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Absolute value of x

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Source: — Data Sufficiency |

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by Dario@VinciaPrep » Tue Mar 08, 2016 1:09 am
Hi!
Statement (1) alone is not sufficient, as x could be 4 or -4.
Statement (2) tells you exactly the same thing, as x could be 4 or -4.
As that information is not enough, using 1&2 together will not answer the question.
Thus the answer is (E).

Remember: when two statements are equal, it could be only (D) or (E)
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by MartyMurray » Tue Mar 08, 2016 7:38 am
Absolute value is the positive distance between a number and 0.

So, for example, the absolute value of 6 is 6, because the distance between 6 and 0 is 6.

The absolute value of -6 is also 6, because the distance between -6 and 0 is 6.

So when you see an absolute value notation in a question, often the way to handle it is by plugging in both of the possible values, positive and negative.

So if you were to see |x| = 6, you would consider the following.

x = 6 or x = -6

This alternative way of expressing the relationship could also be useful in certain circumstances.

x = 6 or -x = 6

For instance, if you were to see |x + y| = 7, then it might be optimal to consider the following.

x + y = 7 or -(x + y) = -x - y = 7
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