Question

In a factory 70% of the workers like oranges and 64% likes apples. If x% like both oranges and apples, then what are the possible values of x?

• A. x ≥ 34
• B. x ≤ 64
• C. 34 ≤ x ≤ 64
• D. None of these

Answer 1

The correct option is C

34 ≤ x ≤ 64

Given data:

Percentage of workers like oranges = 70%

Percentage of workers like apples = 64%

Percentage of workers like both oranges and apples = x%

We need to find the minimum and maximum value of x.

For minimum value of intersection x

If all the workers like either oranges or apples

Then,

n(A∪B) = n(A) + n(B)- n(A∩B)

100 = 70 +64 - n(A∩B)

n(A∩B) = 34%

Intersection can't be less than 34%.

x≥ 34

For maximum value of intersection(x)

Maximum possible area of intersection is area of oranges which is 64% of workers.

Intersection(x) can't be more than 64%.

x ≤ 64

x lies 34 ≤ x ≤ 64