# Sets & Venn Diagrams-4 Possible Types of Questions YouTube Lecture Handouts

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## Venn Diagram Terminology

- Sample/Universe
- Subset
- Element
- Union
- Intersection
- Complement
- Finding A, B, , , and

## Problems on Visualization

## Keywords to Look For!

- Only Regions
- Both Region

## Venn Diagrams and Venn Diagrams with %

Basics of Venn Diagrams

For example,

## 2 Circle Venn Diagram – Visualization

There are 200 students in all. 140 opt for Math, 100 opt for Biology and all of them have atleast opted for one of the subjects.

1. How many of them opted for both the subjects? a. 60

b. 80

c. 40

d. Can՚t Say

2. How many of them opted for Math only? a. 100

b. 60

c. 40

d. Can՚t Say

3. How many of them opted for Biology only? a. 100

b. 60

c. 40

d. Can՚t Say

## Problem Keywords

- Only Regions
- Atleast Regions
- At-Most Regions
- All Three (four etc.)

Here, we have some blocks these blocks has various colors.

First we consider as only two colors either yellow, red and combination of both.

**35 are yellow**

**20 are red**

**15 are both red and yellow**

Find:

1. Total blocks (40)

2. Are only yellow (20) vs yellow (35)

There are 35 blocks are yellow and 20 blocks are red and 15 blocks are both red and yellow.

First calculate second question:

Are only yellow (20) vs yellow (35)

Difference

Blocks are exactly yellow

Similarly, Red Red blocks

Total blocks Blocks

In shortcut way to find total block

## 3 Circle Venn Diagram – Visualization

35 are yellow, 20 are red, 30 are blue, 5- yellow and red, 2 red & blue, 2 - blue & yellow, 6 have only 2 colors.

1. Only red (14) vs. red (20)

2. Only/exactly red and yellow (4) vs. red and yellow (1)

3. Only/exactly either red or yellow (43) vs. either red or yellow (45) vs. either red or yellow or both (50)

4. Are not either red or yellow (27) vs. are not both red and yellow (72)

5. Red and one other color (5) vs. red and other color (6)

6. Exactly 2 colors (6) vs. at least 2 colors (7)

7. All three (1) and total (77)

We find the center region which has 3 colors

Center region is 1.

### 1. Only Red vs. Red

Total red block

Subtract

Difference is only red blocks.

### 2. Only/Exactly Red and Yellow vs. Red and Yellow

Exactly red and yellow both color block

Red and yellow

### 3. Only/Exactly Either Red or Yellow vs. Either Red or Yellow vs. Either Red or Yellow or Both

Yellow and 14 Red

Total

Either red or yellow but not both

Either red or yellow or both

### 4. Are Not Either Red or Yellow (27) vs. Are Not Both Red and Yellow (72)

That means only blue

Not both red and yellow

### 5. Red and One Other Color (5) vs. Red and Other Color (6)

Red and one other color

Red and other color

### 6. Exactly 2 Colors (6) vs. At Least 2 Colors (7)

Only 2 colors

At least 2 color means wither 3 colors

### 7. All Three (1) and Total (77)

Total number of blocks

Similar

## In a Class of 60 Students, 40 % Can Speak Only Hindi, 25 % Can Speak Only English, and Rest of the Students Can Speak Both the Languages. How Many Students Can Speak English?

In a class 60 students,

40 % only speak Hind, 25 % only speak English and remaining students speak both languages.

Total %

So,

Let՚s find out speak only English is of 60 students

So, students speak English

## In Examination, 65 % of the Students Passed in Mathematics, 48 % Passed in Physics, and 30 % Passed in Both. What Percent of Students Failed in Both the Subjects? If There Are 200 Students, then Find the Number of Failed Students

65 % of the students passed in Mathematics

48 % passed in Physics and 30 % passed in both

In square represent total number of students

Area out of the circle region was the students failed in both subjects.

Total students

So, 83 % of students actually pass one of the subjects.

Area out of the circle failed in both the subjects.

Absolute value 17 % of student failed out of 100

So, 200 of students failed in both the subjects.

## In an Examination 20 % of the Students Failed in Math, 15 % in English, and 25 % in Hindi. If 5 % Failed Math & English, 10 % Failed English & Hindi, 15 % Failed Math and Hindi, and 2 % Failed All the Three Subjects, Find Percent of Students Who Passed in All Three Subjects

Find out the area inside the circle:

So, 32 % of students are failed in one of the subjects.

So, 68 % of students are passed in all three subjects.

## 2400 Players Are from MP and up. Each Player Plays One or More of Cricket (C) , Football (F) , Hockey (H) . 45 % Players Are from MP and Remaining from up. From MP, Boys and Girls Are in Ratio 5: 4. Of the Girls from MP, 20 % Play Only C, 10 % Play Only F & 10 % Play Only H. 20 % Play C & F. 20 % Play C & H. 10 % Play F & H. Remaining Play All Three. Players from up, Boys & Girls Are in Ratio 4: 7. Of the Girls from up, 25 % Play Only C, 10 % Play Only F & 8 % Play Only H. 15 % Play C & F. 10 % Play C & H. 15 % Play F & H. How Many Girls from MP and up Play Only Either Cricket or Football?

2400 players from MP and UP

45 % from MP

Remaining from UP

From MP, boys and girls are in ratio .

Ratio , total students

In 5 boys and 4 girls or girls

In MP, 20 % only cricket, 10 % football, total

In UP, 25 % cricket, 10 % football, total

How many girls are there in MP and UP?

## 60 Drink Tea, 70 Drink Coffee, 80 Drink Cold Drink. Among These, There Are 20 Preferring Tea & Coffee, 25 Prefer Tea & Cold Drink and 30 Prefer Coffee & Cold Drink. 5 Students Prefer Tea, Coffee and Cold Drink

- Total Students who prefer at least one drink?
- Students who prefer coffee only?
- Students who prefer cold drinks only?

## Out of 210 Candidates, 105 Were Offered Tea, 50 Were Offered Juice, and 56 Were Offered Water. 32 Were Offered Tea and Juice, 30 Were Offered Juice and Water, and 45 Were Offered Water and Tea

Q. Find maximum and minimum number of candidates who were offered all three?

Q. Find maximum and minimum number of candidates who were offered at least one of these?

## Next Class- Successive %

We will discuss problem of successive percentages, we can solve problem of salary increased or decreased or what is the net change.

✍ Mayank