BTGmoderatorDC wrote:A group of 7 students took a test. In the test, one student scored 100% and 2 students scored 0%. If the median score of the group is 20%, what is the value of the average (arithmetic mean) score of the group of students?

(1) If the students who scored either 0% or 100% are not considered, the median score of the group improves to 25%

(2) If the students who scored either 0% or 100% are not considered, the range of the scores of the group is 10%

OA C

Source: e-GMAT

Say the 7 scores arranged in ascending order are 0, 0, x, 20, y, z, 100. Since the middlemost score would be the 4th one, we assigned 4th score = 20.

To find out the average score, we must know the values of x, y, and z.

Let's take each statement one by one.

(1) If the students who scored either 0% or 100% are not considered, the median score of the group improves to 25%.

Thus, after excluding 1st, 2nd, and the 7th score, we have x, 20, y, z. Since now there are only 4 scores, the median would be the average of 2nd and 3rd value. Thus, 25 = (20 + y)/2 => y = 30. However, we have no idea about the value of x and z. Insufficient.

(2) If the students who scored either 0% or 100% are not considered, the range of the scores of the group is 10%.

=> z - x = 10%. Insufficient

(1) and (2) together

From (1), we have 0, 0, x, 20, 30, z, 100

Note that x ≤ 20 and z ≥ 30. Given that z - x = 10%, the only unique values of x = 20% and z = 30%. Thus, the 7 scores are 0, 0, 20, 20, 30, 30, 100. We can calculate the average. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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