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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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New post 29 Aug 2014, 07:09
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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
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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, 07:22
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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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New post 29 Aug 2014, 07:18
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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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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, 07:24
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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.


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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New post 01 Oct 2014, 22:00
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

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, 10:13
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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.



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, 04:04
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, 04:47
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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, 19:20
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, 21:14
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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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New post 03 Mar 2018, 15:28
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
[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

Final Answer:

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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 05 May 2018, 21:26
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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Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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New post 06 May 2018, 16:24
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).

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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 07 May 2018, 08:25
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 :oops:
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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 07 May 2018, 12:39
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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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New post 08 May 2018, 11:26
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.

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 16 Dec 2018, 02:33
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

Please can someone advice how option B cannot be the right answer for this.

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.
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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 16 Dec 2018, 02:42
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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

Please can someone advice how option B cannot be the right answer for this.

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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New post 16 Dec 2018, 12:11

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.
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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