Are you sure it's B? Wouldn't the square of the reciprocal of -1 be 1, which is greater than 1/100? I would think it would be A:

n<-1/10 => n^2<1/100
so the reciprocal is less than -10

If we pick n = -1/100, then n^2 is 1/10,000, which satisfies the condition.

Reciprocal of n is -100.

Answer is A?

Darn. I didn't read the question properly! Yes it is B. <Edited my previous Post>

If n^2 < 1/100 then,

-1/10 < n < 1/10. Calculating the reciprocal,
the equation will be,
-10 < 1/n > 10. How? Consider a similar equation:

-1/2 < 1/4 < 1/2. Here n = 1/4. Calculate the reciprocal:
-2 < 4 > 2.

But, n is less than zero and so 1/n will also be less than 0. So the equation becomes,
-10 < 1/n (Reciprocal of n) < 0.

Also, n value will is between 0 and -1/10. So any value between 0 and -1 will have a reciprocal with value less than -1. Hence,

-10 < 1/n < -1.

Question states that n is left of zero on the number line. So n is negative. D and E are ruled out

Next part states that its square is less than 1/100...
1/400 is less than 1/100. Its negative root would be -1/20

Reciprocal of -1/20 is -20 which is less than -10

Answer has to be A