Posted: Jul Jul 13, 2010 6:08

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Quote:
I am little confused : The OG says that the answer is D .
if 2 . cannot be true then how the answer D is correct .Please explain me
GMAT Quantitative Review PS 156
Looks like Ian did something wrong at the end. (2 is definitely a MUST BE TRUE.)

But his approach is still good. |x+3| can be rewritten as |x-(-3)|, which means "the distance between x and -3 on the number line."

IF x<-5, IS the distance between x and -3 on the number line >2 ?
Clearly, yes (look at it on the number line). Thus, 2 must be true.

But the easiest way BY FAR, here, is to pick numbers as Stuart said, and as I showed in my post above:


Quote:
If you plug any number that satisfies this inequality into |x+3|, you will see that the result must be >2. For example, let x=-6. Then, |-6+3| = 3. Is 3>2? Yes. Let x=-5.1. Then, |-5.1+3| = 2.1. Is 2.1>2? Yes. We've convinced ourselves that given x<-5, roman numeral 2 must be true.
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A third way of seeing this is to use algebra and a just a wee bit of formal logic (such a "wee" bit of formal logic, that you can even call it commonsense):

|x+3|>2

solves to :

x<-5 OR x>-1

For 2 to be necessarily true, one of these two inequalities must hold true (it's impossible for both of them to hold true simultaneously). So, you can read 2 as:

If x not <-5, then x>-1
and:
If x not >-1, then x<-5.

Because x<-5, we know that x is not>-1.
And we know from the above that if x is not >-1, then x<-5.
So, we are left with the quaint question: If x<-5, does it have to be true that x<-5?
Clearly, yes.
Thus, 2 must be true.

The above is confusing for me ,but I think I am clear about my doubt..

Basically question stems itself say that x<-5 ;
and |x+3|>2
satifies for x<-5
so this is must be true..

so ,I hope I am right
But thanks everyone .
Thanks to all tutors for their efforts.Tutor come here and help us .This is very important for us.

yes, you are right!

and what I meant by the above is just that one of those 2 inequalities must hold true. So, if one doesn't hold, then the other must.

If x<-5, then we know that x>-1 doesn't hold. Thus, the other one must hold: x<-5.

Cheers!