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# M19-36

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Math Expert
Joined: 02 Sep 2009
Posts: 44588

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16 Sep 2014, 01:07
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Difficulty:

95% (hard)

Question Stats:

34% (01:35) correct 66% (01:42) wrong based on 191 sessions

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If $$[x]$$ denotes the largest integer smaller than $$x$$, is $$[x] \gt [-x]$$?

(1) $$x = [x] + 1$$

(2) $$x + 1 \gt 0$$
[Reveal] Spoiler: OA

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Joined: 02 Sep 2009
Posts: 44588

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16 Sep 2014, 01:07
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Official Solution:

Statement (1) by itself is insufficient. S1 only tells that $$x$$ is an integer.

Statement (2) by itself is insufficient.

Statements (1) and (2) combined are insufficient. Adding S2 to S1 will give that $$x$$ is an integer bigger than -1. However, if $$x$$ is 0, the answer is "no" ($$[0] = [0]$$); if $$x$$ is positive, the answer is "yes".

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Joined: 11 Nov 2014
Posts: 3
GPA: 3.3
WE: Information Technology (Computer Software)

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14 Mar 2015, 05:08
Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. S1 only tells that $$x$$ is an integer.

Statement (2) by itself is insufficient.

Statements (1) and (2) combined are insufficient. Adding S2 to S1 will give that $$x$$ is an integer bigger than -1. However, if $$x$$ is 0, the answer is "no" ($$[0] = [0]$$); if $$x$$ is positive, the answer is "yes".

Hi Bunuel,

I think 1st statement is wrong, How can x= [x]+1 ?
because x = [x] + {x}, Where {x} is fractional part, which is always less than 1.
so x = [x] +1 can't be true in any circumstances.
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Joined: 02 Sep 2009
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14 Mar 2015, 06:38
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Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. S1 only tells that $$x$$ is an integer.

Statement (2) by itself is insufficient.

Statements (1) and (2) combined are insufficient. Adding S2 to S1 will give that $$x$$ is an integer bigger than -1. However, if $$x$$ is 0, the answer is "no" ($$[0] = [0]$$); if $$x$$ is positive, the answer is "yes".

Hi Bunuel,

I think 1st statement is wrong, How can x= [x]+1 ?
because x = [x] + {x}, Where {x} is fractional part, which is always less than 1.
so x = [x] +1 can't be true in any circumstances.

x = [x] + 1 is true for all integers. For example, if x = 3, then [3] = 2 (the largest integer smaller than 3), so 3 = 2 + 1.
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14 Mar 2015, 06:43
Bunuel wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. S1 only tells that $$x$$ is an integer.

Statement (2) by itself is insufficient.

Statements (1) and (2) combined are insufficient. Adding S2 to S1 will give that $$x$$ is an integer bigger than -1. However, if $$x$$ is 0, the answer is "no" ($$[0] = [0]$$); if $$x$$ is positive, the answer is "yes".

Hi Bunuel,

I think 1st statement is wrong, How can x= [x]+1 ?
because x = [x] + {x}, Where {x} is fractional part, which is always less than 1.
so x = [x] +1 can't be true in any circumstances.

x = [x] + 1 is true for all integers. For example, if x = 3, then [3] = 2 (the largest integer smaller than 3), so 3 = 2 + 1.

It's "smaller than" , I took it for greatest integer function.
You removed "equal to".
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Joined: 07 Dec 2014
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01 Nov 2015, 00:42
Hi Bunuel,

I have only one doubt.. when we combined two statements.. (1) & (2)..

We understood that "x is an integer" and "x>-1"

So my Q is when x = 0 then [x] = -1; [-x] = 1; Hence [x]<[-x] and for all other cases [x]>[-x]..

Hence insufficient to draw a conclusion, so option E is correct.

But as per you when x is 0 ([0] = [0]).. it is not as per the context of question which says (largest integer smaller than x)

Am I right? let me know.. thanks
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01 Nov 2015, 02:27
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arunmandapaka wrote:
Hi Bunuel,

I have only one doubt.. when we combined two statements.. (1) & (2)..

We understood that "x is an integer" and "x>-1"

So my Q is when x = 0 then [x] = -1; [-x] = 1; Hence [x]<[-x] and for all other cases [x]>[-x]..

Hence insufficient to draw a conclusion, so option E is correct.

But as per you when x is 0 ([0] = [0]).. it is not as per the context of question which says (largest integer smaller than x)

Am I right? let me know.. thanks

If x = 0, then [0] = -1. Since -0 = 0, then [-0] = -1 too.
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04 Jun 2016, 00:35
can the question stem be further solved into asking if "x >2?"

if [x] > [-x], (x-1) > -(x-1), x > 2?
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Joined: 04 May 2014
Posts: 3
GMAT 1: 720 Q50 V37

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20 Aug 2017, 19:19
Hi Bunuel,

With all due respect, I want to point out that there is something wrong with the question and the explanation you have provided to one of the fellow students.

The GIF value of an integer I is the integer I itself and not I-1, something that you have stated and the explanation implies.
It can be understood by the definition and graph plot of the GIF function.
[x] : the greatest integer less than or equal to x. Equal when I is an integer of course.
[6.4]=6
[6]=6
[-6.4]=-7
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21 Aug 2017, 03:34
siddharthasthana2212 wrote:
Hi Bunuel,

With all due respect, I want to point out that there is something wrong with the question and the explanation you have provided to one of the fellow students.

The GIF value of an integer I is the integer I itself and not I-1, something that you have stated and the explanation implies.
It can be understood by the definition and graph plot of the GIF function.
[x] : the greatest integer less than or equal to x. Equal when I is an integer of course.
[6.4]=6
[6]=6
[-6.4]=-7

Not sure I understand what you mean but the function is defined as "the largest integer smaller than..." not "smaller than or equal to...". There are many other functions, this one is as it is.

So, for example, [6.4]=6 and [-6.4]=-7 but [6]=5, not 6 because the largest integer smaller than 6 is 5.
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21 Aug 2017, 04:58
Hi Bunuel,

This is exactly what I want to point out. The GIF is indeed "the greatest integer less than or EQUAL to x."
[6]=6 and not 5.
I am unable to copy the link for some reason, but you can check the definition and graph of the function anywhere.
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21 Aug 2017, 05:04
siddharthasthana2212 wrote:
Hi Bunuel,

This is exactly what I want to point out. The GIF is indeed "the greatest integer less than or EQUAL to x."
[6]=6 and not 5.
I am unable to copy the link for some reason, but you can check the definition and graph of the function anywhere.

It's not that function. It's a different function using same concept and notation.
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Joined: 25 Sep 2017
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25 Sep 2017, 05:45
X +1 > 0
-X
CROSS MULTIPLY
= - X × 0 > X + 1
= 0 > × + 1
Manager
Joined: 04 Jul 2017
Posts: 60
Location: India
Concentration: Marketing, General Management
GPA: 1
WE: Analyst (Consulting)

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30 Sep 2017, 02:17
Bunuel wrote:
If $$[x]$$ denotes the largest integer smaller than $$x$$, is $$[x] \gt [-x]$$?

(1) $$x = [x] + 1$$

(2) $$x + 1 \gt 0$$

This question is part of which topic?
Math Expert
Joined: 02 Sep 2009
Posts: 44588

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30 Sep 2017, 05:06
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aashishagarwal2 wrote:
Bunuel wrote:
If $$[x]$$ denotes the largest integer smaller than $$x$$, is $$[x] \gt [-x]$$?

(1) $$x = [x] + 1$$

(2) $$x + 1 \gt 0$$

This question is part of which topic?

This is a rounding functions question.

Check other Rounding Functions Questions in our Special Questions Directory.
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01 Oct 2017, 09:48
Bunuel wrote:
aashishagarwal2 wrote:
Bunuel wrote:
If $$[x]$$ denotes the largest integer smaller than $$x$$, is $$[x] \gt [-x]$$?

(1) $$x = [x] + 1$$

(2) $$x + 1 \gt 0$$

This question is part of which topic?

This is a rounding functions question.

Check other Rounding Functions Questions in our Special Questions Directory.

What these types "[x]" mean? Whenever such variables inside square brackets appear, I become clueless on to handle them or what they mean.
Math Expert
Joined: 02 Sep 2009
Posts: 44588

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01 Oct 2017, 10:09
aashishagarwal2 wrote:

What these types "[x]" mean? Whenever such variables inside square brackets appear, I become clueless on to handle them or what they mean.

I think practising the questions from that link should help.
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01 Oct 2017, 10:24
Bunuel wrote:
aashishagarwal2 wrote:

What these types "[x]" mean? Whenever such variables inside square brackets appear, I become clueless on to handle them or what they mean.

I think practising the questions from that link should help.

Thanks Bunuel.
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Joined: 26 Mar 2013
Posts: 1612

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02 Oct 2017, 00:41
Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. S1 only tells that $$x$$ is an integer.

Statement (2) by itself is insufficient.

Statements (1) and (2) combined are insufficient. Adding S2 to S1 will give that $$x$$ is an integer bigger than -1. However, if $$x$$ is 0, the answer is "no" ($$[0] = [0]$$); if $$x$$ is positive, the answer is "yes".

Can you elaborate the highlighted part pls? it is not clear enough.
Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 44588

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02 Oct 2017, 00:45
Mo2men wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. S1 only tells that $$x$$ is an integer.

Statement (2) by itself is insufficient.

Statements (1) and (2) combined are insufficient. Adding S2 to S1 will give that $$x$$ is an integer bigger than -1. However, if $$x$$ is 0, the answer is "no" ($$[0] = [0]$$); if $$x$$ is positive, the answer is "yes".

Can you elaborate the highlighted part pls? it is not clear enough.
Thanks

Check here: https://gmatclub.com/forum/if-denotes-t ... 01744.html
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# M19-36

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