gmat prep question

[yvonne12]

if N denotes a number to the left of 0 on the number line such that the square of N is less than that the square of N is less than 1/100, then the recipricol of N must be

less than -10
between -1 and -1/10
between -1/10 and 0
between 0 and 1/10
greater than 10

explain to me how you interpret this, please

[parore26]

Hi,
Here is how I would solve it:
1) The number is left of 0 on the number line, therefore it's negative.
2) The square is less than 1/100, this implies that the number is a negative fraction.
From 1 & 2 we have that N is a negative fraction. Therefore, the reciprocal of N is also negative. This eliminates choices D & E.
You can eliminate C, if you take reciprocal of N = -1/9 then N = -9 and N^2 > 1/100
You can also eliminate B, -1/2 < -1/10 and -1/2 > -1. The reciprocal is -2 and the square is 4. Therefore the answer is A.

Hope this helps.

[yvonne12]

ok , but if its less than -10 would it be the same as the others? I mean squaring any number less than -10 would still make it greater than 1/100 am I missing something here?

or does it mean less than the reciprical of -10

[Cybermusings]

Since the number is to the left of the number line, it is negative and the square of N is less than 1/100
n^2 < 100
Therefore sqr rt of n^2 < sqr rt of 1/100
n<-1/10 (it can't be 1/10...we already know it's negative); so n<-1/10
So reciprocal of n i.e. 1/n < -10
Hence clear choice A

[Scott@TargetTestPrep]

if N denotes a number to the left of 0 on the number line such that the square of N is less than that the square of N is less than 1/100, then the recipricol of N must be

less than -10
between -1 and -1/10
between -1/10 and 0
between 0 and 1/10
greater than 10

We are given that N denotes a number to the left of 0 on the number line such that the square of N is less than 1/100. This means N is negative, and it is between 0 and -1/10 since (-1/10)^2 = 1/100. Thus, N could be equal to values such as -1/11, -1/12, -1/13, etc. Notice that when we square these values, they are all less than 1/100.

Let's take the reciprocal of any of these values listed. The reciprocal of -1/11 is -11. Similarly, the reciprocal of -1/12 is -12, and the reciprocal of -1/13 is -13. Since these reciprocals are all less than -10, answer choice A is correct.

Alternate Solution:

Let's find a value for N such that N is negative and the square of N is less than 1/100. If we take N = -1/20, we see that N^2 = 1/400, which is less than 1/100. Now, the reciprocal of N is 1/N = -20, which is less than -10.

Answer: A