# SAT Math Multiple Choice Question 706: Answer and Explanation

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**Question: 706**

**1.** 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 playing 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:** A

**Explanation:**

**A**

**Data Analysis (probability) MEDIUM**

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.