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555-605 Level|   Absolute Values|                     
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What is the value of |x| ?

(1) x = - |x|
(2) x^2 = 4


Hi Bunuel, this is semi-related to the question, but is lx-2l always going to equal l2-xl? If so, how do I make sense of it? It seems to be true when I plug in numbers. Is this a known property for all real numbers such that l2-xl = l-(x-2)l and since l-(x-2)l=lx-2l, l2-xl=lx-2l would this work?

This is in relation to this problem I saw online:

What is the value of |x−2|?

(1) |x−4|=2

(2) |2−x|=4

Answer was B (2) is sufficient.

Indeed, the property |a - b| = |b - a| holds true for all a and b. Think of |a - b| as the distance between a and b on the number line. Similarly, |b - a| represents the distance between b and a on the same line. Naturally, these two distances are identical.

Back to your problem:

What is the value of |x − 2|?

(1) |x − 4| = 2

Here, x could be 6 or 2. If x = 6, |x − 2| = 4. However, if x = 2, |x − 2| = 0. Two different answers. Not sufficient.

(2) |2 − x| = 4

Since |2 − x| = |x − 2| for all x, then the above statement directly gives the value of |x − 2|. Sufficient.

Alternatively, |2 − x| = 4 implies x could be -2 or 6. Both yield the same value of 4 for |x − 2|. Sufficient.

Answer: B.

Hope it helps.

Very helpful, thank you.!
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