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

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

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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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Math Expert
Joined: 02 Sep 2009
Posts: 47977
If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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29 Aug 2014, 07:22
8
2
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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29 Aug 2014, 07:18
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
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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Joined: 02 Sep 2009
Posts: 47977
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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29 Aug 2014, 07:24
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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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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Joined: 14 Jul 2014
Posts: 94
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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30 Mar 2015, 10:13
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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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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Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course Math Expert Joined: 02 Sep 2009 Posts: 47977 Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink] ### Show Tags 31 Mar 2015, 04:47 1 1 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. _________________ Current Student Joined: 14 Oct 2013 Posts: 45 Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink] ### Show Tags 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? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12189 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink] ### Show Tags 29 May 2015, 21:14 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, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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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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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Manager Joined: 20 Feb 2017 Posts: 138 Location: India Concentration: Operations, Strategy WE: Engineering (Other) Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink] ### Show Tags 05 May 2018, 21:26 Why can' it be A. If x is 0 ; then is it [x] = 1 or 0 . Hence it cannot be the answer. Posted from my mobile device Posted from my mobile device _________________ If you feel the post helped you then do send me the kudos (damn theya re more valuable than$)

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

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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).

GMAT assassins aren't born, they're made,
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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Senior Manager Joined: 14 Oct 2017 Posts: 251 GMAT 1: 710 Q44 V41 Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink] ### Show Tags 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 _________________ My goal: 700 GMAT score - REACHED | My debrief - first attempt 710 (Q44,V41,IR7) If I could help you with my answer, consider giving me Kudos EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12189 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink] ### Show Tags 07 May 2018, 12:39 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. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

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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] = &nbs [#permalink] 08 May 2018, 11:26
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