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Was the median height of the 25 children in a certain class at least 2 Updated on: 24 Jan 2024, 01:26
Originally posted by tickledpink001 on 31 Dec 2023, 02:49.
Last edited by Bunuel on 24 Jan 2024, 01:26, edited 3 times in total.
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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?

(1) The median height of the 25 children was 2 centimeters greater than their average height.
(2) The sum of the heights of the 25 children was less than 2,550 centimeters


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Was the median height of the 25 children in a certain class at least 2 31 Dec 2023, 08:02
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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
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Was the median height of the 25 children in a certain class at least 2 27 Jun 2024, 01:23
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tickledpink001
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?

(1) The median height of the 25 children was 2 centimeters greater than their average height.
(2) The sum of the heights of the 25 children was less than 2,550 centimeters


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­
Given the heights of 25 children, is median of heights at least 2% more than mean of heights?

(1) The median height of the 25 children was 2 centimeters greater than their average height.

Median = Mean + 2 cm
This tells us the absolute difference between the two, not the percentage difference. 
e.g.
If mean = 50 cm, then median = 52 cm and it is 4% more than mean.
If mean = 100 cm, then median = 102 cm and it is exactly 2% more than mean.
But if mean = 200 cm, then median = 202 and it is merely 1% extra.
Not sufficient alone.

(2) The sum of the heights of the 25 children was less than 2,550 centimeters
Obviously not sufficient alone. 

Using both together,
Sum of heights < 2550 i.e. mean < 102 cm
When mean = 100, median = 102 and this is when median is exactly 2% more than mean. 
When mean < 100, median will be more than 2% extra and when mean > 100, median will be less than 2% extra. 

Since we are given that mean < 102, it could be less than 100 or more than 100. Hence median could be more than 2% extra or less than 2% extra. Not sufficient.

Answer (E)
 
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Was the median height of the 25 children in a certain class at least 2 08 Jul 2024, 06:18
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Silly mistake - missed "less than" in (2), which led me to select C instead of E
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Was the median height of the 25 children in a certain class at least 2 20 Aug 2024, 14:03
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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
Show more
­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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Was the median height of the 25 children in a certain class at least 2 21 Aug 2024, 00:12
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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?­
Show more
­
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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Was the median height of the 25 children in a certain class at least 2 21 Aug 2024, 08:47
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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 \(0 < average \leq 100\)?"­
Show more
­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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Was the median height of the 25 children in a certain class at least 2 21 Aug 2024, 11:22
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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!
Show more
­
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 the median height of the 25 children in a certain class at least 2 31 Aug 2025, 09:05
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