First the questions says that n is negative and that n^2 < 1/100.
When you have a inequality such as x > y and x and y are both negative if you square both sides you have to flip the inequality
x > y ---> x^2 < y^2
now if you compare this equivalence to the one in the stimulus
x^2 < y^2 ---> x > y
n^2 < 1/100 ----> n > - 1/10
now you have to calculate the reciprocal
given an inequality x > y ---> 1/x < 1/y if x and y have the same sign
x > y ---> 1/x < 1/y
n > - 1/10 ---> 1/n < -10
if you don't know this equivalences do not get blocked. You can find the answer using backsolving
a) 1/n < -10 ---> 1/n = -11 --> n=-1/11 --> n^2 = 1/121 < 1/100 OK
b) -1 < 1/n < -1/10 --> 1/n = -1/2 --> n = -2 --> n^2 = 4 > 1/100 wrong
c) -1/10 < 1/n < 0 ---> 1/n = -1/11 ---> n = -11 --> n^2 = 121 > 1/100 wrong
d y e make n positive and the stimulus says that n is negative
