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Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]

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29 Aug 2014, 06:18

2

This post received KUDOS

[x] is defined as the least integer greater than or equal to 0 and [x]=0 So, x has to be between -1 and 0 x cannot be equal to -1 as [x] = -1 in that case and x can be equal to 0 as in that case also [x]=0 so, -1< x <= 0 So, Answer will be E

Hope it helps!

goodyear2013 wrote:

If [x] denotes the least integer greater than or equal to x and [x] = 0, which of the following statements must be true? A) x = 0 B) 0 <= x < 1 C) 0 < x <= 1 D) -1 <= x < 0 E) -1 < x <= 0

Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]

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31 Mar 2015, 03:04

goodyear2013 wrote:

If [x] denotes the least integer greater than or equal to x and [x] = 0, which of the following statements must be true?

A. x = 0 B. 0 <= x < 1 C. 0 < x <= 1 D. -1 <= x < 0 E. -1 < x <= 0

Least integer GREATER THAN or EQUAL to x means [x] when rounded off to the nearest integer is GREATER THAN or EQUAL to [x]. Given that [x] = 0 So, [x] can take any value from -1 to 0 (excluding -1 and including 0), it will always be equal to 0. Hence option (E).

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When a question asks "which of the following statements MUST be true?", you can interpret this to mean "which of the following statements is ALWAYS TRUE no matter how many different examples we can come up with?"

In this question, we're told that [X] is the least integer GREATER THAN OR EQUAL to X. We're also told that [X] = 0.

So, while X = 0 is a potential value for X (since 0 is the least integer that is greater than or equal to 0), it is NOT the only potential value.

As an example, X COULD be -1/2

The least integer that is greater than or equal to -1/2 IS 0. Thus, Answer A is NOT always true. With these types of questions, you have to make sure that you're doing enough work to prove when something is ALWAYS true vs. when something is SOMETIMES true.

Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]

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30 Oct 2017, 06:55

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