The correct answer is 4. A short, dense air column can produce the same pressure difference as a tall, less dense air column. The greater thickness can make up for the lesser density, and the pressure difference can come out the same.
If the air columns have the same top and bottom pressures, then (according to the ideal gas law) any density difference must be due to differences in temperature.
An example of this might be a comparison of air columns near the equator and near the pole. Suppose both air columns start at the surface (roughly 1000 mb) and extend up to the 400 mb level, so that each air column contains a little more than half of the total amount of air in the air column above each location. The one near the equator is warmer and less dense than the one near the pole, so it must also be taller. Under typical circumstances (about a 30 C temperature difference between air columns), the air column near the equator will be about 7.3 km tall, while the one near the pole will only be about 6.7 km tall.
Does that mean that the atmosphere over the equator is taller than the atmosphere over the pole? Not quite. Once you get up above about 200 mb (roughly 10 km), the air over the equator is colder than air over the pole. In other words, the north-south temperature gradient reverses. Remember the two stacks of air? At the equator, the air is relatively warm near the ground and relatively cold aloft.
What can all this be used for?
Observations of air pressure at the surface tell you the total of air in the atmosphere. Observations of temperature tell you something about how the pressures and heights are above the surface. When we talk about the geostrophic wind, you'll see how pressures and winds are closely related. If you understand how all these things are tied together, you can do useful things like (1) use a small number of observations and infer a great deal about the structure of the atmosphere; (2) look at a map at one level and know what winds and pressures at other levels must look like; (3) take observations at one point, and know how the temperatures and pressures are changing.
You see, if the pressures, winds, and temperatures were unrelated, understanding the atmosphere on a given day would be quite a challenge. You'd need to look at maps of everything, at all levels. Instead, since pressure and temperature (and wind) are so closely related, it is possible for a weather forecaster to just look at one or two maps at different levels and figure out not only what's happening at other levels, but also what's going to happen!