Question

Quantitative Flag For Review If n denotes a number to the left of 0 on the number line such that the square of n is less than \small \frac{1}{100}, then the reciprocal of n must be

Answer 1

less than -10

Explanation:

Given that ...

n^2 < 1/100 . . . . . and n < 0

|n| < 1/10 . . . . . square root

At face value, this requires n be within 1/10 of zero. However, there is an additional restriction in the problem statement.

-1/10 < n < 0 . . . . range of n stops at 0 due to the restriction on its value

-10 > 1/n . . . . . . . . . reciprocal changes the sense of the comparison

The reciprocal of n must be less than -10.