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Inequalities, Absolute Value, Data sufficiency

Problem Solving — algebra and arithmetic
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by RSK » Mon Feb 20, 2012 8:24 am
Can someone please help me solve this? I have no idea how to do this. Thanks!

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

1) |x-3| >= y
2) |x-3| <= -y
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Source: — Quantitative Reasoning |
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by kul512 » Thu Feb 23, 2012 7:16 am
First Statement
|X-3|>=Y
as LHS is always a positive number, so depending on the value of Y, it will create many value of X.
Insufficient

Second Statement
|X-3|<=-Y
As Y is always non-negative so -Y is always non-positive. That means |X-3| is always less than or equal to a non-positive number, which is only possible when that number is zero. i.e. Y=0. So X=3
Sufficient

Answer B.
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by bharti.2010 » Wed Feb 29, 2012 8:39 pm
Hi,

Can u please explain your solution a little more. I did not understant why in 2nd statement Y is always non -ve. I always get stuck with absolute value questions? Can you help to understand this concept?
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by krusta80 » Thu Mar 01, 2012 8:26 am
bharti.2010 wrote:Hi,

Can u please explain your solution a little more. I did not understant why in 2nd statement Y is always non -ve. I always get stuck with absolute value questions? Can you help to understand this concept?
Y is always non-negative because they state it in the question... y>=0
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