If among $200$ students, $105$ like pizza and $134$ like burger, then the number of students who like only burger can possibly be

- $93$
- $26$
- $23$
- $96$

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3
votes

If among $200$ students, $105$ like pizza and $134$ like burger, then the number of students who like only burger can possibly be

- $93$
- $26$
- $23$
- $96$

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Best answer

2
votes

Given that,

- $n (\text {U}) = 200 $
- $ n (\text {P}) = 105 $
- $ n ( \text {B}) = 134$

Let the number of students who like both pizza and burger be $m.$

And, let the number of students who like neither pizza nor burger be $n.$

From the above Venn diagram,

$ ( 105-m) + m + (134-m) + n = 200 $

$ \Rightarrow – m + n = 200 – 239 $

$ \Rightarrow \boxed{m-n = 39} \quad \longrightarrow (1)$

$ \therefore $ The possible value of $(m , n)$ are $ (39,0), (40-1), \dots , (104,65), (105,66) $

So, the number of students who like only burger, should be in the range.

$ [134-105, 134-39] $

$ = [29,95] $

$\therefore$ From the given options, $93$ can be possible.

Correct Answer $:\text {A}$

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