I am missing something, because I feel the question is not giving me all the information I need. Range is basically calculated by subtracting the extreme values in a series.

To find the range of avg night or day temperatures, I need to be able to find both the values on either extremes in the series that is developed.

Based on the information provided:

Lets assume the avg night temperature is 'n' & the avg day temperature is 'd'.

3 + 2(n) = 4

n + 2(d) = 4

d >= 3

With the information provided above,
night temperatures can be = 1/2, 0, -1/2, -3/2, -2, .......

with day temperatures >=3, the night temperatures can be = -2, -4, -6, -8, -10........

I am lost .... how am I supposed to find the range?

Vemuri wrote:I am missing something, because I feel the question is not giving me all the information I need. Range is basically calculated by subtracting the extreme values in a series.

To find the range of avg night or day temperatures, I need to be able to find both the values on either extremes in the series that is developed.

Based on the information provided:

Lets assume the avg night temperature is 'n' & the avg day temperature is 'd'.

3 + 2(n) = 4

n + 2(d) = 4

d >= 3

With the information provided above,
night temperatures can be = 1/2, 0, -1/2, -3/2, -2, .......

with day temperatures >=3, the night temperatures can be = -2, -4, -6, -8, -10........

I am lost .... how am I supposed to find the range?

Please read this line one more time:
The magnitude of 3 more than two times the average night temperature at Antarctica is 4 at its maximum.
Don't you need to consider an inequality envolving a modulus function?