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# What is the value of x? (1) The mean (arithmetic average) of 14, 6x,

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Math Expert
Joined: 02 Sep 2009
Posts: 56307
What is the value of x? (1) The mean (arithmetic average) of 14, 6x,  [#permalink]

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10 Apr 2018, 04:42
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Difficulty:

55% (hard)

Question Stats:

53% (01:50) correct 47% (01:45) wrong based on 39 sessions

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What is the value of x?

(1) The mean (arithmetic average) of 14, 6x, x^2 and 19 is 6.
(2) The range of 4, 15, x, and 10 is 18

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Joined: 31 Jul 2017
Posts: 14
Re: What is the value of x? (1) The mean (arithmetic average) of 14, 6x,  [#permalink]

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10 Apr 2018, 05:19
As Option 1 gives 2 outputs for x -7 & 1

Option 2 gives the range, here also the range is for X - 4=18---> 22 & 15-x= 18--> -3
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Re: What is the value of x? (1) The mean (arithmetic average) of 14, 6x,  [#permalink]

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10 Apr 2018, 07:54
Bunuel wrote:
What is the value of x?

(1) The mean (arithmetic average) of 14, 6x, x^2 and 19 is 6.
(2) The range of 4, 15, x, and 10 is 18

Statement 1:
Given that (14 + 6x + x^2 + 19)/4 = 6.
Simplifying this we get x^2 + 6x + 9 = 0 or (x+3)^2 = 0 or x = -3. Sufficient.

Statement 2:
Range is the difference between largest and smallest value. Here if x is the smallest number, then x must be -3 (because 15 - (-3) = 18)
Here if x is the largest number, (then 4 becomes smallest), then x must be 22 (because 22 - 4 = 18).
Two values of x, so not sufficient.

Re: What is the value of x? (1) The mean (arithmetic average) of 14, 6x,   [#permalink] 10 Apr 2018, 07:54
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