Data Sufficiency

I had these kinds of tricky questions in my high school, but I forgot it. But now I know
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What is the value of x?

(1) |x| < 2

(2) |x| = 3x – 2

source: ManhattanGMAT

OA: B

1 by itself is obviously not sufficient, since -2 < x <2
2 gives you two options:
a. x>=0 , which is the equivalent of x = 3x - 2, giving you x = 1
b. x<0, so that -x = 3x - 2. For this one you would have 4x = 2, with x =1/2. But 1/2 is not a negative, which means that the given equation has only one possible answer: x = 1.

So I'd go with B.

Great point DanaJ!

exactly; you r right.
this the point which i neglected at the test.
pay attention to these kinds of question later on, especially if you need a high score

WHY? Is trhis considered a difficult one?

I don't get it! What's difficult and what's not in DS? ;(

I don't understand why you set up the equation as a positive x and a -x? I thought absolute value gets rid of negative numbers? So why do you set up -x=3x-2? I'm just not getting this.

DanaJ wrote: b. x<0, so that -x = 3x - 2. For this one you would have 4x = 2, with x =1/2. But 1/2 is not a negative, which means that the given equation has only one possible answer: x = 1.

So I'd go with B.

Hi, what do you mean when you say the given equation has only one possible answer : x=1? What does this have to do with 1/2 not being negative?

mjjking: I do not know if this is a difficult one... I think it all depends on your previous experience with math. For me, it's 8th grade level, although a bit tricky... For someone who has been more focused with humanities (and therefore probably lost touch with math a long time ago - BUT THERE IS NOTHING WRONG WITH THAT!) it might seem a bit complicated. That does NOT, however, mean that you cannot catch up and get a better score than me in quant! All you have to do is practice, ask questions and ask for help. Now, here is your problem: "WHY?" what? Which part do you not understand? Please let me know and I'll be happy to help you!

mdavis: The first statement tells us that the value of x is between -2 and 2, since |x| < 2. There are a lot of possible x-es: -0,345; 1,7234 etc... Therefore it is not sufficient.
The second statement is useless unless you split it up in two. The absolute value does not tell us if x is a negative or a positive number. It just tells us its... absolute value! You should not automatically assume that |x| = x, since x could be a negative. If this is the case, |x| = -x.
-X IS NOT NECESSARILY A NEGATIVE VALUE, it's just the opposite of X!
Let me give you an example: |-2| = 2 (and I think you will agree on this with me). But in the same time 2 = - (-2), so |-2| = -(-2).
So, since you do not know the sign for x, you try to split up the equation in two.
1. x is positive or equal to zero, which is the equivalent of |x| = x. This results in x = 3x - 2, with 1 being the answer. Now you need to check if x = 1 is consistent with your original assumption, that x >= 0. And it is! jackPot! :D
2. x is negative, with |x| = -x (since x is negative, -x will be positive). This means that -x = 3x-2. After solving this equation you get that x = 1/2. Now, again, you have to check if x = 1/2 is consistent with the original assumption that x is negative. But, oops, it doesn't, so that means that -x = 3x -2 does not have a negative solution and therefore it's a dead end.

So in the end, you get just one value for x, which is 1. This is why B is the correct answer.

coffe5251: Please check the above and let me know if you need extra explanations.

DanaJ wrote:1 by itself is obviously not sufficient, since -2 < x <2
2 gives you two options:
a. x>=0 , which is the equivalent of x = 3x - 2, giving you x = 1
b. x<0, so that -x = 3x - 2. For this one you would have 4x = 2, with x =1/2. But 1/2 is not a negative, which means that the given equation has only one possible answer: x = 1.

So I'd go with B.

DanaJ,

You rock and I SUCK!!! I know traps like this but make the mistakes nonetheless.

Ladies/Gents,

For Equalities/inequalities that has Modes, assume negative if you want but once you get the answer, check its validity against the problem. I've seen at least half a dozen of these in last two weeks.