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If [x] denotes the least integer greater than or equal to x and [x] =

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

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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
[Reveal] Spoiler: OA

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

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New post 29 Aug 2014, 06:18
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[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

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

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New post 29 Aug 2014, 06:22
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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


Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ...

Hence, since [x] = 0, then it must be true that \(-1<x\leq{0}\): any number from this range when rounded up gives 0.

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

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Bunuel wrote:
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


Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ...

Hence, since [x] = 0, then it must be true that \(-1x\leq{0}\): any number from this range when rounded up gives 0.

Answer: E.


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

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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



The answer for this is 0 < = x < = 1

However it is not available in the options. The match to the above is -1 < x <= 0

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

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New post 30 Mar 2015, 09:13
Bunuel wrote:
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


Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ...

Hence, since [x] = 0, then it must be true that \(-1x\leq{0}\): any number from this range when rounded up gives 0.

Answer: E.



Hi Bunuel

So just to clarify, if x = -1, then [x] = -1
But since its given that [x] = 0, hence x can be at the least -0.99 and max 0

I think the trap here is greater than or equal to x Thats why "D" is wrong

Is this understanding correct?

Thanks

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

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

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New post 31 Mar 2015, 03:47
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buddyisraelgmat wrote:
Bunuel wrote:
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


Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ...

Hence, since [x] = 0, then it must be true that \(-1x\leq{0}\): any number from this range when rounded up gives 0.

Answer: E.



Hi Bunuel

So just to clarify, if x = -1, then [x] = -1
But since its given that [x] = 0, hence x can be at the least -0.99 and max 0

I think the trap here is greater than or equal to x Thats why "D" is wrong

Is this understanding correct?

Thanks


[x] = 0, means that \(-1<x\leq{0}\): any number from this range when rounded up gives 0.

D is wrong because x can be 0, while D excludes this possibility.
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Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]

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New post 29 May 2015, 18:20
E totally makes sense and I went for that option as well but can someone explain why A is wrong?

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

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New post 29 May 2015, 20:14
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Hi healthjunkie,

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.

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

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Re: If [x] denotes the least integer greater than or equal to x and [x] =   [#permalink] 30 Oct 2017, 06:55
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