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We define that [x] is the least integer greater than of equal to x.

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We define that [x] is the least integer greater than of equal to x.  [#permalink]

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New post 03 Jul 2017, 14:10
4
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A
B
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D
E

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  45% (medium)

Question Stats:

64% (01:41) correct 36% (01:22) wrong based on 103 sessions

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We define that [x] is the least integer greater than of equal to x. [x+1]=?
1) [x] =1
2) [2x]=1
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Posts: 249
Re: We define that [x] is the least integer greater than of equal to x.  [#permalink]

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New post 03 Jul 2017, 22:41
roastedchips wrote:
We define that [x] is the least integer greater than of equal to x. [x+1]=?
1) [x] =1
2) [2x]=1


Hi,

From St(1), we have 0 < x <= 1 => least integer of x+1 = 2 Definite answer.

From St(2), we have 0 < x <= 1/2 => least integer of x+1 = 2 Definite answer.

Answer: (D).

Thanks.
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Re: We define that [x] is the least integer greater than of equal to x.  [#permalink]

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New post 04 Jul 2017, 04:13
3
roastedchips wrote:
We define that [x] is the least integer greater than of equal to x. [x+1]=?
1) [x] =1
2) [2x]=1


1) \([x] =1\)

\(x = 1\)

\([x+1]= [1 + 1] =2\)

Hence I is Sufficient.

2) \([2x]=1\)

\(2x = 1 => x = \frac{1}{2}\)

\([x]\) is the least integer greater than of equal to \(x\). Therefore \(x = 1\).

\([x+1]= [1 + 1] =2\)

Hence II is Sufficient.

Answer (D)...


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Re: We define that [x] is the least integer greater than of equal to x.  [#permalink]

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New post 04 Jul 2017, 06:12
roastedchips wrote:
We define that [x] is the least integer greater than of equal to x. [x+1]=?
1) [x] =1
2) [2x]=1


Let us analyze each statement

Statement 1:
\([x]=1\)
\(0<x<=1\)
\(1<x+1<=2\) (Adding 1 throughout the inequality)
We know that x+1 will be greater than 1 and less than/equal to 2. So the least integer greater than or equal to \(x+1\) is 2.
Hence sufficient.

Statement 2:
\([2x]=1\)
\(0<2x<=1\)
\(0<x<=0.5\) (Dividing by 2 throughout the inequality)
\(1<x+1<=1.5\) (Adding 1 throughout the inequality)
We know \(x+1\) will be greater than 1 and less than/equal to 1.5. So the least integer greater than or equal to \(x+1\) is 2
Hence sufficient

Answer D

Hit kudos if you like the explanation :)
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Re: We define that [x] is the least integer greater than of equal to x.  [#permalink]

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New post 22 Jan 2019, 09:08
@chetan2u:-what does greater than of equal to x mean?
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Re: We define that [x] is the least integer greater than of equal to x.   [#permalink] 22 Jan 2019, 09:08
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We define that [x] is the least integer greater than of equal to x.

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