Because the resistors are in parallel, we can use the equation for finding the total resistance.

Using this equation, any positive numbers we plug into the equation for the resistances will yield a number that is less than any of the resistors individually. Using this property allows for many more resistances to be achieved besides the individual resistors one may have.

First off, we need to find the current coming out of the battery. If we consider  and  in parallel, we can find the equivalent resistance of those two. The circuit will look like

Where

Notice in this figure above that  is in series with . Finding the total equivalent reistance of the circuit will allow us to find the total current coming out of the battery.

The total current coming out of the battery is found using Ohm's Law,

Notice that if  is in series with  than the current coming out of the battery is the same current traveling through  since for a series circuit

This means that the voltage drop across  is just

Nothing can be said for certain about the total resistance. This is because, depending on the strength of the resistors, there can be practically any value for the total resistance. For instance, if our resistors were 1, 1, and 2, respectively, then after using the resistor equations (R¹ and R²), we find that the total resistance is 1 Ohm, which would eliminate the answers "arithmetic mean", "greater than any individual", and "less than any individual", which leaves "somewhere between the highest and lowest" and "none". However, we can use another example to disprove the first of those two. 

Let the resistors equal 100, 100, and 1, respectively. The total resistance for that setup is , which is less than any individual resistor, not in between the highest and lowest, but we've already shown an example that contradicts this finding. Therefore, none of the answers are correct and can be said for certain.

Putting the resistors in parallel makes the total resistance  of the original value. Thus, the current is quadrupled. 

In this question, we're asked to identify an answer choice that will increase the overall resistance of a circuit.

All conducting materials have an intrinsic resistance. This kind of resistance, called resistivity, is dependent on the type of material used to conduct the current. In addition to this, resistance is also dependent on the length of the conducting material as well as the cross-sectional area. A shorter length will lead to a smaller amount of resistance. Likewise, a larger cross-sectional area will result in decreased resistance.

Furthermore, it's important to recall that resistors add in series but add inversely in parallel. The reason for this is because resistors connected in series must all have the same current flowing through them. Because the sum total of the voltage drop of each of them must equal the overall voltage supplied by the external voltage source, the overall current (which will flow through each of them) is decreased. For a constant voltage, a decreased current means that the circuit as a whole must have a greater resistance.