Multiple choice

Last school year, each of the 200 students at a certain high school attended the school for the entire year. If there were 8 cultural performances at the school during the last school year, what was the average (arithmetic mean) number of students attending each cultural performance? 1. Last school year, each student attended at least one cultural performance. 2. Last school year, the average number of cultural performances attended per student was 4.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement 2 gives the average number of performances per student (4). Total attendances = 200 students * 4 = 800. Average per performance = 800 / 8 = 100. Statement 1 is insufficient as it doesn't provide the total number of attendances.

AI explanation

The target question asks for the average number of students attending each performance, calculated as the total number of attendances divided by 8 performances. Statement 1 only states that each of the 200 students attended at least one performance, which does not give the exact total attendances and is therefore insufficient. Statement 2 provides the average number of performances attended per student as 4, meaning the total number of attendances is 200 students times 4, which equals 800; dividing 800 total attendances by 8 performances yields an average of 100. Statement 2 alone is sufficient, but statement 1 alone is not sufficient.

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