RJ7X0DefiningMyX 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%
Solution
Step 1: Analyse Question Stem
• Total number of students = 7
• Number of students, who scored 100% = 1
• Number of students scored 0% = 2
• Median score = score of 4th student = 20
• Let x%, y%, and z% are the score of 3rd, 5th and 6th student respectively.
o 0%, 0%, x%, 20%, y%, z%, 100%
We need to find the average score.
• \(\frac{(0+0+x+20+y+x+100)}{7}=\frac{(x+y+z+120)}{7}\)
o We need to find the sum of x, y, and z.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: If the students who scored 0% or 100% are not considered, the median of the group improves to 25%
• Median of x%, 20%, y%, and z% = 25
o Median = \(\frac{(20+y)}{2}\)
o \(20 + y = 50\)
o \(y = 30\)
• We don’t know the value of x and z.
o We can’t find the sum of x, y, and z.
Hence, statement 1 is not sufficient, we can eliminate the answer options A and D.
Statement 2: If the students who scored 0% or 100% are not considered, the range of the scores of the group is 10%
• The range of x, 20, y, and z = 10
• We cannot find the sum of x, y, and z.
Hence, statement 2 is also not sufficient, we can eliminate the answer options B
Step 3: Analyse Statements by combining.
From statement 1: y = 30
From statement 2: z -x = 10
• x, 20, 30, z
o The only possible value of x is 20 and z is 30 because x cannot be greater than 20 and z cannot be less than 30.
• \(x + y + z = 20 + 30 + 30\)
o Thus, we can find the average.
Hence, the correct answer is
Option C.