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The average (arithmetic mean) of seven distinct integers is

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sandy
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The average (arithmetic mean) of seven distinct integers is [#permalink] New post   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.
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amorphous
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Re: The average (arithmetic mean) of seven distinct integers is [#permalink] New post   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] New post   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] New post   04 Sep 2018, 06:50
The answer is D.

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] New post   04 Sep 2018, 11:38
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Nomad wrote:
The answer is D.

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] New post   07 Sep 2018, 08:17
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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] New post   07 Mar 2020, 05:50
In the given information 1st distinct number is -15 as the problem mentions least
so we can find the sum of the rest 6 distinct numbers, let it be x

-15+x/7 = 12 => -15+x = 84 => x = 99

the sum of remaining 6 distinct number is 99

so, assuming
1st = -15
2nd = 0
3rd = 1
4th = 2
5th = 3
6th = 4
7th = 89

you can plug any number you want which is greater than -15 and sum up to 99, but A will always be the correct one.

Answer is A
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Re: The average (arithmetic mean) of seven distinct integers is [#permalink] New post   09 Jul 2021, 12:06
Is my assumption correct:
set =-15,15,-14,14,-13,13,84
set2= -15,0,1,2,3,4,78
In this case the answer can be D right?
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Re: The average (arithmetic mean) of seven distinct integers is [#permalink] New post   09 Jul 2021, 13:06
rajlal wrote:
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?


I did the same, but I think the least can be negative also..
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Re: The average (arithmetic mean) of seven distinct integers is [#permalink] New post   17 Sep 2022, 02:43
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Given that The average (arithmetic mean) of seven distinct integers is 12, and the least of these integers is –15 and we need to find the maximum possible value of the greatest of these integers

============================================================

Theory
    ‣‣‣ Sum = Mean * Total Number of values.

============================================================

=> Sum = 12 * 7 = 84

Least number is -15, so to find the maximum value of the greatest number we need to make all other numbers as small as possible.

Smallest number is -15, so other integers can be taken close to this
=> Set is -15, -14, -13, -12, -11, -10 and the maximum number = 84 - (-15 -14 -13 -12 -11 -10) = 84 + 75 = 159

Clearly Quantity A(159) > Quantity B(84)

So, Answer will be A.
Hope it helps!

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