If n is not equal to 0, is |n| < 4 ?
(1) n2 > 16
(2) 1/|n| > n


For statement 1, I thought simplfying
n2 > 16 would = n>4 OR n>-4
However, the answer explantion is saying
n2 > 16 would = n>4 OR n<-4
Can someone please tell me why this is so? Thanks

We can rephrase the question by opening up the absolute value sign. There are two scenarios for the inequality |n| < 4.
If n > 0, the question becomes “Is n < 4?”
If n < 0, the question becomes: “Is n > -4?”
We can also combine the questions: “Is -4 < n < 4?” ( n is not equal to 0)

(1) SUFFICIENT: The solution to this inequality is n > 4 (if n > 0) or n < -4 (if n < 0). This provides us with enough information to guarantee that n is definitely NOT between -4 and 4. Remember that an absolute no is sufficient!

(2) INSUFFICIENT: We can multiply both sides of the inequality by |n| since it is definitely positive. To solve the inequality |n| × n < 1, let’s plug values. If we start with negative values, we see that n can be any negative value since |n| × n will always be negative and therefore less than 1. This is already enough to show that the statement is insufficient because n might not be between -4 and 4.
The correct answer is A.

The colord part is wrong. if n^2 > 16, n is either > 4 or <-4 because 16 is positive as n^2 is. so to get the value of n^2 > 16, either 4 or <-4 has to be n.
In inequality, the problem cannot be solves in the sme way as we solve the equation.
for ex: if n^2 = 16, n = 4 or -4.

the same doesnot apply to inequality. so you have to be careful. if n > -4, n could be -3 or 1 or 2 or 3 or so on. If so n^2 cannot be > 16. therefore, if n^2>16, n > 4 or < -4.

Therefore A makes sense...

The last poster makes a good point. You can solve as you would an equation to get the threshhold values (4 and -4), but with inequalities you must be very careful about the direction of the inequality sign.

One helpful thing is to "verbalize" the inequality:
"Is |n| < 4?" can be verbalized as "Is n less than 4 away from zero?" or further as "Is n between -4 and 4?"

"n2 > 16" can be verbalized as "When you square n, you get more than 16" which prompts "Squaring what gets you more than 16? A number 'bigger' than 4, positive or negative." This might make it easier to conclude that n<-4 and 4<n are the right solutions, as it forces you to think about which types of numbers are in that range.

_________________
Emily Sledge
Instructor
ManhattanGMAT