Problem Solving

lukaswelker wrote:
If X ≠ 0, then (√x²)/x =

A) -1
B) 0
C) 1
D) x
E) |x|/x

IMPORTANT thing to memorize: √x² = |x|
So, if we take (√x²)/x and replace √x² with |x|, we get [spoiler]|x|/x[/spoiler]

Answer: E

We can also solve the question by PLUGGING in values and eventually eliminating all answers but one.

Try x = 3
(√x²)/x = (√3²)/3 = 3/3 = 1
So, we can eliminate A, B and D
Since |x|/x becomes |3|/3 = 1, we cannot eliminate E
So, we're left with C or E

Try x = -3
(√x²)/x = (√(-3)²)/(-3) = 3/-3 = -1
So, we can eliminate C
By the process of elimination, we're left with E

Also note that |x|/x becomes |-3|/-3 = -1 PERFECT!

Cheers,
Brent

Hi lukaswelker,

In these types of questions, you might come across MORE than 1 answer that appears to match. When this happens, you have to do some extra work to figure out which answer is SOMETIMES correct and which answer is ALWAYS correct.

Brent's examples showcase this point perfectly. The answer is SOMETIMES "C", but it's ALWAYS [spoiler]"E"[/spoiler]

GMAT assassins aren't born, they're made,
Rich