Absolutely Less Than 4 (CAT 1)

[Parth]

If n is not equal to 0, is |n| < 4 ?

(1) n2 > 16

(2) 1/|n| > n


Stmt 2 :
Is this approach correct ?
n|n|<1
n>0
n^2<1 , n<1 or n<-1, which may or maynot satisfy the stem.
N<0
-n^2<1 or n^2>-1, which is an imaginary number. Thus insufficient.

Can some suggest a better approach !

[RonPurewal]

<gmat>

No imaginary numbers on the GMAT, dude. Your approach is correct right up to that point, though.

When you get to the statement n^2 > -1 (or its equivalent, - n^2 < 1), you look at it and you realize that n^2 is always at least 0, so that statement is ALWAYS true. Therefore, the statement works for all negative numbers.

Because there are negative numbers with |n| < 4 (i.e., the ones between -4 and 0) and negative numbers with |n| not < 4 (all the other ones), this choice is indeed insufficient.

By the way, your approach is pretty much the best thing that's out there, as far as I can tell. The only other efficient approach I can think of is to recognize (intuitively) that numbers equal their own reciprocals at +/- 1, and that the absolute value function changes its behavior at 0. In you figure that out, you'd just parcel out the number line into <-1, -1 through 0, 0 through 1, and >1, and investigate the truth of statement (2) on each interval.

</gmat>

And finally, if you care, there is no concept of order ("<" or ">") for imaginary/complex numbers. If you try to define one, it won't work (this is one of the first fundamental theorems of any respectable complex analysis course).

[yousuf_azim]

What is the ans?

BR

[jnelson0612]

What is the ans?

BR

The answer is A.