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:

170

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280

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220

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250

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Solution

The correct option is A $170$
Total consumers $= 1000 = n (A \cup B)$
Consumers who likes product $A = 720 = n (a)$
Consumers who like product $B = 450 = n (B)$
Now consumers who like both products $= n (A \cap B) = n (A) + n (B) - n (A \cup B)$
$= 720 + 450 - 1000$
$= 170$

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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:

The correct option is A 170Total consumers =1000=n(A∪B)Consumers who likes product A=720=n(a)Consumers who like product B=450=n(B)Now consumers who like both products =n(A∩B)=n(A)+n(B)−n(A∪B)=720+450−1000=170

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:

The correct option is A $170$
Total consumers $= 1000 = n (A \cup B)$
Consumers who likes product $A = 720 = n (a)$
Consumers who like product $B = 450 = n (B)$
Now consumers who like both products $= n (A \cap B) = n (A) + n (B) - n (A \cup B)$
$= 720 + 450 - 1000$
$= 170$