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

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If [x] denotes the least integer greater than or equal to x [#permalink] New post 08 May 2012, 04:34
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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
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Re: If {x} denotes the least integer greater than or equal to x, [#permalink] New post 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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Re: If [x] denotes the least integer greater than or equal to x [#permalink] New post 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.

Answer: C.

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Hope it helps.
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Re: If [x] denotes the least integer greater than or equal to x [#permalink] New post 18 Dec 2012, 00:03
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When answering Data Sufficiency:
(1) Find out the question.
(2) Ponder about the possible values that will lead you to the answer.

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.

Answer: C
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Re: If [x] denotes the least integer greater than or equal to x [#permalink] New post 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
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Re: If [x] denotes the least integer greater than or equal to x [#permalink] New post 09 Jun 2013, 11:57
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ED1290 wrote:
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


Yes, [1.4]=2.

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Hope it helps
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Re: If [x] denotes the least integer greater than or equal to x [#permalink] New post 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.

Answer: C.

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!!
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Re: If [x] denotes the least integer greater than or equal to x [#permalink] New post 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.

Answer: C.

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
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for-all-numbers-t-let-t-be-defined-as-the-greatest-105416.html
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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
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Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

Answer: C.
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Re: If [x] denotes the least integer greater than or equal to x [#permalink] New post 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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