We covered GMAT Roman Numerals questions recently, and like any good teacher, I want to review this topic again to help solidify it in your mind. So, we challenged students on Facebook with a practice question yesterday that combined Roman Numerals with properties of exponents, and got some great responses.
Take a moment to check out the question and the original blog entry on the shortcut strategy for Roman Numerals questions.
Now, let's tackle this!
GMAT Roman Numeral Tip
Remember that when you see a Roman Numeral problem, you should think: "I should start with the answer choice that shows up most frequently so that if I can eliminate it, I can mark out the most answer choices." This will save you time and effort. Remember, every second is valuable on the GMAT, and learning time-saving strategies is every bit as important as (some would argue even MORE important than!) learning math content.
GMAT Number Properties Tip
Next, when you see a Number Properties problem, which is any number that asks how numbers always behave (and exponents are among these), you should think: "I should pick numbers." Learning some rules for properties of special exponents will help out in this problem, too.
What Are Real Numbers?
The problem says "for all real numbers x"...so, what are real numbers? You don't need to know much more about this concept for the GMAT except that they are pretty normal numbers that you are used to working with. The GMAT will never ask you to define a real number. However, you can check out examples of real numbers if you need more clarification on the topic. For your purposes on the GMAT, and in general for picking numbers, this tells you that you want to choose basic, straightforward numbers that are permissible and manageable.
For this problem, check to see what happens when x is positive (2), negative (-1) and zero.
The Strategy in Action
Start with II since it shows up most frequently in the answer choices.
II. . This is a special exponent rule that you need to memorize if you don't know it already. Any number, whether positive, negative, or fractional, raised to the 0 power = 1. You're looking for an answer choice that MUST equal zero, and you've found a that this answer choice does not, so you must eliminate all answer choices that contain statement II. Eliminate answers C, D, and E. Now you only have to try statement I. That was fast work!
I. . If you put in x = 2, you get 8-4=4. Again, you're looking for "MUST equal zero", and you've already found a scenario where it doesn't equal zero, so you must eliminate all answer choices that contain statement I - get rid of answer choice B.
The answer must be A, and you don't even need to spend the time evaluating statement III! Time saved, points gained, GMAT rocked!
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