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The mean of a list of six different positive integers is 68. Four of

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The mean of a list of six different positive integers is 68. Four of  [#permalink]

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New post 26 Mar 2018, 00:12
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The mean of a list of six different positive integers is 68. Four of the integers in the list are 38, 57, 65, and 86. What is the maximum possible value of the greatest of the six integers?

(A) 86
(B) 87
(C) 123
(D) 161
(E) 162

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Re: The mean of a list of six different positive integers is 68. Four of  [#permalink]

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New post 26 Mar 2018, 00:41
161 --> 38+57+65+86 = 246

246 + x(the two other integers) = 6(68)
246 + x = 408
x = 162

Since question stem says 'integer' --> the least has to be 1, and most has to be 161.
So ans = 161.


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Re: The mean of a list of six different positive integers is 68. Four of  [#permalink]

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New post 26 Mar 2018, 09:29
Bunuel wrote:
The mean of a list of six different positive integers is 68. Four of the integers in the list are 38, 57, 65, and 86. What is the maximum possible value of the greatest of the six integers?

(A) 86
(B) 87
(C) 123
(D) 161
(E) 162

To maximize one of two integers, minimize the other.

We need (sum of all numbers) - (sum of given 4) = total left to split between the two unknowns

Sum of all 6 integers
\(A*n = S\)
\(68 * 6 = 408\)


Sum of 4 known integers
\(38+57+65+86 = 246\)

Remaining amount to split between two unknowns:
\((408 - 246) = 162\)
Minimize one number.
Smallest possible integer: 1
The other number, maximized, is 161

Answer D
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Re: The mean of a list of six different positive integers is 68. Four of  [#permalink]

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New post 27 Mar 2018, 11:32
Bunuel wrote:
The mean of a list of six different positive integers is 68. Four of the integers in the list are 38, 57, 65, and 86. What is the maximum possible value of the greatest of the six integers?

(A) 86
(B) 87
(C) 123
(D) 161
(E) 162


The sum of the integers is 6 x 68 = 408.

To maximize the value of the greatest integer, we minimize the sum of the other 5 integers, which means that the value of the smallest integer must be 1. If we let m = the value of the largest integer, the sum of the 6 integers is:

1 + 38 + 57 + 65 + 86 + m = 408

247 + m = 408

m = 161

Answer: D
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Re: The mean of a list of six different positive integers is 68. Four of  [#permalink]

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New post 06 Apr 2018, 01:37
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Bunuel, how is it that the OA is option C (123) instead of option D (161)?
Please clarify.
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Re: The mean of a list of six different positive integers is 68. Four of  [#permalink]

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New post 06 Apr 2018, 02:05
Re: The mean of a list of six different positive integers is 68. Four of &nbs [#permalink] 06 Apr 2018, 02:05
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