Question

A market research group conducted a survey of $1000$ consumers and reported that $720$ consumers liked product A and $450$ consumers liked product B. The least number that must have liked both products is:

• A. $170$
• B. $280$
• C. $220$
• D. $250$

Answer 1

The correct option is A $170$

Total consumers $=1000=n(A\cup B)$

Consumers who likes product $A=720=n\left(a\right)$

Consumers who like product $B=450=n\left(B\right)$

Now consumers who like both products $=n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)$

$=720+450-1000$

$=170$