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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, 06:09
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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
[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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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

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: 43892
If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]

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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.

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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, 06:24
Expert's post
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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.

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, 21:00
1
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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

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Manager
Joined: 14 Jul 2014
Posts: 96
Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]

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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.

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: 1904
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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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: 43892 Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink] ### Show Tags 31 Mar 2015, 03:47 1 This post received KUDOS Expert's post 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, 18:20 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: 11069 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink] ### Show Tags 29 May 2015, 20:14 1 This post received KUDOS Expert's post 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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30 Oct 2017, 06:55
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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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