Tips on Solving Reasoning Questions Based on Venn Diagrams

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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 ? (a) (b)
(c) (d) 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 12 the languages only?

Solution

4 The people who can
speak English and Hindi 3 5 is
represented by the portion of intersection
of the circle and the upper square only. The no.
here is 5. 6 7 2 So 5
people can speak Hindi and English both.
8 11 Question
How many persons can speak all languages?
Solution 10 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 8 10 7
• and square represents government employees.
  6 13
• 12
• Question How many men are educated but not
  urban? 9 4 14
• (a) 9 (b) 5 11
• (c) 4 (d) 11
• Solution 5
• 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
  ?
• 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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