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
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absolute values
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parallel_chase
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x is not equal to 0brandonw3 wrote: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
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.
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niraj_a
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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.
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.
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lunarpower
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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.
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.
Ron has been teaching various standardized tests for 20 years.
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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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Learn more about ron
