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Set S contains seven distinct integers [#permalink]
18 Nov 2009, 20:35

00:00

A

B

C

D

E

Difficulty:

5% (low)

Question Stats:

57% (01:42) correct
42% (01:47) wrong based on 7 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

Re: Set S contains seven distinct integers [#permalink]
18 Nov 2009, 20:51

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

Re: Set S contains seven distinct integers [#permalink]
18 Nov 2009, 20:58

Expert's post

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

Re: Set S contains seven distinct integers [#permalink]
19 Nov 2009, 05:20

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

highest possible average [#permalink]
27 May 2010, 00:53

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
_________________

press kudos, if you like the explanation, appreciate the effort or encourage people to respond.

Re: highest possible average [#permalink]
29 May 2010, 01:11

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

Re: highest possible average [#permalink]
30 May 2010, 03:34

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

Re: highest possible average [#permalink]
30 May 2010, 11:44

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".

Re: highest possible average [#permalink]
30 May 2010, 12:09

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.
_________________

If you found the reply to be helpful, give kudos.

gmatclubot

Re: highest possible average
[#permalink]
30 May 2010, 12:09