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

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Math Expert
Joined: 02 Sep 2009
Posts: 44599
The mean of a list of six different positive integers is 68. Four of [#permalink]

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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
[Reveal] Spoiler: OA

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Posts: 361
Re: The mean of a list of six different positive integers is 68. Four of [#permalink]

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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.

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

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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

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

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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

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

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06 Apr 2018, 01:37
1
KUDOS
Bunuel, how is it that the OA is option C (123) instead of option D (161)?
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Joined: 02 Sep 2009
Posts: 44599
Re: The mean of a list of six different positive integers is 68. Four of [#permalink]

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06 Apr 2018, 02:05
RLokesh wrote:
Bunuel, how is it that the OA is option C (123) instead of option D (161)?

The OA is D. Edited. Thank you.
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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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