If denotes the greatest integer less than or equal to z and = -1 which of the following statements must be true? A. z = -1 B. -2 prep.JPG

is the greatest integer less than or equal to z means that some function rounds DOWN a number to the nearest integer. For example =1, =2, =-2, ... Now, since = -1, then -1\leq{z} ANY number from this range when rounded down to the nearest integer is -1. Answer: D. Similar questions to practice: if-denotes-the-least-integer-greater-than-or-equal-to-x-132223.html if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html for-all-numbers-t-let-t-be-defined-as-the-greatest-105416.html is-x-an-odd-integer-1-x-2-2x-99856.html for-all-z-denotes-the-least-integer-greater-than-or-110561.html denotes-to-be-the-least-integer-no-less-than-x-is-130841.html for-all-numbers-t-let-t-be-defined-as-the-greatest-105416.html if-is-the-greatest-integer-less-than-or-equal-to-x-what-144277.html how-x-become-fraction-if-its-been-said-an-integer-94687.html awkward-ds-105416.html help-data-sufficiency-equation-and-inequalities-99856.html if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html denotes-to-be-the-least-integer-no-less-than-x-is-130841.html is-the-greatest-integer-less-than-or-equal-to-the-real-n-154006.html Hope it helps. P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you,

If question asks " denotes the greatest integer less than or equal to z and = 0 ", then can we say 0<=Z<1 ? Regards, Ammu

Yes. = 0, would mean that 0\leq{z} ANY number from this range when rounded down to the nearest integer is 0. Check other Rounding Functions Questions in our Special Questions Directory . Hope it helps.

Hi Bunuel, Just a question. Why do you think it could not be A?

Because z is not necessarily -1, it could be any number from -1 to 0 ( -1\leq{z}<0 ), for example, -1/2. Check other Rounding Functions Questions in our Special Questions Directory . Hope it helps.

But the question states that it is an integer... What do I missing?

The questions says that z ] is an integer, not z. Please re-read the question and solution and follow the links to the similar problems to understand better.

Thanks for your reply, I get it.

Dear Bunuel, Although I completely agree that the answer is indeed option D here, however option A is not wrong also. If we plug in the value given in option A, we indeed satisfy the condition given. Does the inclusion of option A not make choosing the correct answer slightly ambiguous. I mean why give an option such as A at all in the exam. What trick am I missing here? Thanks in advance, Madhav

The question asks which of the following statements MUST be true, not could be true. z could be -1, but it could also be, for example, -1/2. Thus A is not a statement which must be true. Check other Rounding Functions Questions in our Special Questions Directory . Hope it helps.

I really cannot understand why A cannot be the answer. Z=-1 = -1 Condition satisfies. I have read the theory and solved all the questions in the link, I don't know what am I missing