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# The average (arithmetic mean) of seven distinct integers is

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The average (arithmetic mean) of seven distinct integers is [#permalink]  30 Aug 2018, 07:40
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The average (arithmetic mean) of seven distinct integers is 12, and the least of these integers is –15.

 Quantity A Quantity B The maximum possible value of the greatest of these integers $$84$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The average (arithmetic mean) of seven distinct integers is [#permalink]  04 Sep 2018, 02:01
Dear Sandy, need explanation, pls
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Re: The average (arithmetic mean) of seven distinct integers is [#permalink]  04 Sep 2018, 06:50

The average of seven distinct integers is 12. That means that the sum of seven distinct integers is 84.

Since the lowest integer in the set is -15, it means that the sum of the biggest six integers is 84-(-15) = 99.

From here, the maximum value can be less, equal, or greater than 84.

Set 1: -15, [ 0, 1, 2, 3, 4, 30, 59 ]
Set 2: -15, [ 0, 1, 2, 3, 4, 5, 84 ]
Set 3: -15, [ -1, 0, 1, 2, 3, 4, 90 ]
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Re: The average (arithmetic mean) of seven distinct integers is [#permalink]  04 Sep 2018, 11:38

The average of seven distinct integers is 12. That means that the sum of seven distinct integers is 84.

Since the lowest integer in the set is -15, it means that the sum of the biggest six integers is 84-(-15) = 99.

From here, the maximum value can be less, equal, or greater than 84.

Set 1: -15, [ 0, 1, 2, 3, 4, 30, 59 ]
Set 2: -15, [ 0, 1, 2, 3, 4, 5, 84 ]
Set 3: -15, [ -1, 0, 1, 2, 3, 4, 90 ]

Yes, but that makes A correct, not D. Read it again. It says "The maximum possible value of the greatest of these integers".
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Re: The average (arithmetic mean) of seven distinct integers is [#permalink]  07 Sep 2018, 08:17
Can anyone give the solution to this?

My approach:
There are 7 terms, -15 is lowest.
So
(-15+x1+x2+x3+x4+x5+x6)/7 =12
In order to get maximum we set all to zero and then find the average which gives
-15+0+0+0+0+0+x = 84
x = 84+15
x=99

Is this approach correct?
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Re: The average (arithmetic mean) of seven distinct integers is [#permalink]  07 Sep 2018, 09:16
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First find the sum of all the 7 numbers which is equal to avg time no of terms = 7*12 = 84
Now, if the lowest of the 7 terms is -15 and all terms are different, in order to make the greatest no as great as possible we have to limit other numbers to as small as possible.
Therefore the six numbers should be -15,-14,-13,-12,-11,-10. The sum of these numbers = -75
we know that -75+x = 84 therefore x = 159.
Hence the maximum possible value of greatest number is 159.
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Re: The average (arithmetic mean) of seven distinct integers is   [#permalink] 07 Sep 2018, 09:16
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# The average (arithmetic mean) of seven distinct integers is

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