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09 Jul 2025, 06:34
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Total = 90
Let scores be J, Y and S
Was average = median ?
Statement 1:
y = s+20
j + 2s + 20 = 90
j + 2s = 70
Not sufficient.
Statement 2:
j = 30
n = 3
mean = 30
y + s = 60
Either y = s = 30 or one will be <30 and one will be >30. Either way, mean = median.
Sufficient.
Answer is B.
Let scores be J, Y and S
Was average = median ?
Statement 1:
y = s+20
j + 2s + 20 = 90
j + 2s = 70
Not sufficient.
Statement 2:
j = 30
n = 3
mean = 30
y + s = 60
Either y = s = 30 or one will be <30 and one will be >30. Either way, mean = median.
Sufficient.
Answer is B.
Bunuel
09 Jul 2025, 06:40
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Jacob, Yuki, and Stephen
Total of their scores on the test was 90
Was the average (arithmetic mean) of the 3 scores equal to the median of the 3 scores?
We know that, average of the 3 scores = 90/3 = 30
Need to check if the median is same as mean
Given statements,
(1) Yuki's score was 20 greater than Stephen’s score.
Let Stepehen score = x
=> Yuki = x + 20
Jacob = y
=> Total = x+x+20+y = 90
=> 2x + y = 70
=> y = 70-2x
This is solved for multiple values,
x = 20 => y = 70-40 = 30 => Scores are 20,30,40
=> Median = 30 , Average = 30
Median = Average
x = 15 => y = 70-30 = 40 => Scores are 15,35,40
=> Median = 35, Average = 30
Median!=Average
Statement (1) is NOT sufficient
(2) Jacob's score was 30.
Let Stephen and Yuki score be x and y
=> x+30+y=90
=> x + y =60
From this we can say that,
Among x and y, one has to be greater than 30 and one lesser than 30 to satisfy the above condition
Due to this condition 30 is the middle number making it the median number
=> Average = Median for all possibilities
So,
B. Statement (2) ALONE is sufficient, but statement (1) alone is not.
Total of their scores on the test was 90
Was the average (arithmetic mean) of the 3 scores equal to the median of the 3 scores?
We know that, average of the 3 scores = 90/3 = 30
Need to check if the median is same as mean
Given statements,
(1) Yuki's score was 20 greater than Stephen’s score.
Let Stepehen score = x
=> Yuki = x + 20
Jacob = y
=> Total = x+x+20+y = 90
=> 2x + y = 70
=> y = 70-2x
This is solved for multiple values,
x = 20 => y = 70-40 = 30 => Scores are 20,30,40
=> Median = 30 , Average = 30
Median = Average
x = 15 => y = 70-30 = 40 => Scores are 15,35,40
=> Median = 35, Average = 30
Median!=Average
Statement (1) is NOT sufficient
(2) Jacob's score was 30.
Let Stephen and Yuki score be x and y
=> x+30+y=90
=> x + y =60
From this we can say that,
Among x and y, one has to be greater than 30 and one lesser than 30 to satisfy the above condition
Due to this condition 30 is the middle number making it the median number
=> Average = Median for all possibilities
So,
B. Statement (2) ALONE is sufficient, but statement (1) alone is not.
09 Jul 2025, 06:59
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Correct Answer: Yes, median and mean can be same.
We can answer this using Statement II alone.
Given we have:
Total Score= 90
Mean= 90/3= 30
Check the given statements:
(1) Yuki's score was 20 greater than Stephen’s score.
Let's solve this using an example
if we take score of Yuki= 15
Score of Stephen must be= 35
Score of Jacob= 40
Here median is 35. Hence we cannot solve this question using this statement alone.
(2) Jacob's score was 30.
Here we check this using taking maximum values and minimum values.
If we take maximum value= 50
One value must be= 10
Jacob= 30
10, 30, 50
Hence we can have our answer using this.
Now take minimum value= 5
One value must be= 55
Jacob= 30
5, 30, 55
Hence we can have our answer using this also. Similarly any number can work on this scenarios.
We can answer this using Statement II alone.
We can answer this using Statement II alone.
Given we have:
Total Score= 90
Mean= 90/3= 30
Check the given statements:
(1) Yuki's score was 20 greater than Stephen’s score.
Let's solve this using an example
if we take score of Yuki= 15
Score of Stephen must be= 35
Score of Jacob= 40
Here median is 35. Hence we cannot solve this question using this statement alone.
(2) Jacob's score was 30.
Here we check this using taking maximum values and minimum values.
If we take maximum value= 50
One value must be= 10
Jacob= 30
10, 30, 50
Hence we can have our answer using this.
Now take minimum value= 5
One value must be= 55
Jacob= 30
5, 30, 55
Hence we can have our answer using this also. Similarly any number can work on this scenarios.
We can answer this using Statement II alone.
