Question

A survey shows that 63% of the Americans like cheese
whereas 76% like apples. If x% of the Americans like both
cheese and apples, then
(a) x = 39 (b) x = 63
(c) 39 ≤ x ≤ 63 (d) none of these

Answer 1

Answer:

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∪A)=n(C)+n(A)−n(C∩A)

⇒n(C∪A)=63+76−x

⇒x=139−n(C∪A)

Now, n(C∪A)≤100

⇒139−n(C∪A)≥139−100=39

⇒x≥39

Also, n(C∩A)≤n(C) and n(C∩A)≤n(A)

⇒x≤63

∴39≤x≤63.

Step-by-step explanation:

hope it helps you