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

[VJesus12]

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%

Answer: C

Source: e-GMAT

[deloitte247]

Total Students = 7
1 student scored 100%
2 students scored 0%
7 - 3 = 4
Median score = 20% remaining 3 students
Target question=what is the value of the average (arithmetic mean) score of the group of students
Let score of average remaining students = x, y, and z $$Average=\frac{0+0+x+20+y+z+100}{7}=\frac{x+y+z+10}{7}$$
$$find\ \ \left(x+y+z\right)$$

Statement 1
If the students who score 0% and 100% are not considered the median of the group improves to 25%
Total students considered= 4 $$x,\ y,\ 2\ and\ 20\%=\ x,\ y,20\%\ and\ z$$ $$Median=\frac{y+20}{2}=25$$ $$y+20=50\ adnd\ y\ =\ 30$$
Let the value of x and z is unknown so the statement 1 is NOT SUFFICIENT.

Statement 2
If the student who score 0 and 100% are not considered the range of the score of the group is 10% scores to reconsider = x, y, 20, z
Range = z-x = 10 this does not give us the sum of x+y + z So the statement 2 is NOT SUFFICIENT.


Considering both statements together
Consider theses four scores x, y, 20 and z
From statement 1==> y = 30
From statement 2 ==> z-x = 10
x, 20, 30 , z
for z-x= 10 in this scenario
z = 30 and x=20
x+y+z=20+30+30 = 80 $$Average=\frac{80+120}{7}=\frac{200}{7}=28.6\%$$

Both statement combined together are SUFFICIENT.. $$Answer\ is\ Option\ C$$