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Math Expert V
Joined: 02 Sep 2009
Posts: 55266
The mean of a list of six different positive integers is 68. Four of  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 72% (01:46) correct 28% (02:01) wrong based on 91 sessions

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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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Senior Manager  S
Joined: 15 Jan 2017
Posts: 351
Re: The mean of a list of six different positive integers is 68. Four of  [#permalink]

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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.

Will wait for OA
Senior SC Moderator V
Joined: 22 May 2016
Posts: 2755
Re: The mean of a list of six different positive integers is 68. Four of  [#permalink]

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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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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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Intern  B
Joined: 27 Aug 2016
Posts: 15
Re: The mean of a list of six different positive integers is 68. Four of  [#permalink]

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1
Bunuel, how is it that the OA is option C (123) instead of option D (161)?
Please clarify.
Math Expert V
Joined: 02 Sep 2009
Posts: 55266
Re: The mean of a list of six different positive integers is 68. Four of  [#permalink]

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RLokesh wrote:
Bunuel, how is it that the OA is option C (123) instead of option D (161)?
Please clarify.

The OA is D. Edited. Thank you.
_________________ Re: The mean of a list of six different positive integers is 68. Four of   [#permalink] 06 Apr 2018, 02:05
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