In a survey of 80 students, 55 students stated that they play a varsity sport, and 35 stated that they are taking at least one AP level course. Which of the following statements must be true?a)At least 10 of these students are both play ing a varsity sport and taking at least one AP level course.b)Less than half of the students who play a varsity sport are also taking at least one AP level course.c)The number of students who do not play a varsity sport is greater than the number of students who do not take at least one AP level course.d)At least one student who takes an AP level course does NOT play a varsity sport.Correct answer is option 'A'. Can you explain this answer?

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In a survey of 80 students, 55 students stated that they play a varsity sport, and 35 stated that they are taking at least one AP level course. Which of the following statements must be true?

a)
At least 10 of these students are both play ing a varsity sport and taking at least one AP level course.
b)
Less than half of the students who play a varsity sport are also taking at least one AP level course.
c)
The number of students who do not play a varsity sport is greater than the number of students who do not take at least one AP level course.
d)
At least one student who takes an AP level course does NOT play a varsity sport.

Correct answer is option 'A'. Can you explain this answer?

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In a survey of 80 students, 55 students stated that they play a varsit...

Since the sum of 55 and 35 is 90, which is 10 greater than 80, there must be at least 10 in the overlap between the two sets. Statement (B) is not necessarily true, because it is possible that all 35 students taking AP courses are also varsity athletes, which is more than half of 55. Statement (C) is not true because 80 - 55 = 25 students do not play varsity sports, and 80 - 35 = 45 students do not take at least one AP course. Statement (D) is not necessarily true, because 35 students take at least one AP course and 25 students do not play a varsity sport, and this sum, 35 + 25 = 60, is less than the total number of students, so it is possible that there is no overlap between these two sets.

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In a survey of 80 students, 55 students stated that they play a varsit...

Understanding the Problem
In a survey of 80 students:
- 55 students play a varsity sport.
- 35 students are taking at least one AP level course.
We need to analyze the statements to determine which one must be true.
Analyzing Statement A
- Statement A: At least 10 of these students are both playing a varsity sport and taking at least one AP level course.
To evaluate this statement, we can use the principle of inclusion-exclusion. The total number of students is 80. If we sum the students in both categories:
- Students playing a varsity sport: 55
- Students taking an AP level course: 35
Total = 55 + 35 = 90
Since there are only 80 students, there must be some overlap, which means some students are counted in both groups.
To find the minimum overlap (students who do both), we subtract the total number of students from the sum:
Overlap = Total in both categories - Total students
= 90 - 80 = 10
Therefore, at least 10 students must be participating in both activities, making Statement A true.
Evaluating Other Statements
- Statement B: Less than half of the students who play a varsity sport are also taking an AP course.
This statement does not have to be true because the overlap could be more than 27 (which is half of 55).
- Statement C: The number of students who do not play a varsity sport is greater than those who do not take at least one AP level course.
This statement doesn't hold true without additional data.
- Statement D: At least one student who takes an AP level course does NOT play a varsity sport.
This may not be true if all AP students are also varsity athletes.
Conclusion
Thus, the only statement that must be true is:
- Statement A: At least 10 of these students are both playing a varsity sport and taking at least one AP level course.

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In a survey of 80 students, 55 students stated that they play a varsity sport, and 35 stated that they are taking at least one AP level course. Which of the following statements must be true?a)At least 10 of these students are both play ing a varsity sport and taking at least one AP level course.b)Less than half of the students who play a varsity sport are also taking at least one AP level course.c)The number of students who do not play a varsity sport is greater than the number of students who do not take at least one AP level course.d)At least one student who takes an AP level course does NOT play a varsity sport.Correct answer is option 'A'. Can you explain this answer?

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In a survey of 80 students, 55 students stated that they play a varsity sport, and 35 stated that they are taking at least one AP level course. Which of the following statements must be true?a)At least 10 of these students are both play ing a varsity sport and taking at least one AP level course.b)Less than half of the students who play a varsity sport are also taking at least one AP level course.c)The number of students who do not play a varsity sport is greater than the number of students who do not take at least one AP level course.d)At least one student who takes an AP level course does NOT play a varsity sport.Correct answer is option 'A'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about In a survey of 80 students, 55 students stated that they play a varsity sport, and 35 stated that they are taking at least one AP level course. Which of the following statements must be true?a)At least 10 of these students are both play ing a varsity sport and taking at least one AP level course.b)Less than half of the students who play a varsity sport are also taking at least one AP level course.c)The number of students who do not play a varsity sport is greater than the number of students who do not take at least one AP level course.d)At least one student who takes an AP level course does NOT play a varsity sport.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a survey of 80 students, 55 students stated that they play a varsity sport, and 35 stated that they are taking at least one AP level course. Which of the following statements must be true?a)At least 10 of these students are both play ing a varsity sport and taking at least one AP level course.b)Less than half of the students who play a varsity sport are also taking at least one AP level course.c)The number of students who do not play a varsity sport is greater than the number of students who do not take at least one AP level course.d)At least one student who takes an AP level course does NOT play a varsity sport.Correct answer is option 'A'. Can you explain this answer?.

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