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

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Intern
Joined: 18 Apr 2013
Posts: 34
We define that [x] is the least integer greater than of equal to x.  [#permalink]

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03 Jul 2017, 14:10
4
00:00

Difficulty:

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
Manager
Joined: 17 May 2015
Posts: 249
Re: We define that [x] is the least integer greater than of equal to x.  [#permalink]

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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.

Thanks.
Director
Joined: 04 Dec 2015
Posts: 740
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
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Re: We define that [x] is the least integer greater than of equal to x.  [#permalink]

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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.

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Intern
Joined: 11 Aug 2016
Posts: 47
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Re: We define that [x] is the least integer greater than of equal to x.  [#permalink]

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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

Hit kudos if you like the explanation
Manager
Joined: 11 Jun 2018
Posts: 62
Re: We define that [x] is the least integer greater than of equal to x.  [#permalink]

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22 Jan 2019, 09:08
@chetan2u:-what does greater than of equal to x mean?
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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