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If [x] denotes the greatest integer less than or equal to x

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If [x] denotes the greatest integer less than or equal to x [#permalink] New post 23 May 2010, 08:06
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If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?

(1) 5x + 1 = 3 + 2x

(2) 0 < x < 1

hello GMAT guy!!

well i m confused about a certain problem [ 100th data sufficieny on OG 12th ed] here they define x as a integer but in the explanation they solve it as if x is is a fraction not an integer...can any one have better explanation...
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Dec 2012, 09:30, edited 2 times in total.
Edited the question and added the OA
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Re: How x become fraction if its been said an integer [#permalink] New post 23 May 2010, 08:30
musabber wrote:
hello GMAT guy!!

well i m confused about a certain problem [ 100th data sufficieny on OG 12th ed] here they define x as a integer but in the explanation they solve it as if x is is a fraction not an integer...can any one have better explanation...

If [x] denotes the greatest integer less than or equal
to x, is [x] = 0 ?[data suff prob number 100 from OG 12th edition]

(1) 5x + 1 = 3 + 2x

(2) 0 < x < 1


x is not defined as an integer here. the function [x] is defined as an integer, therefore x can be a fraction

[4] = 4
[4.9] = 4
[3/2] = 1

get it?
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Re: How x become fraction if its been said an integer [#permalink] New post 23 May 2010, 09:40
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musabber wrote:
hello GMAT guy!!

well i m confused about a certain problem [ 100th data sufficieny on OG 12th ed] here they define x as a integer but in the explanation they solve it as if x is is a fraction not an integer...can any one have better explanation...

If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?[data suff prob number 100 from OG 12th edition]

(1) 5x + 1 = 3 + 2x

(2) 0 < x < 1


If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?

Here x is not said to be an integer. Stem defines some function, represented by the symbol [], as the function which rounds down any number to an integer value:

[3.4]=3, [2]=2, [-7.5]=-8, ...

Q: is [x]=0? Or is 0\leq{x}<1?

(1) 5x + 1 = 3 + 2x --> x=\frac{2}{3} --> [\frac{2}{3}]=0. Sufficient.

(2) 0 < x < 1 --> any x from this range will round down to 0, so [x]=0. Sufficient.

Answer: D.

Hope it helps.
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Re: How x become fraction if its been said an integer [#permalink] New post 23 May 2010, 10:05
Thank you Gmat guys for ur reply, Now i m clear....Well...kinda tricky problem indeed!!!..... :(
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If [x] denotes the greatest integer ... [#permalink] New post 29 Oct 2010, 10:08
Hi all,

this is from OG 12 q.100/p.281

If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?
(1) 5x + 1 = 3 + 2x
(2) 0 < x < 1

The answer mentions that this [x] = 0 is equivalent to 0 ≤ x < 1.

I have hard time understanding it.

What would be [x] = 5 ?

5 <= x < 6 ???
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Re: If [x] denotes the greatest integer ... [#permalink] New post 29 Oct 2010, 10:17
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lordspace wrote:
Hi all,

this is from OG 12 q.100/p.281

If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?
(1) 5x + 1 = 3 + 2x
(2) 0 < x < 1

The answer mentions that this [x] = 0 is equivalent to 0 ≤ x < 1.

I have hard time understanding it.

What would be [x] = 5 ?

5 <= x < 6 ???


Merging similar topics. Please refer to the solution above.

As for your question:
If [x]=5 then yes, 5\leq{x}<6, as ANY x from this range if round down to the integer gives 5. The same way if [x]=0 then 0\leq{x}<1, as ANY x from this range if round down to the integer gives 0.

Hope it's clear.
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Re: How x become fraction if its been said an integer [#permalink] New post 29 Oct 2010, 21:02
Thanks Bunuel for the answer & merging my question with other questions.
I understand the the lower limit but find it hard to grasp the upper limit.
can the upper limit always be x+1 for [x] ?
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Re: How x become fraction if its been said an integer [#permalink] New post 31 Oct 2010, 08:47
Expert's post
lordspace wrote:
Thanks Bunuel for the answer & merging my question with other questions.
I understand the the lower limit but find it hard to grasp the upper limit.
can the upper limit always be x+1 for [x] ?


No upper limit is not x+1 for [x]. For example if [x]=5 then x<6 because if it's more than or equal to 6 then 5 won't be the greatest integer less than or equal to x.

More examples:

[5]=5;
[5.3]=5;
[5.9]=5;
[6]=6;
[-0.1]=-1;
...

Hope it's clear.
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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

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Re: If [x] denotes the greatest integer less than or equal to x [#permalink] New post 18 Dec 2012, 00:12
What value of x would give [x]=0?
According to the rule given in the problem: [x] denotes the greatest integer less than or equal to x.
0<= x < 1 will give us [x] = 0.

(1) 5x + 1 = 3 + 2x
3x = 2
x = 2/3 which satisfies 0 <= x < 1 Thus SUFFICIENT.

(2) 0 < x < 1 SUFFICIENT.

Answer: D
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Re: If [x] denotes the greatest integer less than or equal to x   [#permalink] 18 Dec 2012, 00:12
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