## if y is greater than or equal to 0,

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guest612

### if y is greater than or equal to 0,

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

1. |x-3| is greater than or equal to y
2. |x-3| is less than or equal to -y (note, this one is negative y!)

I took this MBA practice two days ago and it's still not clear. From this, my weakest area is definitely Data Sufficiency but I think it's more of a content issue than approach. In any case, can you please tell me how statement 2 answers the question? Given in the question that y is greater than or equal to zero, I flip the inequalities sign when I divide by the equation by -1. Thus, (3+x) is greater than or equal to y. Then I subtract 3 from both sides but still don't get a value for x. I must be doing this all wrong. Please help!
RonPurewal
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### Re: if y is greater than or equal to 0,

they're being tricky little #\$@^&*'s here.

but first, i must address this:
guest612 wrote:I flip the inequalities sign when I divide by the equation by -1. Thus, (3+x) is greater than or equal to y.

no no no! no!
and by the way, no!

the expression in question is an ABSOLUTE VALUE, |x - 3|. two things about this expression:
(1) you ABSOLUTELY CANNOT remove the absolute value bars and replace all the minus signs with plus signs (i.e., produce x + 3). this will always, always, ALWAYS be wrong.
if you don't see what's so wrong about this, then compare |10 - 3| and 10 + 3; that ought to get the idea across. remember, any statement that's false for numbers is also false for variables, because variables stand for numbers.
(2) what it IS equivalent to is either
(x - 3), if x - 3 is nonnegative (i.e., if x > 3), or
(-x + 3), the opposite of the expression within the bars, if x - 3 is negative (i.e., if x < 3).
if you don't know the value of x, there is no way to remove the absolute value bars, so don't try.

think about the number properties associated with absolute values. in particular, the most important property of absolute values - which, fortunately, is also one of their simplest and most easily understood - is this:
absolute values can't be negative.

this observation alone is actually enough to solve this problem. here's how:
(1): all this tells you is that |x - 3|, an absolute value, is at least some positive number. this isn't much of a restriction, as it could be anything greater than that number, so there's no way you'll get a unique value for x. insufficient.
(2): (-y) is 0 or less, and the absolute value must be at or below this value.
combined with the basic observation that appears in boldface above, this tells you that y must be 0, and that the absolute value itself must also be 0. (think about the other possibilities for (-y) if this doesn't make sense to you right away). therefore, |x - 3| = 0, so x must be 3. sufficient!
guest612

### thanks

thanks, ron, for your responses, which have been really great! i took the exam tonight! i improved on quant but choked on verbal which is usually my forte. will have to take it again. but thanks again for all your help! i read through your replies last night and it helped my confidence in quant which i think made a difference.
RonPurewal
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Posts: 19747
Joined: Tue Aug 14, 2007 8:23 am

### Re: thanks

guest612 wrote:thanks, ron, for your responses, which have been really great! i took the exam tonight! i improved on quant but choked on verbal which is usually my forte. will have to take it again. but thanks again for all your help! i read through your replies last night and it helped my confidence in quant which i think made a difference.

glad i could help.

hope you can lay it down on verbal if you decide to retake the exam.
good luck with applications, etc
colinporter101
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### Re: if y is greater than or equal to 0,

Thanks for the help, I struggled with this problem too. It helps sometimes to take a step back and look a the problem instead of just crunching numbers right away.
RonPurewal
Students

Posts: 19747
Joined: Tue Aug 14, 2007 8:23 am

### Re: if y is greater than or equal to 0,

colinporter101 wrote:Thanks for the help, I struggled with this problem too. It helps sometimes to take a step back and look a the problem instead of just crunching numbers right away.

that is probably the single most important lesson you can learn about the gmat quant section.