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CAT 2018 Slot 1 — QA Question 33

Venn DiagramEasy

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

Answer & solution

Correct answer: 93

  • A

    26

  • B

    96

  • 93

  • D

    23

Solution

Easy

"Only burger" can vary depending on the overlap between pizza-lovers and burger-lovers. Find the smallest and largest possible "only burger" counts; the correct option is the one value that falls inside that range.

1

Maximum overlap → minimum "only burger". Overlap is largest when all 105105 pizza-lovers also like burgers.

only burgermin⁡=134−105=29\begin{aligned} &\text{only burger}_{\min} = 134 - 105 = 29 \end{aligned}

So the answer must be at least 2929; this rules out 2626 and 2323.

2

Minimum overlap → maximum "only burger". The 105105 pizza-lovers occupy seats among the 200200; the rest can be burger-only.

only burgermax⁡=200−105=95\begin{aligned} &\text{only burger}_{\max} = 200 - 105 = 95 \end{aligned}

So the answer is at most 9595; this rules out 9696.

3

Pick the feasible value. The "only burger" count must lie in [29, 95][29,\,95].

29≤only burger≤95 ⇒ 93 is the only possible option29 \le \text{only burger} \le 95 \ \Rightarrow\ 93 \text{ is the only possible option}
Only burger=93\text{Only burger} = 93

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CAT 2018 Slot 1 QA Q33 — Venn Diagram solution | TheCATExam