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If the average (arithmetic mean) of 5 different numbers is 12, what is

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Bunuel
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If the average (arithmetic mean) of 5 different numbers is 12, what is [#permalink] New post   12 Nov 2017, 23:49
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If the average (arithmetic mean) of 5 different numbers is 12, what is the median of the 5 numbers?

(1) The median of the 5 numbers is equal to 1/3 of the sum of the 4 numbers other than the median.
(2) The sum of the 4 numbers other than the median is equal to 45.
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D
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Re: If the average (arithmetic mean) of 5 different numbers is 12, what is [#permalink] New post   12 Nov 2017, 23:57
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Let the five numbers be a,b,c,d,e with c as the median.
Now a+b+c+d+e=5*12
=60

From st1
c=1/3*(a+b+d+e)
3c=a+b+d+e
Using question stem,
3c=60-c
Solving c=15. Sufficient

From st2
c+45=60
Solving
c=15

Sufficient


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Re: If the average (arithmetic mean) of 5 different numbers is 12, what is [#permalink] New post   13 Nov 2017, 00:10
Let numbers be a,b,c,d,e and median be c

average = 12 = (a+b+c+d+e)/5
=> a+b+c+d+e = 60

(1) The median of the 5 numbers is equal to 1/3 of the sum of the 4 numbers other than the median.
Given c = (a+b+d+e)/3
=> a+b+d+e = 3c

as a+b+c+d+e = 60
=> 3c+c=60
=> 4c=60
c=15
Sufficient

(2) The sum of the 4 numbers other than the median is equal to 45.
given a+b+d+e = 45

as a+b+c+d+e = 60
=> 45+c=60
c=15
Sufficient

Answer:D
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Re: If the average (arithmetic mean) of 5 different numbers is 12, what is [#permalink] New post   13 Nov 2017, 00:30
Since we are given the average, we can find total Sum of the numbers which equals 5*12=60
(1) We can find the Median in terms of other 4 numbers in the set:
M=1/3*(x1+x2+x3+x4)
(x1+x2+x3+x4)=3M
3M+M=60
M=15
(2) x1+x2+x3+x4+M=60
45+M=60
M=15

Sufficient.

Answer D.
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Re: If the average (arithmetic mean) of 5 different numbers is 12, what is [#permalink] New post   14 Jan 2022, 04:14
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Re: If the average (arithmetic mean) of 5 different numbers is 12, what is [#permalink]
14 Jan 2022, 04:14
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