Nice explanation, selango!
Since I tutored one of my students on a question similar to this last night, I figured I'd chime in with a quick mini-lesson, as I think statement 2 brings up a great point:
Statements are not only facts, but also constraints
The statements that the test gives you are helpful in two ways - they're facts that you can use to prove something about the question, but they're also constraints in that the let you know which numbers are possible to try and which simply don't count. Let's focus on that "constraints" part:
When the statement says that (integer) k raised to the 4th power is less than or equal to zero, you can only choose numbers for which that condition is met, which rules out:
Positive integers (try 1: 1^4 = 1, which is not less than/= 0, and larger positive integers will only get bigger when taken exponentially)
Negative integers (try -1: -1^4 = 1, and you're in the same position as above
Fractions: You're only allowed to use integers
What's left? Only 0, so we're able to solve for the exact value of integer k.
Seeing statements as constraints is helpful whenever you'd like to try numbers to see how they react, as those constraints quite often limit you to a small enough subset of numbers that it becomes clear what you need to do. The next step, on most questions, is to test the limits of those constraints and make sure that you try everything that's allowable within them. For example, a statement that says that "x is nonnegative" doesn't just mean that positive numbers are allowable, as 0 is also "nonnegative".
In essence, the statements as constraints act as the "rules of the game" - they let you know that "you can pick any number, as long as it fits within these boundaries". Learning to think that way can be especially helpful on these questions (and learning to think of them as a game can make studying that much more enjoyable...seriously!).
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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