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If [x] denotes the greatest integer less than or equal to x [#permalink]
23 May 2010, 08:06

00:00

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Difficulty:

15% (low)

Question Stats:

80% (01:41) correct
19% (00:41) wrong based on 179 sessions

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...

Re: How x become fraction if its been said an integer [#permalink]
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]
23 May 2010, 09:40

2

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Expert's post

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:

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.

Re: How x become fraction if its been said an integer [#permalink]
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] ?

Re: How x become fraction if its been said an integer [#permalink]
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.

Re: If [x] denotes the greatest integer less than or equal to x [#permalink]
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 < 1will 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