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

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Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If y>=0, What is the value of x?  [#permalink]

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06 Mar 2016, 21:26
truongynhi wrote:
Hi chetan2u,

Thank you for the prompt reply. But I still have a doubt.

Take the inequation $$x^2<4$$ for example. We then have $$|x|<2$$, which means $$-2<x<2$$. What I understand is that x must be greater than -2 AND less than 2 for the inequalitiy to hold. So I think this is an AND scenario.

If, however, $$x^2>4$$, then $$x<-2$$ OR $$x>2$$. This is clearly an OR scenario. Here OR makes sense to me.

My inequality skill is pretty rusty. Thank you for bearing with me. I very appreciate your help!

Hi truongynhi,

I am happy to help you and clear a few doubts you have..

WHAt does OR and AND mean..

1) Take the inequation $$x^2<4$$ for example. We then have $$|x|<2$$, which means $$-2<x<2$$
So here too you had 2 inequalities, x<2 and x>-2..
x<2 can mean x is -3 so this is a solution when we are using OR since we are not looking at both together..
But here x<2 and x>-2 has a range which OVERLAPS, so this is the combined solution for two inequalities..
when you are choosing a value in this range, you are using AND, since taht value will satisfy both the inequalities..

2)If, however, $$x^2>4$$, then $$x<-2$$ OR $$x>2$$. This is clearly an OR scenario.
YES, this is OR situation, because there is no overlap and hence there is no possiblity of a combined solution..
any solution will satisfy just one inequality..

Now when you have two variable as in the case of Q mentioned here..
3+y≤x≤3−y.. you cannot take this as a solution..
WHY..
because the two inequalities you have combined have come in two different scenarios of OR while taking value of x..
there is no OVERLAP in values of x.. x<3 for one inequality and x>= 3 for other..
so don't combine the two..

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: If y>=0, What is the value of x?  [#permalink]

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09 Mar 2016, 08:01
Man this question really Gave me a hard time but at the end i did answer it correctly

The thing to watch out here was that in the 2nd statement as a modulus value is compared to a negative value => it must be zero as mod is always positive..
Fantastic question
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Re: If y>=0, What is the value of x?  [#permalink]

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09 Apr 2018, 02:01
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Re: If y>=0, What is the value of x?   [#permalink] 09 Apr 2018, 02:01

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