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Wed Jan 22, 2020 6:53 am

Manhattan Prep

10 students took a chemistry exam that was graded on a scale of 0 to 100. Five of the students were in Dr. Adams' class and the other five students were in Dr. Brown's class. Is the median score for Dr. Adams' students greater than the median score for Dr. Brown's students?

1) The range of scores for students in Dr. Adams’ class was 40 to 80, while the range of scores for students in Dr. Brown’s class was 50 to 90.

2) If the students are paired in study teams such that each student from Dr. Adams’ class has a partner from Dr. Brown’s class, there is a way to pair the 10 students such that the higher scorer in each pair is one of Dr. Brown’s students.

OA B

Let's take each statement one by one.

1) The range of scores for students in Dr. Adams’ class was 40 to 80, while the range of scores for students in Dr. Brown’s class was 50 to 90.

Case 1: Say

• Scores of students of Dr. Adam's class are 40, 40, 40, 40 and 80. Median = 40
• Scores of students of Dr. Brown's class are 50, 50, 50, 50 and 90. Median = 50 > 40.

The answer is yes.

Case 2: Say

• Scores of students of Dr. Adam's class are 40, 80, 80, 80 and 80. Median = 80
• Scores of students of Dr. Brown's class are 50, 50, 50, 50 and 90. Median = 50 < 80.

The answer is no.

No unique answer. Insufficient.

2) If the students are paired in study teams such that each student from Dr. Adams’ class has a partner from Dr. Brown’s class, there is a way to pair the 10 students such that the higher scorer in each pair is one of Dr. Brown’s students.

Since all higher scorers are from Dr. Brown's class, the five scores of Br. Bown's students when arranged in ascending order would be greater than that of Dr. Adam's class. Thus, the median score for Dr. Adams' students would be greater than the median score for Dr. Brown's students.

The correct answer: B

Hope this helps!

-Jay
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