A Survey shows that 63% of the americans like cheese whereas 76% like apples. if x% of the americans like both cheese and apples, that we have 

A Survey shows that 63% of the americans like cheese whereas 76% like apples. if x% of the americans like both cheese and apples, that we have  Correct Answer 39 <u>&lt;</u> x <u>&lt;</u> 63

Formulas used:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

Calculation: 

Given:

Number of americans who like cheese n(C) = 63

Number of americans who like apple n(A) = 76

Total number of person = 100 (since 100%)

Number of americans who like both n(A ∩ B) = x

Now, n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

⇒ 100 - 63 + 76 - x

⇒ 100 = 139 - 100 

⇒ x = 139 - 100 

⇒ x = 39 

This is the minimum value of x

Now, let us look for the highest value of x, the intersection or the common portion between A and C, it would be larger when one set takes in more of the other.

Thus, when the smallest set gets completely absorbed into the larger and in that situation 

Then x = 63 

so 39 < x <  63