prep question

jc114 wrote:x=/= 0, |x|<1?

1. x/|x|<x

2. x<|x|

how would you solve this, without plugging in numbers (probably take forever)

ok .. here goes ...

mod(x) is the positive value of x ...

.... so x/mod(x) will be equal to either 1 or -1 ...

now the first statemnet says that x/mod(x) < x ... now x can take either fraction or intgere values and can either be negative or positive ...

now there are 2 cases for which the first statement is satisfied .... first when x>1 or when x is between -1 and 0 .... for the rest of the cases that is when x is between 0 and 1... and when x is less than -1... x/mod(x) will be greater than x ... so we have 2 values of x which satisfies the first condition ... in one case (when x is between -1 and 0) mod(x)<1.. and in the other case (when x is greater than 1) mod(x)>1 .. so statement one does not give a defnite answer .. so insufficient

the second statement says that x<mod(x) .. which just means that x is negative ( if x was positve the x = mod(x)) ... but again mod(x) can be either > or < 1 .. so second statement is againd insufficient ...


..... now combine the 2 statements the second says that x is negative and the first says that x/mod(x)<x .. this is possible only when x is between -1 and 0 .. so mod(x)<1 .. so the ans is C..


... i am sorry if the explanation seems gibberish ...

in the second condition, how does x<0=> mean that either x<=0 or -1<x<0?

jc114 wrote:in the second condition, how does x<0=> mean that either x<=0 or -1<x<0?

i am sorry ... but i do not understand what is it that u r meaning to ask ..