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.
Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Aug 09, 2018 11:13 pm

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swerve wrote: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.
Given: There are 5 students in Dr. A's class and there are 5 students in Dr. B's class. They took a chemistry exam that was graded on a scale of 0 to 100.

Question: Is the median score for Dr. A's students greater than the median score for Dr. B's students?

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 Dr. A's students scored 40, 40, 40, 40 and 80, thus, median = 40, and Dr. B's students scored 50, 90, 90, 90, 90, thus, median = 90; the answer is No.
Case 2: Say Dr. A's students scored 40, 40, 80, 80 and 80, thus, median = 80, and Dr. B's students scored 50, 50, 50, 90, 90, thus, median = 50; the answer is Yes.

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.

Say Dr. A's students scored p, q, r, s, and t; thus, Dr. A's students scored p+, q+, r+, s+, and t+, where p+ > p; q+ > q; r+ > r; s+ > s; t+ > t. This is the only possibility to compy with Statement 2.

Median of Dr. A's class = r, and Median of Dr. B's class = r+ > r. The answer is No. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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