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If y >= 0, what is the value of x?

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Harish Dorai
 Post subject: If y >= 0, what is the value of x?
 Post Posted: Sat Aug 11, 2007 10:11 am 
If y >= 0, what is the value of x?

1) |x - 3| >= y

2) |x - 3| <= -y

I was confused by this question. It says y >=0 in the question and Statement(2) says |x - 3| <= -y.
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anadi
 Post subject: solution is in the confusion
 Post Posted: Sat Aug 11, 2007 3:25 pm 
You have mentioned the solution yourself,

1) Is insufficient, it gives a range of values till infinity. Both =ve and -ve side.

2) |x - 3| <= -y and y>=0. Here in any case y cannot be greater than 0 since left side is always +ve or 0. So the only solution is x=3 and y = 0.

Hence 2 alone is sufficient.
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Harish Dorai
 Post subject:
 Post Posted: Sat Aug 11, 2007 7:46 pm 
Great! B is the right answer.
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Guest
 Post subject:
 Post Posted: Mon Sep 08, 2008 8:06 pm 
Hi instructors,

Could you please expand on what you mean when you state that x must = 3 in statement 2?

Thank you
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Guest
 Post subject: Can someone expalin why Y has to be zero and not someother p
 Post Posted: Mon Sep 22, 2008 9:17 pm 
Can someone elaborate the solution?
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mbarshaik
 Post subject:
 Post Posted: Sun Oct 12, 2008 3:39 pm 
Lets take the first case.

|x - 3| >= y

Y>=0

so x = 3 or x > 3 or < 3..Not sufficient

Second case

|x - 3| <= -y

Multiply both sides by -1

- |x - 3| >= y
If x = 3 then y = 0

If you take any other value |x - 3| is positive so thsi will lead to LHS being negative and y cannot be < 0. So only x = 3 is the possibility.
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RonPurewal
 Post subject:
 Post Posted: Thu Oct 30, 2008 8:23 am 
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http://www.manhattangmat.com/forums/if- ... t2675.html
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