question about absolute values

jamesk486 · Posted: Mon Aug 18, 2008 10:38 pm Post subject: question about absolute values

Is |x|>1?
(1) |x|>3
(2)|x+8| > 3 |x-2|

(1) is sufficient
but i had a question about (2)
so there are 4 cases, (i) when |x+8| >0, (ii) |x+8|<0, (iii) |x-2|<0, and (iv) |x-2| >0

so then is this how you solve it?
case (i) |x+8| > 3 |x-2| (both are positive)
case (ii) -|x+8| > 3 |x-2|
case (iii) -|x+8| > -3 |x-2| (both are negative)
case (iv) |x+8| > -3 |x-2|

is this right??

gmatters2vj · Posted: Mon Aug 18, 2008 10:48 pm Post subject:

Hi James,
Do u really need to solve it?

For case 2 i have the following explanation:

|x+8| > 3 |x-2|

Please note that this condition is true for x=0 i.e.
when x=0, 8>6. For this |x|<1.
But when we take x=2
we get 10>0 which is true. For this |x|>1.

Thus insufficient.

Answer must be A.
Whats the answer?

Thanks