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Senior Manager  Joined: 21 Oct 2013
Posts: 408
If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 67% (01:05) correct 33% (01:10) wrong based on 680 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 60727
If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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8
5
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, [-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.

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

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3
[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

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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Math Expert V
Joined: 02 Sep 2009
Posts: 60727
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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1
1
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, [-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.

Check other Rounding Functions Questions in our Special Questions Directory.
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Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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1
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

Manager  Joined: 14 Jul 2014
Posts: 88
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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1
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, [-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.

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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Joined: 06 Nov 2014
Posts: 1868
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

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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Math Expert V
Joined: 02 Sep 2009
Posts: 60727
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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1
2
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, [-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.

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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Intern  Joined: 14 Oct 2013
Posts: 42
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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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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1
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.

GMAT assassins aren't born, they're made,
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Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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Hi All,

This is an example of a Symbolism question; these types of questions provide you with a "made up" math symbol, tell you what it "means" mathematically, then ask you to perform a calculation with it.

Here, we're told that [X] = the LEAST INTEGER that is greater than or equal to X.

In these situations, it helps to come up with some quick examples, so that you are clear on the concept:

For example:
 = 1
[1/2] = 1
[-2.5] = -2
Etc.

With this prompt, we're asked to figure out this…

[X] = 0

So what COULD X be so that the LEAST integer that would be greater than (or equal) X is 0?

X COULD be 0, of course.
X would have to be negative….
BUT it CAN'T be -1, since [-1] = -1

It would have be 0 and any negative fraction greater than -1

GMAT assassins aren't born, they're made,
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Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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Why can' it be A. If x is 0 ; then is it [x] = 1 or 0 . Hence it cannot be the answer.

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Posted from my mobile device
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Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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Hi Raksat,

This question asks what MUST be true (which really means "which of the following is ALWAYS true no matter how many different examples you can come up with?"). Answer A is SOMETIMES true (X COULD be 0, but it could also be other values).

GMAT assassins aren't born, they're made,
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Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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This is the first time I encountered those [] marks in the GMAT quant section. Is it something that could also appear or already has appeared on the actual test?

I am aware that it isn't that complex, but it is surprising to encounter something completly new to me after studying for the GMAT for a few months EMPOWERgmat Instructor V
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Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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1
Hi Masterscorp,

This is an example of a Symbolism question; these types of questions provide you with a "made up" math symbol, tell you what it "means" mathematically, then ask you to perform a calculation with it. To reiterate: these [ ] marks are a made up math symbol that applies to THIS question ONLY; they don't represent some branch of math that you're unaware of.

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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

We are given that [x] denotes the least integer greater than or equal to x and that [x] = 0.

So some numbers x can be include: 0, -0.1, -0.5, -0.9 and -0.999.

Thus, we see that x must be greater than -1 but less than or equal to 0.

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Re: 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?

B. 0 <= x < 1
E. -1 < x <= 0

I was in doubt between B & E.

If x= 0.4, least integer would be 0 ( supports B ).
If x= 0.8, least integer still would be 0 ( as X < 1) , support B ?

Please can someone help me understand why B is incorrect.
Math Expert V
Joined: 02 Sep 2009
Posts: 60727
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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

B. 0 <= x < 1
E. -1 < x <= 0

I was in doubt between B & E.

If x= 0.4, least integer would be 0 ( supports B ).
If x= 0.8, least integer still would be 0 ( as X < 1) , support B ?

Please can someone help me understand why B is incorrect.

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

If x = 0.4, then the least integer which is GREATER than x is 1, NOT 0.
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Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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Solution

Given:
• [x] denotes the least integer greater than or equal to x.

Approach and Working:

[x] = x, if x is an integer.
And if x is not an integer then [x]= Least integer greater than x.

Now, [x]=0 for x=0 and when -1 < x <0.

Therefore, the correct answer is 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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_________________ Re: If [x] denotes the least integer greater than or equal to x and [x] =   [#permalink] 16 Jan 2020, 00:49
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