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10 Jul 2019, 07:45
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65%
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Question Stats:
60% (02:34) correct
40%
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wrong
based on 334
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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%
(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%
10 Jul 2019, 23:43
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From the Question we can arrange the scores in order as - 0,0,a,b,c,d,100
Since median is 20, b=20---> series is 0,0,a,20,c,d.
Now ,
(1) says that median of a,20,c,d is 25---> so c=30. But a could be anything from 0-20; d could be anything from 30-100, so we cant find average --->insuffecient.
(2) says that range of scores of a,b,c,d is 10%. it means that we know d-a = 10. Since we know from qn that b=20, we know a,band d all should range around 10-30, but we dont know the exact values of any of those.----> Clearly insufficient.
Considering both 1&2,
c-d (ie 30-20) is already 10%, so a and d should also be 20 and 30 respectively in order to maintain the range as 10.
the series now is 0,0,20,20,30,30,100. Average could be found with this.
Since median is 20, b=20---> series is 0,0,a,20,c,d.
Now ,
(1) says that median of a,20,c,d is 25---> so c=30. But a could be anything from 0-20; d could be anything from 30-100, so we cant find average --->insuffecient.
(2) says that range of scores of a,b,c,d is 10%. it means that we know d-a = 10. Since we know from qn that b=20, we know a,band d all should range around 10-30, but we dont know the exact values of any of those.----> Clearly insufficient.
Considering both 1&2,
c-d (ie 30-20) is already 10%, so a and d should also be 20 and 30 respectively in order to maintain the range as 10.
the series now is 0,0,20,20,30,30,100. Average could be found with this.
15 Apr 2020, 05:56
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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%
- • \(\frac{(0+0+x+20+y+x+100)}{7}=\frac{(x+y+z+120)}{7}\)
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 \(y = 30\)
- o We can’t find the sum of x, y, and z.
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
- o \(z – x = 10\)
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.
- o Thus, we can find the average.
