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

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

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

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New post 21 May 2018, 10:24
1
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]

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New post 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

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

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New post 21 May 2018, 21:23
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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Re: If "x" denotes the greatest integer less than or equal to x  [#permalink]

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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]

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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]

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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 &nbs [#permalink] 22 May 2018, 09:00
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