Venn Diagrams
Logical Reasoning

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Q.

At a T-shirt auction, 42 Reds United T-shirts were sold and 30 Blues T-shirts were sold. No one bought more than one T-shirt of the same type and everyone bought at least one. If 60 people participated in the auction, how many bought both T-shirts?

 A.

10

 B.

12

 C.

14

 D.

16

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Solution:
Option(B) is correct

Number of people who bought Reds United T-shirts = n(R) = 42

Number of people who bought Blues T-shirts = n(B) = 30

Let the number of people who bought both

T-shirts = n(R B) = x

The total number of people participating in the auction = n(R B) = 60

As everyone bought at least one T-shirt,

n(RB) = n(R) + n(B) - n(RB)

x = 42 + 30 – 60

x = 12

The number of people who bought both T-shirts = n(R B) = 12

Alternatively, the question can be easily solved by Venn diagram.

Answer image for Venn Diagrams, Logical Reasoning:2317-1

$\because$ It is given that everyone bought at least one T-shirt,

From the diagram, we can see that

42 - x + x + 30 - x = 60

x = 12


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