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Silly mistake - missed "less than" in (2), which led me to select C instead of E
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chetan2u
Was the median height of the 25 children in a certain class at least 2 percent greater than the average (arithmetic mean) height of the 25 children?
Is median height\(\geq \) 102 % of Average height.

(1) The median height of the 25 children was 2 centimeters greater than their average height.
Median height =Average height+2
If Average height is 100cm or less, 2cm will be at least 2% of the average height. Answer is YES
If Average height >100cm, answer is NO.
Insufficient

(2) The sum of the heights of the 25 children was less than 2,550 centimeters
So Average \(\leq \frac{2550}{25}\) or 102cm.
Nothing about Median height.
Insufficient


Combined
If average height is 100 or less, answer is yes.
If Average height is between 100 and 102, answer is No.
insufficient


E
­I want to know what I am doing incorrectly in my approach:

question is asking if the median is at least 2% greater than the average, which in equation is:

(median/average) - 1 >= 0.02

(1) states median is 2 cm greater than the average height, hence median = average + 2

substituting this into the equation above, i get: (average + 2)/(average) - 1 >= 0.02
simplify:
(average)/(average) + (2)/(average) - 1 >= 0.02
1 + (2/average) - 1 >= 0.02
2/average >= 0.02
2/0.02 >= average

average <= 100

given average is less than or equal to 100, at its max value:
average = 100, median = 102 -> median is at least 2% greater than average

if average is any value below 100, median is larger by more than 2%:
i.e. if average = 50, median = 52

52/50 -1 = 0.04 or 4%

by this logic, wouldn't (1) be sufficient to answer the question?­
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nishantc1999

chetan2u
Was the median height of the 25 children in a certain class at least 2 percent greater than the average (arithmetic mean) height of the 25 children?
Is median height\(\geq \) 102 % of Average height.

(1) The median height of the 25 children was 2 centimeters greater than their average height.
Median height =Average height+2
If Average height is 100cm or less, 2cm will be at least 2% of the average height. Answer is YES
If Average height >100cm, answer is NO.
Insufficient

(2) The sum of the heights of the 25 children was less than 2,550 centimeters
So Average \(\leq \frac{2550}{25}\) or 102cm.
Nothing about Median height.
Insufficient


Combined
If average height is 100 or less, answer is yes.
If Average height is between 100 and 102, answer is No.
insufficient


E
­I want to know what I am doing incorrectly in my approach:

question is asking if the median is at least 2% greater than the average, which in equation is:

(median/average) - 1 >= 0.02

(1) states median is 2 cm greater than the average height, hence median = average + 2

substituting this into the equation above, i get: (average + 2)/(average) - 1 >= 0.02
simplify:
(average)/(average) + (2)/(average) - 1 >= 0.02
1 + (2/average) - 1 >= 0.02
2/average >= 0.02
2/0.02 >= average

average <= 100

given average is less than or equal to 100, at its max value:
average = 100, median = 102 -> median is at least 2% greater than average

if average is any value below 100, median is larger by more than 2%:
i.e. if average = 50, median = 52

52/50 -1 = 0.04 or 4%

by this logic, wouldn't (1) be sufficient to answer the question?­
­
From (1) we do not get that \(0 < average \leq 100\). When you substitute median = average + 2 into the question "is \(\frac{median}{average} - 1 \geq 0.02\)?", the question becomes "is \(0 < average \leq 100\)?"­
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Bunuel

nishantc1999

chetan2u
Was the median height of the 25 children in a certain class at least 2 percent greater than the average (arithmetic mean) height of the 25 children?
Is median height\(\geq \) 102 % of Average height.

(1) The median height of the 25 children was 2 centimeters greater than their average height.
Median height =Average height+2
If Average height is 100cm or less, 2cm will be at least 2% of the average height. Answer is YES
If Average height >100cm, answer is NO.
Insufficient

(2) The sum of the heights of the 25 children was less than 2,550 centimeters
So Average \(\leq \frac{2550}{25}\) or 102cm.
Nothing about Median height.
Insufficient


Combined
If average height is 100 or less, answer is yes.
If Average height is between 100 and 102, answer is No.
insufficient


E
­I want to know what I am doing incorrectly in my approach:

question is asking if the median is at least 2% greater than the average, which in equation is:

(median/average) - 1 >= 0.02

(1) states median is 2 cm greater than the average height, hence median = average + 2

substituting this into the equation above, i get: (average + 2)/(average) - 1 >= 0.02
simplify:
(average)/(average) + (2)/(average) - 1 >= 0.02
1 + (2/average) - 1 >= 0.02
2/average >= 0.02
2/0.02 >= average

average <= 100

given average is less than or equal to 100, at its max value:
average = 100, median = 102 -> median is at least 2% greater than average

if average is any value below 100, median is larger by more than 2%:
i.e. if average = 50, median = 52

52/50 -1 = 0.04 or 4%

by this logic, wouldn't (1) be sufficient to answer the question?­
­
From (1) we do not get that \(0 < average \leq 100\). When you substitute median = average + 2 into the question "is \(\frac{median}{average} - 1 \geq 0.02\)?", the question becomes "is \(0 < average \leq 100\)?"­
­Thanks so much for the response! If I understand correctly, the mistake I made was assuming the median/average - 1 >= 0.02 to be true when really it is the initial question that is asked. and if you simplify that with median = average + 2, then the question simply changes to average <= 100, and it doesn't confirm that the average is in fact <= 100.

thanks so much!
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nishantc1999

Bunuel

nishantc1999

­I want to know what I am doing incorrectly in my approach:

question is asking if the median is at least 2% greater than the average, which in equation is:

(median/average) - 1 >= 0.02

(1) states median is 2 cm greater than the average height, hence median = average + 2

substituting this into the equation above, i get: (average + 2)/(average) - 1 >= 0.02
simplify:
(average)/(average) + (2)/(average) - 1 >= 0.02
1 + (2/average) - 1 >= 0.02
2/average >= 0.02
2/0.02 >= average

average <= 100

given average is less than or equal to 100, at its max value:
average = 100, median = 102 -> median is at least 2% greater than average

if average is any value below 100, median is larger by more than 2%:
i.e. if average = 50, median = 52

52/50 -1 = 0.04 or 4%

by this logic, wouldn't (1) be sufficient to answer the question?­
­
From (1) we do not get that \(0 < average \leq 100\). When you substitute median = average + 2 into the question "is \(\frac{median}{average} - 1 \geq 0.02\)?", the question becomes "is \(0 < average \leq 100\)?"­
­Thanks so much for the response! If I understand correctly, the mistake I made was assuming the median/average - 1 >= 0.02 to be true when really it is the initial question that is asked. and if you simplify that with median = average + 2, then the question simply changes to average <= 100, and it doesn't confirm that the average is in fact <= 100.

thanks so much!
­
The initial question was "is \(\frac{median}{average} - 1 \geq 0.02\)?". Then, after substituting, ­median = average + 2 into the question, you just rephrased the question into "is \(0 < average \leq 100\)?"­
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was median > (102/100)* avg ?

1) median = 2cm + Avg --- we can find some giants that are really really big and force this difference to be less than 2%., and force this to show a much greater difference that exceeds a 2% ratio, by selecting some really really short people.

2) this constraint narrows down the giants, and really short people so...
ill take 2 edge cases:

avg = 2550/25 = 102
avg = 25/25 = 1 , no info on median, so i cant say for sure.

1),2) -> median = 2+ 102 ----> 104/102 = 1.01960784314 ... so thats 1.9 percent (so no)
median = 2+ 1 ----> 3/1 = 3 ... thats 200% greater (so yes)

E.
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