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# If "x" denotes the greatest integer less than or equal to x

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Intern
Joined: 16 May 2018
Posts: 17
If "x" denotes the greatest integer less than or equal to x  [#permalink]

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21 May 2018, 10:00
6
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Difficulty:

65% (hard)

Question Stats:

35% (01:08) correct 65% (01:13) wrong based on 63 sessions

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

(1) −1 < x < 1
(2) x < 0
Manager
Joined: 01 Aug 2017
Posts: 192
Location: India
Schools: ISB '20 (S), IIMA (S)
GMAT 1: 500 Q47 V15
GPA: 3.4
WE: Information Technology (Computer Software)
Re: If "x" denotes the greatest integer less than or equal to x  [#permalink]

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21 May 2018, 10:24
1
If "x" denotes the greatest integer less than or equal to x, is "x"=0?
(1)−1<x<1
(2)x<0

Statement 1 :-

-1<x<1

Let x be 0.5. "0.5" is greatest integer less than or equal to 0.5. . This implies "x" = 1. Ans - No

Let x be -0.5 . "-0.5" is greatest integer less than or equal to -0.5. This implies "x" = 0. Ans - Yes

No definite value of x. Not sufficient.

Statement 2 :-
x<0.

Let x be -2.5 . "-2.5" is greatest integer less than or equal to -2.5. This implies "x" = -2.

Let x be -1.5 . "-1.5" is greatest integer less than or equal to -1.5. This implies "x" = -1.

For all the cases x is not ZERO.
Hence Sufficient.

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Sudhanshu

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Joined: 30 Mar 2017
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Re: If "x" denotes the greatest integer less than or equal to x  [#permalink]

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21 May 2018, 16:06
1
Is "x"=0? First thing I did was write out the range of x we're trying to confirm.
"x"=0 ---> $$0<=x<1$$

Statement 1
−1<x<1
From our initial analysis, we can quickly see that answer can be YES (e.g. if x=0) or NO (e.g. if x=-0.5).
Not sufficient

Statement 2
x<0
Going back to our initial analysis, we need to find if x lies in this range [0,1). Statement 2 tells us that x is less than 0, so answer is NO.
Sufficient

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Joined: 02 Sep 2009
Posts: 49430
Re: If "x" denotes the greatest integer less than or equal to x  [#permalink]

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21 May 2018, 21:23
Intern
Joined: 12 Feb 2018
Posts: 7
Location: India
GMAT 1: 480 Q47 V12
GPA: 3.4
Re: If "x" denotes the greatest integer less than or equal to x  [#permalink]

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21 May 2018, 23:36
SudhanshuSingh wrote:
If "x" denotes the greatest integer less than or equal to x, is "x"=0?
(1)−1<x<1
(2)x<0

Statement 1 :-

-1<x<1

Let x be 0.5. "0.5" is greatest integer less than or equal to 0.5. . This implies "x" = 1. Ans - No

Let x be -0.5 . "-0.5" is greatest integer less than or equal to -0.5. This implies "x" = 0. Ans - Yes

No definite value of x. Not sufficient.

Statement 2 :-
x<0.

Let x be -2.5 . "-2.5" is greatest integer less than or equal to -2.5. This implies "x" = -2.

Let x be -1.5 . "-1.5" is greatest integer less than or equal to -1.5. This implies "x" = -1.

For all the cases x is not ZERO.
Hence Sufficient.

Greatest integer less than or equal to means if the no. Is 1.5 = 1 , -1.5 = -2

Statement 1
If x= 0.5 then greatest integer less than or equal to will be 0
If x = - 0.5 then greatest integer less than or equal to will be -1

Statement 2

If x = - 0.5 then greatest integer less than or equal to will be -1
X= -1.5 then -2 .....so on

So it is always less than 0.hence sufficient

Option (b)
Intern
Joined: 16 Aug 2015
Posts: 18
Location: India
Re: If "x" denotes the greatest integer less than or equal to x  [#permalink]

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22 May 2018, 01:30
For "x" to be 0, range of x should be [0,1)

(1) "x"can be -1 or 0 depending on the value of x
(2) "x" is not 0 since x fall out of desired range, therefore sufficient

Director
Joined: 02 Oct 2017
Posts: 616
Re: If "x" denotes the greatest integer less than or equal to x  [#permalink]

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22 May 2018, 09:00
(1) −1 < x < 1

If x lies bw -1 and zero then greatest integer less than or equal to x is -1

But if x lies bw 0 and 1 then greatest integer less than equal to x is zero

Multiple cases so Insufficient

(2) x < 0

X can take values as -1,-2,-3 etc
But not zero
So sufficient

Give kudos if it helps

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Re: If "x" denotes the greatest integer less than or equal to x &nbs [#permalink] 22 May 2018, 09:00
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