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Set S contains seven distinct integers [#permalink]
 18 Nov 2009, 21:35
Question Stats:
50% (01:55) correct
50% (01:47) wrong based on 0 sessions
Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?
m
10m/7
10m/7 – 9/7
5m/7 + 3/7
5m
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Re: Set S contains seven distinct integers [#permalink]
18 Nov 2009, 21:51
kairoshan wrote: Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?
m
10m/7
10m/7 – 9/7
5m/7 + 3/7
5m 10m/7 -9/7 lets consider m = 7 and set as [4,5,6,7,12,13,14] all distinct and will give highest possible average
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Re: Set S contains seven distinct integers [#permalink]
18 Nov 2009, 21:58
1. m is median --> x x x m x x x 2. 2m is the maximum value. x x x m x x 2m 3. because integers are distinct, we should find as large integers as we can under above restrictions: x x (m-1) m x (2m-1) 1m (m-3) (m-2) (m-1) m (2m-2) (2m-1) 2m Sum = 10m-9 Average = 10/7m-9/7 So, C
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Re: Set S contains seven distinct integers [#permalink]
19 Nov 2009, 06:20
walker wrote: 1. m is median --> x x x m x x x
2. 2m is the maximum value. x x x m x x 2m
3. because integers are distinct, we should find as larger integers as we can under above restrictions:
x x (m-1) m x (2m-1) 1m
(m-3) (m-2) (m-1) m (2m-2) (2m-1) 2m
Sum = 10m+9
Average = 10/7m-9/7
So, C Nice solution Walker!
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highest possible average [#permalink]
27 May 2010, 01:53
Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ? m 10m/7 10m/7 – 9/7 5m/7 + 3/7 5m
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Re: highest possible average [#permalink]
27 May 2010, 02:21
1
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Answer is 10m/7 - 9/7.
Information provided in problem statement -
1. 7 distinct integers
2. Median is m
3. All values less than or equal to 2m
Based on this information, the 7 elements for highest possible average would be m-3, m-2, m-1, m, 2m-2, 2m-1, 2m.
And the average would be (10m - 9)/7 which is same as 10m/7 - 9/7.
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Re: highest possible average [#permalink]
29 May 2010, 02:11
Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?
m
10m/7
10m/7 – 9/7
5m/7 + 3/7
5m
mean of 7 numbers = (Sum of 7 numbers)/7
To find the highest mean we need to maximise the numerator.
since m in the median and we've 7 numbers so m will take the 4th position i.e. the Set S must have(for max avg)
m, m, m, m, 2m, 2m, 2m
Max avg mean = (m + m + m + m + 2m + 2m + 2m)/7 = 10m/7
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Re: highest possible average [#permalink]
30 May 2010, 04:34
OA is C But why cant the set be m,m,m,m,2m,2m,2m it is a set and m can be the median, and average will be more than m-3,m-2,m-1,m,2m-2,2m-1,2m Amiman wrote: Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?
m
10m/7
10m/7 – 9/7
5m/7 + 3/7
5m
mean of 7 numbers = (Sum of 7 numbers)/7
To find the highest mean we need to maximise the numerator.
since m in the median and we've 7 numbers so m will take the 4th position i.e. the Set S must have(for max avg)
m, m, m, m, 2m, 2m, 2m
Max avg mean = (m + m + m + m + 2m + 2m + 2m)/7 = 10m/7
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Re: highest possible average [#permalink]
30 May 2010, 12:44
BlueRobin wrote: OA is C But why cant the set be m,m,m,m,2m,2m,2m it is a set and m can be the median, and average will be more than m-3,m-2,m-1,m,2m-2,2m-1,2m Amiman wrote: [highlight]Set S contains seven distinct integers[/highlight]. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?
m
10m/7
10m/7 – 9/7
5m/7 + 3/7
5m
mean of 7 numbers = (Sum of 7 numbers)/7
To find the highest mean we need to maximise the numerator.
since m in the median and we've 7 numbers so m will take the 4th position i.e. the Set S must have(for max avg)
m, m, m, m, 2m, 2m, 2m
Max avg mean = (m + m + m + m + 2m + 2m + 2m)/7 = 10m/7 Note that "Set S contains seven distinct integers".
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Re: highest possible average [#permalink]
30 May 2010, 13:09
Fistail wrote: BlueRobin wrote: OA is C But why cant the set be m,m,m,m,2m,2m,2m it is a set and m can be the median, and average will be more than m-3,m-2,m-1,m,2m-2,2m-1,2m Amiman wrote: [highlight]Set S contains seven distinct integers[/highlight]. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?
m
10m/7
10m/7 – 9/7
5m/7 + 3/7
5m
mean of 7 numbers = (Sum of 7 numbers)/7
To find the highest mean we need to maximise the numerator.
since m in the median and we've 7 numbers so m will take the 4th position i.e. the Set S must have(for max avg)
m, m, m, m, 2m, 2m, 2m
Max avg mean = (m + m + m + m + 2m + 2m + 2m)/7 = 10m/7 Note that "Set S contains seven distinct integers". Yeah thanks for point zzzzzzzzzzzz that out, i am awake now.
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Re: highest possible average
[#permalink]
30 May 2010, 13:09
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