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If [x] denotes the largest integer smaller than x, is [x]>[−x]?
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PathFinder007
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If [x] denotes the largest integer smaller than x, is [x]>[−x]? [#permalink] New post  Updated on: 14 Jul 2015, 09:44
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If [x] denotes the largest integer smaller than x, is [x]>[−x]?

(1) x=[x]+1

(2) x+1>0

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Originally posted by PathFinder007 on 14 Jul 2015, 09:12.
Last edited by Bunuel on 14 Jul 2015, 09:44, edited 1 time in total.
Edited the question.
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Re: If [x] denotes the largest integer smaller than x, is [x]>[−x]? [#permalink] New post  14 Jul 2015, 09:29
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PathFinder007 wrote:
If [x] denotes the largest integer smaller than x, is [x]>[−x]?
(1) x=[x]+1

(2) x+1>0

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.


Question : is [x]>[−x]?

Statement 1: x=[x]+1

i.e. x = 3 then [x]=2 i.e. x=[x]+1 and [3] i.e. 2>[−3] i.e. (-4)
i.e. x = 1 then [x]=0 i.e. x=[x]+1 and [1] i.e. 0>[−1] i.e. (-2)
i.e. x = -1 then [x]=-2 i.e. x=[x]+1 and [-1] i.e. -2 is NOT Greater than [1] i.e. (0)
NOT SUFFICIENT

Statement 2: x+1>0
i.e. x > -1
i.e. x = 3 then [x]=2 and [3] i.e. 2>[−3] i.e. (-4)
i.e. x = 1 then [x]=0 and [1] i.e. 0>[−1] i.e. (-2)
i.e. x = 0 then [x]=-1 and [0] i.e. (-1) is NOT Greater than [0] i.e. (-1)
NOT SUFFICIENT

Combining the two statements:

i.e. x = 0 then [x]=-1 i.e. x=[x]+1 and [0] i.e. (-1) is NOT Greater than [0] i.e. (-1)
i.e. x = 1 then [x]=0 i.e. x=[x]+1 and [1] i.e. 0>[−1] i.e. (-2)
NOT SUFFICIENT

Answer: Option E
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Re: If [x] denotes the largest integer smaller than x, is [x]>[−x]? [#permalink] New post  15 Jul 2015, 08:48
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Guys, I suppose it's a DS question, not PS. Maybe it should be reclassified?
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Re: If [x] denotes the largest integer smaller than x, is [x]>[−x]? [#permalink] New post  15 Jul 2015, 08:50
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sVn91 wrote:
Guys, I suppose it's a DS question, not PS. Maybe it should be reclassified?


Moved to DS forum. Thank you.
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Re: If [x] denotes the largest integer smaller than x, is [x]>[−x]? [#permalink] New post  10 Nov 2018, 12:36
GMATinsight wrote:
PathFinder007 wrote:
If [x] denotes the largest integer smaller than x, is [x]>[−x]?
(1) x=[x]+1

(2) x+1>0

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.


Question : is [x]>[−x]?

Statement 1: x=[x]+1

i.e. x = 3 then [x]=2 i.e. x=[x]+1 and [3] i.e. 2>[−3] i.e. (-4)
i.e. x = 1 then [x]=0 i.e. x=[x]+1 and [1] i.e. 0>[−1] i.e. (-2)
i.e. x = -1 then [x]=-2 i.e. x=[x]+1 and [-1] i.e. -2 is NOT Greater than [1] i.e. (0)
NOT SUFFICIENT

Statement 2: x+1>0
i.e. x > -1
i.e. x = 3 then [x]=2 and [3] i.e. 2>[−3] i.e. (-4)
i.e. x = 1 then [x]=0 and [1] i.e. 0>[−1] i.e. (-2)
i.e. x = 0 then [x]=-1 and [0] i.e. (-1) is NOT Greater than [0] i.e. (-1)
NOT SUFFICIENT

Combining the two statements:

i.e. x = 0 then [x]=-1 i.e. x=[x]+1 and [0] i.e. (-1) is NOT Greater than [0] i.e. (-1)
i.e. x = 1 then [x]=0 i.e. x=[x]+1 and [1] i.e. 0>[−1] i.e. (-2)
NOT SUFFICIENT

Answer: Option E


For-
Statement 1: x=[x]+1

i.e. x = 3 then [x]=2 i.e. x=[x]+1 and [3] i.e. 2>[−3] i.e. (-4)

What is -4 and how did you get it (its not clear). Can you please elaborate?

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Re: If [x] denotes the largest integer smaller than x, is [x]>[−x]? [#permalink] New post  10 Nov 2018, 20:18
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s111 wrote:
GMATinsight wrote:
PathFinder007 wrote:
If [x] denotes the largest integer smaller than x, is [x]>[−x]?
(1) x=[x]+1

(2) x+1>0

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.


Question : is [x]>[−x]?

Statement 1: x=[x]+1

i.e. x = 3 then [x]=2 i.e. x=[x]+1 and [3] i.e. 2>[−3] i.e. (-4)
i.e. x = 1 then [x]=0 i.e. x=[x]+1 and [1] i.e. 0>[−1] i.e. (-2)
i.e. x = -1 then [x]=-2 i.e. x=[x]+1 and [-1] i.e. -2 is NOT Greater than [1] i.e. (0)
NOT SUFFICIENT

Statement 2: x+1>0
i.e. x > -1
i.e. x = 3 then [x]=2 and [3] i.e. 2>[−3] i.e. (-4)
i.e. x = 1 then [x]=0 and [1] i.e. 0>[−1] i.e. (-2)
i.e. x = 0 then [x]=-1 and [0] i.e. (-1) is NOT Greater than [0] i.e. (-1)
NOT SUFFICIENT

Combining the two statements:

i.e. x = 0 then [x]=-1 i.e. x=[x]+1 and [0] i.e. (-1) is NOT Greater than [0] i.e. (-1)
i.e. x = 1 then [x]=0 i.e. x=[x]+1 and [1] i.e. 0>[−1] i.e. (-2)
NOT SUFFICIENT

Answer: Option E


For-
Statement 1: x=[x]+1

i.e. x = 3 then [x]=2 i.e. x=[x]+1 and [3] i.e. 2>[−3] i.e. (-4)

What is -4 and how did you get it (its not clear). Can you please elaborate?

Posted from my mobile device


s111

Using the highlighted part above we need to answer the question is [x]>[−x]?

so x = 3 then [x]=2 i.e. x=[x]+1 is done to check if the value x = 3 is acceptable as per the 1st statement or not since it's acceptable because it satisfies the first statement so now we need to know what kind of answer does this value of x gives for the primary question which is is [x]>[−x]?

Never forget the primary question in DS which in this question is is [x]>[−x]?

we find all values of x using statement to check whether there is consistency in the answers or not in order to call the statement sufficient or insufficient
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