# CAT 2018 Set-1 | Question: 74

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

1. $93$
2. $26$
3. $23$
4. $96$

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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