Quant16 DS54 - Is N closer to 50 than to 75?

[NarbehS23]

This is a DS question.
The question states: Is the value of n closer to 50 than to 75?
The statements are:
(1) 75-n>n-50
(2) n>60

I put C as the answer.

the book gives A as the answer.

It says that it is equidistant when 75-n = n - 50 consequently when looking at statement (1) the book states the statement is sufficient. But this layout/setup only looks for the scenario in which n is between 75 and 50. it doesn't consider the fact that n could be large than both or smaller than both (e.g. a negative number).

Am I missing something? Thank you for any input.

[RonPurewal]

"it doesn't consider the fact that n could be large than both or smaller than both"

^^ ok... but have YOU "considered this fact"?
if you try plugging in just a couple of values in these ranges, you'll notice pretty quickly why this issue isn't an issue.

if n is bigger than 75, then (75 – n) is a negative number, and (n – 50) is a positive number... so, clearly, no such number will satisfy the statement.

if n is smaller than 50, then (75 – n) is a positive number, and (n – 50) is a negative number... so, just as clearly, ALL such numbers will satisfy the statement.