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MDM4U - Mathematics of Data Management 12 (2025-26) - A

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Question text In a club of 25 students:- 14 play basketball- 12 play soccer- 6 play both sports Student 1:"I was asked to find how many students play only soccer. I subtracted: 12 – 6 = 6."Answer 1 Question 46[select: , The student is correct; subtracting overlap gives 6 students who play only soccer., The student is incorrect; they should have added, not subtracted. The correct answer is 18., The student is incorrect; only 3 play soccer, and 9 play both.] Student 2:"I was asked to find how many students play neither sport. I did 25 – 14 – 12 + 6 = 5."Answer 2 Question 46[select: , The student is incorrect; the answer should be 3 because overlap was double-counted., The student is incorrect; permutations should have been used instead, the correct value is 42., The student is correct; inclusion-exclusion correctly gives 5 students who play neither sport.] Student 3:"I was asked to find how many students play at least one sport. I did 14 + 12 = 26."Answer 3 Question 46[select: , The student is correct; 26 is accurate for at least one sport., The student is incorrect; the overlap must be subtracted. The correct total is 20., The student is incorrect; they should have used multiplication, and the total is 84.]

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To tackle this, I’ll walk through each student’s approach and the reasoning behind their results step by step. Student 1: The question about how many play only soccer requires understanding the overlap between the two sports. The total who play soccer is 12, and the overlap (players who play both) is 6. Subtracting the overlap from the soccer total to get those who play only soccer is 12 − 6 = 6. This logic is correct because it removes the players counted in ......Login to view full explanation

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