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

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

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New post 26 Dec 2017, 00:12
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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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New post 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.

Our answer is (A)
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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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New post 26 Dec 2017, 17:55
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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.

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

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