Question

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 were diagnosed with high blood pressure. What is the minimum number of people who were having diabetes and high blood pressure?

• A. $0$
• B. $10$
• C. $20$
• D. $30$

Answer 1

Answer: (C)

$20$

Let $A$ be the set containing people diagnosed with diabetes and $B$ be the set containing people diagnosed with Blood pressure.

We know set formula

$n(A\cup B)+n(A\cap B)=n\left(A\right)+n\left(B\right)$

$n(A\cap B)=x$ are people having both

$n(A\cup B)$ are total people

$n\left(A\right)$ is people having diabetes and $n\left(B\right)$ is having blood pressure.

$\Rightarrow 50+x=40+30x=20$

Thus, there should be minimum of 20 people having both.