The average (arithmetic mean) of 7 numbers in a certain list is 12. Th

Question

The average (arithmetic mean) of 7 numbers in a certain list is 12. The average of the 4 smallest numbers in this list is 8, while the average of the 4 greatest numbers in this list is 20. How much greater is the sum of the 3 greatest numbers in the list than the sum of the 3 smallest numbers in the list?

(A) 4
(B) 14
(C) 28
(D) 48
(E) 52

(A) 4
(B) 14
(C) 28
(D) 48
(E) 52

mahi816 · Answer

Medium level question.
Given that mean of 7 numbers=12, so sum of all numbers=84-------1)

similarly sum of smallest four numbers...a+b+c+d=32-----2)

Sum of greatest 4 numbers d+e+f+g=80---3)

2)+3) . - 1)

d=28

then (e+f+g) - (a+b+c) = 52-4=48

ANS:D

PKN · Answer

Given, the sum of 7 numbers=12*7=84
Sum of the 4 smallest numbers=4*8=32----(a)
Sum of the 4 greatest numbers=4*20=80 (here 3 numbers are different from the smallest numbers, one number is common to both smallest and greatest numbers)--(b)

To find:- sum of 3 greatest numbers-sum of 3 smallest numbers

3S+common number+3G +common number=80+32=112
=84+common number=112-84=28
So, common number=28

Now, from(a), 3S+common number=32
Or, 3S=32-28=4

from(b), 3G+common number=80
Or, 3G=80-28=52

So, 3G-3S=52-4=48

Where 3S and 3G denote the sum of 3 greatest numbers and sum of 3 smallest numbers respectively.

Ans. (D)

rahulkashyap · Answer

shouldnt the question be more clear in saying that the max 4 and min 4 are part OF the 7 list?

it could be that there is a master list of 15 nos, and we have 4 min, 4 max and 7 unrelated nos in between

Beminhae · Answer

C. 48
a+b+c+d+e+f+g=12(7)=84
a+b+c+d=8(4)=32
d+e+f+g=20(4)=80
so we can find d
d = (32+80)-84
d = 28
To get the sum of the 3 greatest and smallest numbers, we have, 
a+b+c = 80-d
a+b+c = 80-28 = 52
e+f+g = 32-28 = 4
Thus,
52 - 4 = 48 is the difference

Posted from my mobile device

PKN · Answer

Hi  rahulkashyap ,
IMO,
The average (arithmetic mean) of 7 numbers in a   certain list   is 12. The average of the 4 smallest numbers   in this list   is 8, while the average of the 4 greatest numbers   in this list   is 20.

"In this list"---> refers to "list of 7 numbers"

JeffTargetTestPrep · Answer

The sum of all the numbers is 7 x 12 = 84, the sum of the 4 smallest numbers is 32, and the sum of the 4 greatest numbers is 80.

We note that the 4 smallest numbers and the 4 greatest numbers both contain the middle number; if we were to add the sum of the 4 smallest numbers and the sum of the 4 greatest numbers, we see that we will obtain the sum of all the numbers plus the repeated middle number, since it was added twice. So if we let n = the repeated, middle number, then we can create the equation:

84 = 32 - n + 80

n = 112 - 84

n = 28

So the sum of the 3 smallest numbers is 32 - 28 = 4 and the sum of the largest 3 numbers is 80 - 28 = 52, so the difference is 52 - 4 = 48.

Answer: D

Abhishek009 · Answer

a + b + c + d + e + f + g = 84  { Let the numbers be in ascending order }

a + b + c + d = 32 ------------------------( I )

d + e + f + g = 80 ------------------------( II )

Now,  ( a + b + c + d ) + ( d + e + f + g ) = 112

So,  (a + b + c + d + e + f + g ) + d = 112

Or,  84 + d = 112

Or,  d = 28

Now substitute  d = 28  in equation (II) we get  e + f + g = 52  -------->  Sum of 3 greatest integers

Now substitute  d = 28  in equation (I) we get  a + b + c = 4  -------->  Sum of 3 smallest integers

So, the required difference is  52 - 4 = 48  , Answer must be (D)

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The average (arithmetic mean) of 7 numbers in a certain list is 12. Th

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