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# The mean, median, unique mode, and range of a collection of eight inte

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Math Expert
Joined: 02 Sep 2009
Posts: 59589
The mean, median, unique mode, and range of a collection of eight inte  [#permalink]

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15 Mar 2019, 00:00
00:00

Difficulty:

95% (hard)

Question Stats:

25% (03:22) correct 75% (02:19) wrong based on 20 sessions

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TOUGH QUESTION:

The mean, median, unique mode, and range of a collection of eight integers are all equal to 8. The largest integer that can be an element of this collection is

(A) 11

(B) 12

(C) 13

(D) 14

(E) 15

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The mean, median, unique mode, and range of a collection of eight inte  [#permalink]

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15 Mar 2019, 04:16
Bunuel wrote:

TOUGH QUESTION:

The mean, median, unique mode, and range of a collection of eight integers are all equal to 8. The largest integer that can be an element of this collection is

(A) 11

(B) 12

(C) 13

(D) 14

(E) 15

Mean = Median = Mode = Range = 8

_ _ _ _ _ _ _ $$x{max}$$

The eight terms that we have now are (Satisfying Range = 8 condition)

$$x-8$$ _ _ _ _ _ _ $$x_{max}$$

The eight terms that we have now are (Satisfying Median = Mode = 8 condition)

$$x-8$$ _ _ 8 8 _ _ $$x_{max}$$

The eight terms that we have now are (Satisfying Mean = 8 condition)

Trying to maximize x (i.e. x-8 as well) and minimize everything else

we get, 6 6 6 8 8 8 8 14

i.e. $$x_{max} = 14$$

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Joined: 18 Jan 2019
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Re: The mean, median, unique mode, and range of a collection of eight inte  [#permalink]

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17 Mar 2019, 09:58
GMATinsight wrote:
Bunuel wrote:

TOUGH QUESTION:

The mean, median, unique mode, and range of a collection of eight integers are all equal to 8. The largest integer that can be an element of this collection is

(A) 11

(B) 12

(C) 13

(D) 14

(E) 15

Mean = Median = Mode = Range = 8

_ _ _ _ _ _ _ $$x{max}$$

The eight terms that we have now are (Satisfying Range = 8 condition)

$$x-8$$ _ _ _ _ _ _ $$x_{max}$$

The eight terms that we have now are (Satisfying Median = Mode = 8 condition)

$$x-8$$ _ _ 8 8 _ _ $$x_{max}$$

The eight terms that we have now are (Satisfying Mean = 8 condition)

Trying to maximize x (i.e. x-8 as well) and minimize everything else

we get, 6 6 6 8 8 8 8 14

i.e. $$x_{max} = 14$$

can you please show steps of working out? I understand up to the median, but how did you manage to find every term, thanks
Re: The mean, median, unique mode, and range of a collection of eight inte   [#permalink] 17 Mar 2019, 09:58
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