Directions:Read the following information and answer the following questions below.In a class of 90 students, 80 students like burger or pizza. 62 like burger and 56 like pizza.Q.How many don’t like burger?a)18b)28c)38d)48Correct answer is option 'B'. Can you explain this answer?

Question

Directions:Read the following information and answer the following questions below.In a class of 90 students, 80 students like burger or pizza. 62 like burger and 56 like pizza.Q.How many don&rsquo;t like burger?a)18b)28c)38d)48Correct answer is option 'B'. Can you explain this answer?

Answer

Here let set A be burger and set B be pizza

Therefore A = 62, B = 56, A ∩ B = 80
(A U B) + 80 = 62 + 56
(A U B) = 38

Thus no. of students who like only burger = 62 – 38 = 24

And no. of students who like only pizza = 56 – 38 = 18.

Also out of 90 since 80 like burger or pizza, we have 10 such students who like none of them.

From the information given, we can draw following Venn diagram,

(A U B) + (A ∩ B) = A + B

From the Venn diagram, people who don’t like burger are the ones who like only pizza and the ones who like neither pizza nor burger. Thus no. of students who don’t like burger
= 18 + 10 = 28.

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