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

  less than -10

Step-by-step 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.

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step-by-step explanation: