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In a group of 50 people, two tests were conducted, one for diabetes and one for blood pressure. 30 people were diagnosed with diabetes and 40 people with pressure. What is the minimum number of people who were having diabetes and high blood pressure?

In a group of 50 people, two tests were conducted, one for diabetes and one for blood pressure. 30 people were diagnosed with diabetes and 40 people with pressure. What is the minimum number of people who were having diabetes and high blood pressure? Correct Answer 20

Concept:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

Calculation:

Let, A be the number of people tested for diabetes and B be the number of people tested for blood pressure and there are 50 people tested either for diabetes or blood pressure 

So, n(A) = 30, n(B) = 40, n(A ∪ B) = 50

n(A ∩ B) = ?

We know,

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

⇒ n(A ∩ B) = 30 + 40 - 50

= 20

Hence, option (3) is correct.

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