When the voltage across a steady resistance is doubled, the current?

I'm actually going ahead in the book (DC Circuits) so this isn't really homework but I figured the tag was appropriate ... the name of the chapter is Ohm's Law and Watt's Law.

Problem: Calculate the power dissipated in the load resistor, R, for each of the circuits. Circuit (a) : V = 10V; I = 100mA; R = ?; Since I know V and I use formula P = IV: P = IV = (100mA) (10V) = 1 W.

The next question is what I'm not sure а bout:

Question: What is the power in the circuit (a) above if the voltage is doubled? (Hint: Consider the effect on current).

What I did initially was: P = IV = (100mA) (2V) = 2 W

But then I looked at the answer and it said 4 W, then I looked at the Hint again. Then I remembered in the book early on it said "If the voltage increases across a resistor, current will increase."

So question is: When solving problems I have to increase (or decrease) current (I) every time voltage (V) is increased (decreased) in a problem, right? How about the other way around, when increasing current (I), you need to increase voltage (V). I'm pretty sure that's how they got 4 W, but want to make sure before I head to the next section of the book.

P = IV = (200mA) (2V) = 4 W