EgmatQuantExpert wrote:
If x is not equal to 0 or -1, what is the value of |x-2|?
(1) \(\frac{(|x+1|)}{(-|x|x^3)}>0\)
(2) \(x^4 = 16\)
This is
Question 1 for
the e-GMAT Question Series on Absolute Value. Official ExplanationIn order to find the value of |x-2|, we first need to know the value of x. From question statement, we know that x is not equal to 0 or -1. Let's see if St. 1 and/or 2 can get us a unique value of x.
Analyzing St. 1 Independently
\(\frac{(|x+1|)}{(-|x|x^3 )}>0\)Multiplying both sides by a positive number doesn’t impact the sign of inequality. So, multiplying both sides by \(\frac{(|x|)}{(|x+1|)}\), we get:
\(\frac{(-1)}{x^3} >0\)
(Note that we could multiply both sides by this number because we were told that x ≠ -1. Therefore, x + 1 ≠ 0 (division by 0 is not defined))Now, multiplying both sides by -1 will reverse the sign of inequality. We get:
\(\frac{1}{x^3}<0\)
\(x^3\) will have the same +/- sign as x
This means, \(1/x\) is negative.
This means, x is negative.
This information is not sufficient to find the value of x.
Analyzing St. 2 independently
\(x^4 = 16\)That is, \(x^4 - 2^4 = 0\)
\((x^2 + 2^2)(x+2)(x-2) = 0\)
This gives us, x = 2 or -2
Since we don’t get a unique value of x, not sufficient.
Combining St. 1 and St. 2From St. 1, x is negative
From St. 2, x = 2 or -2
Combining both, x = -2
Sufficient.
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