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10 students took a chemistry exam that was graded on a scale

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10 students took a chemistry exam that was graded on a scale

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Source: Manhattan GMAT

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.

The OA is B.

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Is the median score for Dr. Adams' students greater than the median score for Dr. Brown's students
Statement 1; Given that
Dr. Adams' class range is 40-80
Dr. Brown's class range is 50-90
We can have
(1) Scores in Dr. Adams' class to be = 40, 50, 70, 80, 90. So, median is 70. For this, the median score for Dr Adams' student is greater than that of Dr Brown's student.
But we can also have,
(2) Scores in Dr. Adams' class to be = 40, 50, 75, 80, 80. So, median is 75.
Scores in Dr. Brown's class to be = 50, 60, 80, 85, 90. So, median is 80.

We cannot ascertain if the median score for Dr. Adam's student is greater or not. Hence, statement 1 is INSUFFICIENT.

Statement 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 10 students such that the higher scores in each pair is one of Dr. Brown's students.

With this, it can be concluded that all students of Dr. Brown's class have scores higher than all students of Dr. Adams' class. So, it is certain and definite that the median of Dr. Adams' class is less than the median of Dr. Brown's class. Hence, statement 2 alone is SUFFICIENT

ANSWER = OPTION B

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