EMPOWERgmatRichC
Hi sssjav,
Based on the information we're given at the beginning of the prompt, we know that X can be any value from -5 to +5 INCLUSIVE. That 'restriction' is what we have to work with when trying to determine which of the three Roman Numerals is ALWAYS TRUE.
III. 25 ≥ x^2 ≥ -25
Roman Numeral 3 asks us to think about SQUARED terms. With the given range of values that we have to work with, the range of the squared terms would be 0 through +25, inclusive. Regardless of the exact value that you choose for X, X^2 will ALWAYS fall into the range provided by Roman Numeral 3 every time, so Roman Numeral 3 IS true.
GMAT assassins aren't born, they're made,
Rich
I agree to the points you've made, but my doubt remains unresolved.
What you're saying is that for the concerned values of x ( [-5,5] ), Statement-III will always be
true - Even though the solution set of statement-III
alone might include some values other than those with which we are concerned (All As are Bs, but all Bs are not As).
so what you mean to say is that in a Venn-Diagram-Language, the shape/circle representing [-5,5] will lie enclosed within a bigger shape/circle of statement-III. (You can choose to ignore this statement if it it sounds confusing but you understood my point)
However, by the above logic, even statement-I and statement-II will be
true for the concerned values of x, even though the solution sets of the statements might include values other than the ones that belong to [-5,5] and/or might not include some of the values from the set [-5,5].
Now the questions asks us which of the given statements are "true" - according to me, there could only be two possible answers : if we go by the above logic, then all the three statements are true, and If we go by the logic that which of the statements truly represent the all the values of x, then none of the statements will be true. (as all of them represent some values which are either more or less than the concerned set)
However, in another case, if it is asked, that which of the given statements will
include ALL the concerned values of x, then statement-III is the best option available. I understand that this is what is meant to have been asked from the question. The thing that I need assistance with is understanding the language of the question - and narrow down on the correct meaning of the question. Where exactly did I interpret the question wrongly? Or what is it that I'm missing?
EDIT : Just read bunuel's reply that gmat does not deal with imaginary number values, that clears up my doubt. Thanks to both of you for your resplies!