If the pressure on a gas sample is tripled and the absolute temperature is quadrupled, by what factor will the volume of the sample change?

Let as assume the simplest calculation by assuming that the gas is ideal. Therefore, the equation would be PV=nRT, where P is pressure, V is volume, n is the amount of moles of gas, R is the gas constant and T is the absolute pressure. Let us further assume that the amount of gas, n, is constant before and after the change. With that being said, the volume is equal to

V = nRT/P = kT/P

The term k is lumped as a constant because they are the same before and after the change. Next, we find the ratio of V1 (before the change) and V2 (after the change).

V2/V1 = (k*4T/3P)/(kT/P)

Cancelling out like terms would yield

V2/V1 = 4/3

Therefore, the volume after the change is 4/3 of the original volume. This means that the volume increased by (4/3-1 = 1/3 or 33%) 33% after the change of conditions.