Question

If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be _______.

A. less than -10B. between -1 and -1/10C. between -1/10 and 0D. between 0 and -1/10E. greater than 10

Answer 1

Answer: E. Greater than 10

Explanation:

First, know that number to the left of a number line are negative and the square of any negative number will be positive and a perfect square.

Since the square of the unknown number is less than 1/100 i.e 0.01 then the possible unknown number 'n' can be -0.01 itself, of which the square of -0.01 will give us 0.0001 (1/10,000) i.e a value less than 0.01.

The reciprocal of 1/10000 is 10,000 which is a value greater than 10.