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# What is the value of |x|? (1) The average (arithmetic mean) of x^2 and

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Math Expert
Joined: 02 Sep 2009
Posts: 50000
What is the value of |x|? (1) The average (arithmetic mean) of x^2 and  [#permalink]

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26 Dec 2017, 00:12
2
1
00:00

Difficulty:

25% (medium)

Question Stats:

72% (00:52) correct 28% (01:11) wrong based on 99 sessions

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What is the value of |x|?

(1) The average (arithmetic mean) of x^2 and 16 is 12.5
(2) x = –|x|

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Joined: 07 Dec 2017
Posts: 714
Re: What is the value of |x|? (1) The average (arithmetic mean) of x^2 and  [#permalink]

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26 Dec 2017, 01:05
Bunuel wrote:
What is the value of |x|?

(1) The average (arithmetic mean) of x^2 and 16 is 12.5
(2) x = –|x|

We'll solve this question by relying on properties of the absolute value (without calculation).
This is a Logical approach.

Simplifying (1) gives us a quadratic equation x^2 = some number.
Then the two values of x are the positive and negative roots of the same number so they share the same absolute value.
Therefore there is only one solution for |x|.
Sufficient!

(2) Any negative number (or 0) can fulfill this property (try and see!).
Insufficient.

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Re: What is the value of |x|? (1) The average (arithmetic mean) of x^2 and  [#permalink]

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26 Dec 2017, 17:55
1
Bunuel wrote:
What is the value of |x|?

(1) The average (arithmetic mean) of x^2 and 16 is 12.5
(2) x = –|x|

What is the absolute value of $$x$$?
(1) The average (arithmetic mean) of x^2 and 16 is 12.5 So, $$\frac{x^2+16}{2}=12.5$$ then, $$x^2 = 25-16 = 9$$, $$x = 3, or -3$$; absolute value of $$|x|=3$$; sufficient.

(2) x = –|x|. Then, $$x$$ is less than or equal to $$0$$; could be 0 or any negative..; insufficient.

Re: What is the value of |x|? (1) The average (arithmetic mean) of x^2 and &nbs [#permalink] 26 Dec 2017, 17:55
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