanation - Required proportion = [latex] \frac {25}{(25 + 20)} = \frac {25}{45} = \frac {5}{9}[/latex]
3. What is the difference in the number of students who are adequate weight, vaccinated and adequately nourished and those who are underweight, vaccinated and adequately nourished?

A. 0 B. 5 C. 10 D. 15

Answer - Option A
Explanation - Hence, the required difference is 10-10 = 0.
4. What is the ratio of vaccinated to non-vaccinated among children who were underweight?

A. 1 : 3 B. 1: 4 C. 1 : 2 D. 2 : 5

Answer - Option A
Explanation - Hence, out of 60 children who are underweight, 15 are vaccinated and 45 are not vaccinated. Hence, ratio is 1:3.
5. How many children were malnourished, underweight and vaccinated?

A. 0 B. 5 C. 15 D. 10

Answer - Option B
Explanation - Hence, 5 children are malnourished, underweight and vaccinated.