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Q.

A survey shows that 63% of Americans like cheese whereas 76% like apples. If x% of the American like both cheese and apples, then


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a

x = 39

b

x = 63

c

39⩽x⩽63

d

None of these 

answer is C.

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Detailed Solution

Let C and A denotes the percentage of people likes cheese and apples respectively. Given, n(C)=63 , n(A)=76  and  n(C∩A)=x.
We know that,
n(C U A) = n(C)+n(A)−n(C∩A)
n(C U A)= 63+76−x
x= 139−n(C U A)
Now, n(C U A) ≤ 100
139−n(C U A) ≥ 139−100=39
x ≥ 39
Also, n(C∩A) ≤ n(C) and n(C∩A) ≤ n(A)
x ≤ 63
39 ≤ x  ≤63.
Hence, The correct answer is option (3).
 
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