What is the value of x ?

(1) √(x^2) = 19. Since \(\sqrt{x^2}=|x|\), then we have that |x| = 19. Thus x = 19 or -19. Not sufficient.

(2) √(19^2) = x --> x = 19. Sufficient.

Answer: B.

Note for (1): \(\sqrt{x^2}=|x|\), when \(x\leq{0}\), then \(\sqrt{x^2}=-x=-negative=positive\) and when \(x\geq{0}\), then \(\sqrt{x^2}=x=positive\).

Note for (2): When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{25}=5\), NOT +5 or -5. In contrast, the equation \(x^2=25\) has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT.

For more check here: http://gmatclub.com/forum/exponents-and ... 74993.html
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Asked: What is the value of x ?

(1) √(x^2) = 19
|x| = 19
x = 19 or -19
NOT SUFFICIENT

(2) √(19^2) = x
x = 19
SUFFICIENT

IMO B
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