The "Brain Power" Section The Thinking Skills section is designed to be the hardest part to "study" for because it tests your raw logic. It replaced the old "General Ability" test and is much tougher.
Type 1: Who is Telling the Truth? (Knights and Knaves) You will often see a question like this: Person A says: "Person B is lying." Person B says: "Person A is telling the truth." Question: If one is a Knight (always truthful) and one is a Knave (always lies), who is who?
How to solve it: Test a "Hypothesis." Pretend Person A is telling the truth. If A is truthful, then B is a liar (based on A's statement). Let's check B's statement: B says "A is telling the truth." If B is a liar, he would lie about A. So B would say "A is a liar" or claim A is lying. Wait, B said A is telling the truth. If B is a liar, his statement must be false. This gets confusing! The best trick is to look for contradictions.
Simpler Method: If A says "B is lying" and B says "A is lying"—they can't both be telling the truth. One must be lying. If A says "We are both lying"—A must be a liar. (Because if A was telling the truth, his statement "we are both lying" would make him a liar, which is impossible).
Type 2: Necessary vs. Sufficient Conditions This sounds like university philosophy, but it's simple: Necessary (The Requirement): You need oxygen to start a fire. Oxygen is necessary. But oxygen alone won't start a fire (you need a spark). Sufficient (The Guarantee): If you are a Poodle, you are guaranteed to be a dog. Being a Poodle is sufficient to prove you are a dog.
The Trap: Questions will try to trick you by reversing these. Statement: "If it rains, the grass gets wet." Trap: "The grass is wet, so it must have rained." Why it's wrong: The sprinkler could have been on! Rain is sufficient to make grass wet, but not necessary (other things can do it too).