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is [x] =0 ? (OG13)

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by alex.gellatly » Thu Aug 02, 2012 10:20 pm
If [x] denotes the least integer greater than or equal to x, is [x] =0 ?
(1) -1 < x < 1
(2) x < 0

Not really sure how to approach this one...
Thanks
A useful website I found that has every quant OG video explanation:

https://www.beatthegmat.com/useful-websi ... tml#475231
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by eagleeye » Fri Aug 03, 2012 3:27 am
alex.gellatly wrote:If [x] denotes the least integer greater than or equal to x, is [x] =0 ?
(1) -1 < x < 1
(2) x < 0

Not really sure how to approach this one...
Thanks
I read the question wrong earlier, i read it as less than or equal to. Thx vk.
Least integer greater than or equal to x means that:

If x = 2.99999, [x] = 3
If x = 2.01, [x] = 3
If x = -2.01, [x] = -2
If x = 0.01, [x] = 1
If x= 0.99, [x] =1
If x= 0, [x] = 0
If x = -0.00001, [x] = 0
If x= -0.99999, [x] = 0
We need to find if [x] = 0,
This is only possible if -1<x<=0
So, the question rephrases to Is -1<x<=0, with this in mind, let's see the options.

(1) -1 < x < 1
x can be less than 0 or greater than it, Insufficient.


(2) x < 0
clearly, x may be less than -1, Insufficient.
Together we, get
-1 <x<0. Sufficient
C is correct :)
Last edited by eagleeye on Fri Aug 03, 2012 4:24 am, edited 1 time in total.
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by vk_vinayak » Fri Aug 03, 2012 4:00 am
alex.gellatly wrote:If [x] denotes the least integer greater than or equal to x, is [x] =0 ?
(1) -1 < x < 1
(2) x < 0

Not really sure how to approach this one...
Thanks
According to definition, we need to rephrase the question Is -1 < x < 0? or x=0?

1. If x= -0.5 the [x]=0 and if x=0.5, then [x]=1. NOT SUFFICIENT.

2. x can be any -ve value. NOT .

1 and 2 combined, -1 < x < 0. SUFFICIENT. Hence answer is C.
- VK

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