Statement 1) (x+1)(|x|-1) > 0
We have two cases when
1)x > 0 , |x| = x
(x+1)(|x|-1)>0 becomes (x+1)(x-1)>0
x^2 -1 > 0 i.e. x > 1 or x < -1 but we have assumed x > 0 so x > 1.
2) x < 0 , |x| = -x
(x+1)(|x|-1)>0 becomes (x+1)(-x-1)>0
-(x + 1 )^2 > 0 i.e. (x + 1 )^2 < 0 but square of any number can never be negative. So the case fails.
From Cases above we have x > 1. Sufficient!!!
Statement 2) |x|<5 means -5 < x < 5. Not Sufficient!!!
Answer A.
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DS: Absolute Value again!
Source: Beat The GMAT — Data Sufficiency |
the solution posted above is quite good.la1214 wrote:Hello,
Experts please help!!
Is x>1?
1. (x+1)(|x|-1)>0
2.|x|<5
Thanks
if you would rather not take such an algebraically intense approach, you can also try to find individual cases of "yes" and "no".
for either of the statements, if you can find both "yes" and "no", then the statement is insufficient; if you can't, then it's sufficient.
--
for statement 1:
Getting "yes"
if you plug in a really big number for x (say, x = 1000), then that number will definitely satisfy statement 1, and it will give a "yes" answer to the question.
Getting "no"
now, the goal is to get a number that actually satisfies statement 1 but isn't greater than 1.
but ...
* x = 1 doesn't work in statement 1, because the product will be 0.
* if x is anything between -1 and 1, then (x + 1) will be positive but (|x| - 1) will be negative, so statement 1 won't work.
* x = -1 doesn't work in statement 1 either; it makes the product 0 again.
* finally, no value of x below -1 will work in statement 1, because, for such values, (x + 1) is positive but (|x| - 1) is negative.
so, it's not possible to get a "no" answer with statement 1, so statement 1 is sufficient.
--
statement 2:
* if you let x = 0 (which satisfies statement 2), then you get a "no" answer to the question.
* if you let x = 2 (which also satisfies statement 2), then you get a "yes" answer to the question.
so, statement 2 is insufficient.
Ron has been teaching various standardized tests for 20 years.
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Pueden hacerle preguntas a Ron en castellano
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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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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
--
Learn more about ron
I have problem with inequalities can some one provide me a link for this topic, your help is appreciated.
Thank you.
Thank you.
