24. the temperature, t, of a given mass of gas varies inversely with its volume, v. the temperature of 500 cm^3 of a certain gas is 2.5 degrees celsius. what will the temperature be when it is compressed to a volume of 100cm^3? 160 degrees celsius 12.5 degrees celsius 2,500 degrees celsius 1,250 degrees celsius

None of the given choices is the correct solution. 

The setup of the problem is a correct, if somewhat weird, description
of the ideal gas laws, but the temperature involved in the law is the
ABSOLUTE temperature, NOT the Celsius or Fahrenheit one, or
any other scale where 'zero' is not 'Absolute Zero'.

Zero Celsius is (about) 273 Celsius-size degrees above Absolute Zero. 
So the original temperature of the gas is  (273 + 2.5) = 275.5 Kelvins
(Celsius degrees above absolute zero).  THAT's the temperature that's
going to change in inverse proportion to the volume.
(if the pressure doesn't change)

The volume has been multiplied by  100cm³/500cm³ = 1/5 .

Since the temperature changes inversely, it will be multiplied by  5 .

Final absolute temperature = (5) x (original absolute temperature) =

                                           (5) x (275.5 K) =

                                             1377.5 K .

The final Celsius temperature is  (1377.5 - 273) = 1104.5 °C.

"But those are the choices in the assignment !"
Then the person who wrote the question in the assignment is wrong.
None of the choices they gave is correct.