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The average (arithmetic mean) of 4 different integers is 75.
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26 Aug 2016, 07:40
26 Aug 2016, 07:40
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The average (arithmetic mean) of 4 different integers is 75. If the largest integer is 90, what is the least possible value of the smallest integer?
A)1
B)19
C)29
D)30
E)33
A)1
B)19
C)29
D)30
E)33
Re: The average (arithmetic mean) of 4
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26 Aug 2016, 09:21
26 Aug 2016, 09:21
Suppose four different integers are : a,b,c & d.The average of these four different integers is :
\(Avg\) = (a+b+c+d)/4 = 75
=>
Sum of these four different integers is : sum = a+b+c+d = 300
The difference between the largest integer and the average is : 90-75 = 15
if largest integer is 90 (suppose d=90) then a+b+c = 300-90 = 210
=> Average of a,b & c is : (a+b+c)/3 = 210/3 = 70
How have you calculated that the least integer should be 33 (option E)?I have tried to calculate but finding it difficult;could you please share the detailed solution?
\(Avg\) = (a+b+c+d)/4 = 75
=>
Sum of these four different integers is : sum = a+b+c+d = 300
The difference between the largest integer and the average is : 90-75 = 15
if largest integer is 90 (suppose d=90) then a+b+c = 300-90 = 210
=> Average of a,b & c is : (a+b+c)/3 = 210/3 = 70
How have you calculated that the least integer should be 33 (option E)?I have tried to calculate but finding it difficult;could you please share the detailed solution?
Re: The average (arithmetic mean) of 4
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26 Aug 2016, 10:24
26 Aug 2016, 10:24
2
Expert Reply
Hi phoenixio,
Well the mean is given to be 75. Let the integers be x,y,z, 90.
So we know that:
\(\frac{(x+y+z+90)}{4}\)= 75
\(x+y+z= 210\)
Lets say z is the smallest. So in order for z to be smallest possible x and y should be largest values possible.
Now we also know that \(x,y,z < 90\) (since 90 is the largest integer) and x,y,z, 90 are "different".
So x = 89 and y= 88 satisfy this criteria:
Hence \(z = 210 - 89 -88 =33\).
Cheers
PS: Source of the Que ?
Well the mean is given to be 75. Let the integers be x,y,z, 90.
So we know that:
\(\frac{(x+y+z+90)}{4}\)= 75
\(x+y+z= 210\)
Lets say z is the smallest. So in order for z to be smallest possible x and y should be largest values possible.
Now we also know that \(x,y,z < 90\) (since 90 is the largest integer) and x,y,z, 90 are "different".
So x = 89 and y= 88 satisfy this criteria:
Hence \(z = 210 - 89 -88 =33\).
Cheers
PS: Source of the Que ?
