CAT 2024 Slot 3 QA Question 9

Multiple choice (+3 / −1) · Modern Math · Set Theory · Try it, then check the answer and solution below.

In a group of 250 students, the percentage of girls was at least

44\%

and at most

60\%

. The rest of the students were boys. Each student opted for either swimming or running or both. If

50\%

of the boys and

80\%

of the girls opted for swimming while

70\%

of the boys and

60\%

of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are

⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: D

Answer and solution

Answer: D) $72and$ 80 , respectively

📌 Core Concept

The problem involves set theory and the principle of inclusion-exclusion. The formula used is: $

|A \cup B| = |A| + |B| - |A \cap B|

where

A

is the set of swimmers and

B

is the set of runners.

🔢 Step-by-Step Solution

Determine the number of girls (G) and boys (B):

Total students = 250

G

is between 110 (44% of 250) and 150 (60% of 250)

B = 250 - G , so

B$ is between 100 and 140

Calculate the number of swimmers

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