Absolute Value!!!!

john1234 · Posted: Sat Jul 19, 2008 8:18 pm Post subject: Absolute Value!!!!

If y is greater than or equal to 0,what is the value of x

1) lx-3l is greater than or equal to y

2) lx-3l is greater than or equal to -y

Thanx for any help

gabriel · Posted: Sun Jul 20, 2008 6:18 am Post subject: Re: Absolute Value!!!!

john1234 · Posted: Sun Jul 20, 2008 9:08 pm Post subject:

Thanks. OA is B.

ravibits · Posted: Wed Jul 23, 2008 11:08 pm Post subject: Re: Absolute Value!!!!

enniguy · Posted: Thu Jul 24, 2008 4:00 am Post subject: Re: Absolute Value!!!!

enniguy · Posted: Thu Jul 24, 2008 7:05 am Post subject:

Ans: E

I did not conclude in my previous explanation.

Look at it this way,
consider y = 2, as y >=0 from question.

2nd statement:
|x - 3| {LHS} >= -y {RHS}

Then,
|x - 3| {LHS} >= -2 {RHS}.

This means, LHS can be -1, 0, 1, 2 , ... etc.
But since LHS should always be positive or 0, RHS should also be positive or 0.

Now, RHS is -y. RHS can be 0 when y is 0.
RHS can be positive when y is negative. e.g: -(-3)
But y>=0 from question and y is not greater than 0 from above (RHS cant be positive and y cannot be greater than 0).

That leaves us y = 0.

This brings us to the equation,
|x-3| >= 0

Now,
|x-3| >= 0 leaves 2 cases.

Case 1:- -(x-3) >= 0 and
Case 2:- +(x-3) >= 0.

Consider, Case 1.
Step 2 : x-3 <= 0
Step 3 : x <= 3

Consider Case 2.
Step 2 : x-3 >= 0
Step 3: x >= 3

From both Case 1 and case 2,
x can be any integer.

So, Statement 2 is insufficient.

reachac · Posted: Thu Jul 24, 2008 11:21 am Post subject:

I am not convinced with the explanation provided for B being the answer...can anyone explain better please.

Ian Stewart · Posted: Thu Jul 24, 2008 6:29 pm Post subject:

reachac · Posted: Fri Jul 25, 2008 6:08 am Post subject:

Thanks Ian Smile