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

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Math Expert
Joined: 02 Sep 2009
Posts: 52902
The average (arithmetic mean) of 7 numbers in a certain list is 12. Th  [#permalink]

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29 Aug 2018, 23:33
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Difficulty:

45% (medium)

Question Stats:

75% (02:20) correct 25% (02:34) wrong based on 68 sessions

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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

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Re: The average (arithmetic mean) of 7 numbers in a certain list is 12. Th  [#permalink]

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30 Aug 2018, 00:09
Say,
A+B+C+D = 4*8 = 32 --- Eq (1)
Then,
D+E+F+G = 4*20 = 80 --- Eq (2)

Hence, Eq2-Eq1
= D + (E+F+G) - (A+B+C) - D
= (E+F+G) - (A+B+C) , i.e. difference between the sums of the three greatest number and the three smallest numbers
= 80 - 32
= 48

I have one doubt, the information about the average of the set is not used. So, is it possible that in GMAT unnecessary information may be available in the questions?
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Joined: 26 Dec 2016
Posts: 12
Re: The average (arithmetic mean) of 7 numbers in a certain list is 12. Th  [#permalink]

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30 Aug 2018, 00:17
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
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Re: The average (arithmetic mean) of 7 numbers in a certain list is 12. Th  [#permalink]

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30 Aug 2018, 00:28
Bunuel wrote:
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

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)
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Re: The average (arithmetic mean) of 7 numbers in a certain list is 12. Th  [#permalink]

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30 Aug 2018, 00:52
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
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Joined: 29 Aug 2018
Posts: 4
Re: The average (arithmetic mean) of 7 numbers in a certain list is 12. Th  [#permalink]

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30 Aug 2018, 00:56
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

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Re: The average (arithmetic mean) of 7 numbers in a certain list is 12. Th  [#permalink]

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30 Aug 2018, 01:06
rahulkashyap wrote:
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

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"
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PKN

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Re: The average (arithmetic mean) of 7 numbers in a certain list is 12. Th  [#permalink]

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30 Aug 2018, 01:11
The average (arithmetic mean) of 7 numbers in a certain list is 12. The average of the 4 smallest numbers in this list

7 numbers are part of "a list"

The average of 4 smallest in "this list"

Don't you think its ambiguous?

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Re: The average (arithmetic mean) of 7 numbers in a certain list is 12. Th  [#permalink]

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04 Sep 2018, 03:52
Bunuel wrote:
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

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.

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Re: The average (arithmetic mean) of 7 numbers in a certain list is 12. Th  [#permalink]

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04 Sep 2018, 07:39
Bunuel wrote:
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

$$a + b + c + d + e + f + g = 84$$ { 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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Re: The average (arithmetic mean) of 7 numbers in a certain list is 12. Th   [#permalink] 04 Sep 2018, 07:39
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