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

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jfdelgado
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If "x" denotes the greatest integer less than or equal to x [#permalink] New post   21 May 2018, 10:00
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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
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B
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Re: If "x" denotes the greatest integer less than or equal to x [#permalink] New post   21 May 2018, 16:06
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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

Answer: B
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Re: If "x" denotes the greatest integer less than or equal to x [#permalink] New post   21 May 2018, 10:24
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jfdelgado 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.

Answer B.
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Re: If "x" denotes the greatest integer less than or equal to x [#permalink] New post   21 May 2018, 21:23
Expert Reply
jfdelgado wrote:
If "x" denotes the greatest integer less than or equal to x, is "x" = 0?

(1) −1 < x < 1
(2) x < 0


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Hope it helps.
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Re: If "x" denotes the greatest integer less than or equal to x [#permalink] New post   21 May 2018, 23:36
SudhanshuSingh wrote:
jfdelgado 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.

Answer B.


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

So not possible to answer

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)
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Re: If "x" denotes the greatest integer less than or equal to x [#permalink] New post   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

Answer: B
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Re: If "x" denotes the greatest integer less than or equal to x [#permalink] New post   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

B is answer

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Re: If "x" denotes the greatest integer less than or equal to x [#permalink] New post   04 Mar 2020, 13:51
jfdelgado wrote:
If "x" denotes the greatest integer less than or equal to x, is "x" = 0?

(1) −1 < x < 1
(2) x < 0

Hello Bunuel
It seems that this question is the duplication of THIS official question
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Re: If "x" denotes the greatest integer less than or equal to x [#permalink] New post   05 Mar 2020, 00:33
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Asad wrote:
jfdelgado wrote:
If "x" denotes the greatest integer less than or equal to x, is "x" = 0?

(1) −1 < x < 1
(2) x < 0

Hello Bunuel
It seems that this question is the duplication of THIS official question


Those two are different. The one from your link reads "least integer greater than or equal to x"
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Re: If "x" denotes the greatest integer less than or equal to x [#permalink] New post   05 Mar 2020, 00:39
I've checked the words "least" and "greatest" before making attention to you, but it seems that its my mistake.
Ok
Thank u...

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Re: If "x" denotes the greatest integer less than or equal to x [#permalink] New post   06 Aug 2023, 14:50
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Re: If "x" denotes the greatest integer less than or equal to x [#permalink]
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