absolute values

[brandonw3]

If X does not equal 0, then (square root of X^2)/X=

A) -1
B) 0
C) 1
D) X
E) lXl/X

thanks,
Brandon

[parallel_chase]

If X does not equal 0, then (square root of X^2)/X=

A) -1
B) 0
C) 1
D) X
E) lXl/X

thanks,
Brandon

x is not equal to 0
there can two case here

if x = +2
sqrt x^2 / x = sqrt 2^2/ 2 = sqrt 4/ 2 = 2/2 = 1

if x = -2
sqrt x^2 / x = sqrt (-2)^2/ -2 = sqrt 4/ -2 = 2/-2 = -1

Since we know that sqrt x^2 will always be positive and x can be either negative or positive.

lxl/x should be the answer.

Hence E.

Hope this helps.

[cramya]

Nice work there parallel chase!

[raunekk]

E for me 2,,,

@parallel chase

impeccable explanation !!!!

[niraj_a]

i didn't really understand parallel_chases's explanation the first time.

i did it buy trying different numbers, and also using numbers where the numerator was smaller than the denominator. the results helped eliminate A through D.

[lunarpower]

so you should DEFINITELY know the following:

IMPORTANT PIECE OF KNOWLEDGE:
√(x^2) is equal to |x|.

PUT THIS ON A FLASH CARD if you don't know it.

in other words, if you square a number and then take the square root of that quantity, you don't necessarily get the original number back; instead, you get the absolute value of the original number.

here's why: when you square the number, you get a positive value no matter what. in other words, the squared version - which is automatically positive - doesn't "remember" whether the original number was positive or negative. then, when you take the square root, you wind up with a number that's still positive, regardless of the sign of the number you started with.
that's the exact definition of absolute value.

examples / illustrations:
(-5)^2 is 25. take the square root and you get +5, which is the absolute value of -5.
5^2 is also 25. take the square root and you get +5, which is the absolute value of 5 as well.

--

btw, what's the source of this question? it seems as though the gmat folks would put a little more substance into the questions; if you know the takeaway above (which you should - remember, flash cards are your friends), then this problem's solution is immediate.

if this is indeed an official problem, i'm rather surprised.