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,

$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cup B)$

$100=70+64-n(A\cup B)$

$n(A\cup B)=34\%$

Intersection can't be less than $34\%$.

$x\ge 34$

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 $64\%$.

$x\le 64$

x lies $34\le x\le 64$