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

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Intern
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If [x] denotes the least integer greater than or equal to x [#permalink]  08 May 2012, 04:34
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Question Stats:

56% (01:48) correct 44% (00:47) wrong based on 728 sessions
If [x] denotes the least integer greater than or equal to x, is [x] = 0?

(1) -1< x< 1
(2) x < 0
[Reveal] Spoiler: OA
Intern
Joined: 13 Mar 2012
Posts: 20
GMAT 1: 700 Q50 V34
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Kudos [?]: 22 [2] , given: 9

Re: If {x} denotes the least integer greater than or equal to x, [#permalink]  08 May 2012, 05:56
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1) -1<x<1
if x=-0.5; {x}=0;
if x=0.5; {x}= 1
not sufficient
2)if x<0
itself not suficient, i.e cant be 0 or -1 or any negative int.

however 1) & 2) together are sufficient with -1<x<0 , {x}=0

therefore c
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Kudos [?]: 45331 [4] , given: 6740

Re: If [x] denotes the least integer greater than or equal to x [#permalink]  09 May 2012, 00:53
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If [x] denotes the least integer greater than or equal to x, is [x] = 0?

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

Question: is $$[x]=0$$? --> is $$-1<x\leq{0}$$?

(1) -1< x< 1. Not sufficient.
(2) x < 0. Not sufficient.

(1)+(2) -1<x<0. Sufficient.

Similar questions to practice:
how-x-become-fraction-if-its-been-said-an-integer-94687.html
awkward-ds-105416.html
help-data-sufficiency-equation-and-inequalities-99856.html
if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html
denotes-to-be-the-least-integer-no-less-than-x-is-130841.html

Hope it helps.
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Concentration: Marketing, Finance
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Kudos [?]: 278 [1] , given: 11

Re: If [x] denotes the least integer greater than or equal to x [#permalink]  18 Dec 2012, 00:03
1
KUDOS
(1) Find out the question.

Solution:
(1) Question: Is [x] = 0?
(2) Possible values of x: [x] = 0 would mean x is greater than -1 but less than 0.

Statement 1: -1 < x < 1
x=0.5 would give [x] = 1
x=-0.5 would give [x] = 0
INSUFFICIENT.

Statement 2: x < 0
x = -0.5 would give [x] = 0
x = -1 would give [x]=-1
INSUFFICIENT

Together: -1 < x < 0 This is the range of x that we know will give [x] = 0. SUFFICIENT.

_________________

Impossible is nothing to God.

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Kudos [?]: 0 [0], given: 3

Re: If [x] denotes the least integer greater than or equal to x [#permalink]  09 Jun 2013, 11:53
I got the right answer but the question is tricky for me: "if [x] denotes the least integer greater than or equal to x"... does it concern only numbers like [1.5]=2; [-1.5]=-1;... or [1.4] will also be rounded to 2?

Thank's
Math Expert
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Posts: 28316
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Kudos [?]: 45331 [1] , given: 6740

Re: If [x] denotes the least integer greater than or equal to x [#permalink]  09 Jun 2013, 11:57
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Manager
Joined: 01 Jan 2013
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Location: India
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Kudos [?]: 16 [0], given: 131

Re: If [x] denotes the least integer greater than or equal to x [#permalink]  03 Nov 2013, 23:31
Bunuel wrote:
If [x] denotes the least integer greater than or equal to x, is [x] = 0?

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

Question: is $$[x]=0$$? --> is $$-1<x\leq{0}$$?

(1) -1< x< 1. Not sufficient.
(2) x < 0. Not sufficient.

(1)+(2) -1<x<0. Sufficient.

Similar questions to practice:
how-x-become-fraction-if-its-been-said-an-integer-94687.html
awkward-ds-105416.html
help-data-sufficiency-equation-and-inequalities-99856.html
if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html
denotes-to-be-the-least-integer-no-less-than-x-is-130841.html

Hope it helps.

Hi Bunuel,
Can you post some 650+ - 700 level PS/DS questions on greatest integer function.

Thanks!!
Math Expert
Joined: 02 Sep 2009
Posts: 28316
Followers: 4482

Kudos [?]: 45331 [0], given: 6740

Re: If [x] denotes the least integer greater than or equal to x [#permalink]  03 Nov 2013, 23:42
Expert's post
abid1986 wrote:
Bunuel wrote:
If [x] denotes the least integer greater than or equal to x, is [x] = 0?

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

Question: is $$[x]=0$$? --> is $$-1<x\leq{0}$$?

(1) -1< x< 1. Not sufficient.
(2) x < 0. Not sufficient.

(1)+(2) -1<x<0. Sufficient.

Similar questions to practice:
how-x-become-fraction-if-its-been-said-an-integer-94687.html
awkward-ds-105416.html
help-data-sufficiency-equation-and-inequalities-99856.html
if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html
denotes-to-be-the-least-integer-no-less-than-x-is-130841.html

Hope it helps.

Hi Bunuel,
Can you post some 650+ - 700 level PS/DS questions on greatest integer function.

Thanks!!

Similar questions:
if-denotes-the-least-integer-greater-than-or-equal-to-x-132223.html
if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html
for-all-numbers-t-let-t-be-defined-as-the-greatest-105416.html
is-x-an-odd-integer-1-x-2-2x-99856.html
for-all-z-denotes-the-least-integer-greater-than-or-110561.html
denotes-to-be-the-least-integer-no-less-than-x-is-130841.html
for-all-numbers-t-let-t-be-defined-as-the-greatest-105416.html
if-is-the-greatest-integer-less-than-or-equal-to-x-what-144277.html
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help-data-sufficiency-equation-and-inequalities-99856.html
if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html
denotes-to-be-the-least-integer-no-less-than-x-is-130841.html
is-the-greatest-integer-less-than-or-equal-to-the-real-n-154006.html
if-denotes-the-greatest-integer-less-than-or-equal-to-z-162078.html

Hope it helps.
_________________
Intern
Joined: 02 Jan 2014
Posts: 12
Followers: 0

Kudos [?]: 8 [0], given: 15

Re: If [x] denotes the least integer greater than or equal to x [#permalink]  24 Apr 2014, 06:38
If [x] denotes the least integer greater than or equal to x, is [x] = 0?

(1) -1< x< 1
[-0.5] = 0 but [0.5] = 1. Not sufficient

(2) x < 0
[-0.5] = 0 but [-1] = -1 and [-2] = -2. Not sufficient

(1)+(2) -1<x<0
[-0.5] = 0. Sufficient

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Kudos [?]: 60 [0], given: 0

Re: If [x] denotes the least integer greater than or equal to x [#permalink]  28 Jun 2015, 01:50
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Re: If [x] denotes the least integer greater than or equal to x   [#permalink] 28 Jun 2015, 01:50
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