3 TIPS on cracking Reasoning Questions on Venn Diagrams

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Tip #1: Start working from the outermost Venn diagram and gradually move inwards

Question: Which of the following diagrams indicates the best relation between Women, Mothers and Engineers?

Solution:

Some women are mothers and some are engineers. All mothers are women, and some mothers are engineers. However, not all engineers are women. So, the answer is A.

Question: In an organization of pollution control board, engineers are represented by a circle, legal experts by a square and environmentalist by a triangle. Who is most represented in the board as shown in the following figure?

(a)   Environmentalists with Legal background                      

(b)   Legal Experts

(c)   Engineers with legal background

(d)   Environmentalists with engineering background

Solution:

We have to assume that the shape with the largest area is the most represented. Among the given options, D (i.e.) Environmentalists with Engineering background has the largest area. Thus, the correct answer is D.

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Tip #2: Reduce the question as the overlapping of different portions of the Venn diagram

In the following figure Upper Square represents the persons who know English, triangle those who know Marathi, Lower Square to those who know Telugu and circle those who know Hindi. In the different regions of the diagram, the counts are given.

Question: How many persons can speak English and Hindi both the languages only?                                                     

Solution:                                                                                                

The people who can speak English and Hindi is represented by the portion of intersection of the circle and the upper square only. The no. here is 5. So 5 people can speak Hindi and English both.

Question: How many persons can speak all languages?                                   

Solution:                                                                             

The people speaking all languages is represented by the portion of the Venn diagram that has all the figures overlapping. Since there is no such area where all the figures are overlapping, it means that no person can speak all the languages.

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Tip #3: The portion outside a figure represents the complement of the quantity inside it

In the following diagram rectangle represents men, Triangle represents educated, Circle represents urban and square represents government employees.

Question: How many men are educated but not urban?              

(a)  9

(b)  5

(c)  4

(d)  11

Solution:

Educated but non-urban men is represented by the portion of the triangle that overlaps with the rectangle but not the circle. Thus, 11 men are educated but not urban. The correct answer is D.

Question: Which one of the following represents a woman who is urban as well as government employee?

(a)  7

(b)  13

(c)  10

(d)  6

Solution:

Since the rectangle represents men, the portions of the other shapes that do not overlap with the rectangle represent women. The portion of the circle that overlaps with the square but not with the rectangle represents urban women who are government employees. Thus the answer is 10, i.e., C.

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