CAT 2024 - Slot 3 Quant Question 1
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CAT 2024 Slot 3 - Quant
Total number of students is 250, and we are told that, The percentage of girls was at least 44% and at most 60%.
So the number of girls range from, 0.44 (250) ≤ Girls ≤ 0.6 (250)
110 ≤ Girls ≤ 150
Statement 1:
If 50% of the boys and 80% of the girls opted for swimming, that means if the total number of Boys is B, Girls is G where B + G = 250
Swimming is: 0.5B + 0.8G
Statement 2:
If 70% of the boys and 60% of the girls opted for running, that means
Running is 0.7B + 0.6G
Total number of enrolments for swimming and running together will be
(0.7B + 0.6G) + (0.5B + 0.8G) = 1.2B + 1.4G
Using the overlapping principle, where I represents people who have enrolled only for one activity and II represents number of people who have enrolled for two activities.
We know that, I + II = 250 = B + G
I + 2II = 1.2B + 1.4G
Subtracting the two equations,
II = 0.2B + 0.4G
II = 0.2 (B + 2G)
Using B + G = 250
II = 0.2 (250 G)
G can at-most be 150 and at least 110.
So maximum value of II will be 0.2 (250 + 150) = 80
Minimum value of II will be 0.2 (250 + 110) = 72