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For all real numbers x, [x] is defined as the smallest integer that is

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For all real numbers x, [x] is defined as the smallest integer that is [#permalink] New post   28 Mar 2024, 01:01
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­For all real numbers x, [x] is defined as the smallest integer that is greater than 2x. Is [2x] = 0 ?

(1) [x] = 0
(2) [3x] = 0­
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Bunuel
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Re: For all real numbers x, [x] is defined as the smallest integer that is [#permalink] New post   28 Mar 2024, 01:17
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ruis wrote:
­For all real numbers x, [x] is defined as the smallest integer that is greater than 2x. Is [2x] = 0 ?

(1) [x] = 0
(2) [3x] = 0­

­
Here is a very similar question:

https://gmatclub.com/forum/denotes-to-b ... l#p3206723

Can you please tell the source of the question? Thank you!
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Re: For all real numbers x, [x] is defined as the smallest integer that is [#permalink] New post   28 Mar 2024, 01:28
Bunuel wrote:
ruis wrote:
­For all real numbers x, [x] is defined as the smallest integer that is greater than 2x. Is [2x] = 0 ?

(1) [x] = 0
(2) [3x] = 0­

­
Here is a very similar question:

https://gmatclub.com/forum/denotes-to-b ... l#p3206723

Can you please tell the source of the question? Thank you!

­Thank you Bunuel! Apologies I do not know the souce of the question. My cousin gave me a pile of printed exercises to practice with and it does not state the source :( I believe it comes from a teacher he had 5 years ago when preparing the GMAT
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Re: For all real numbers x, [x] is defined as the smallest integer that is [#permalink] New post   28 Mar 2024, 01:48
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ruis wrote:
Bunuel wrote:
ruis wrote:
­For all real numbers x, [x] is defined as the smallest integer that is greater than 2x. Is [2x] = 0 ?

(1) [x] = 0
(2) [3x] = 0­

­
Here is a very similar question:

https://gmatclub.com/forum/denotes-to-b ... l#p3206723

Can you please tell the source of the question? Thank you!

­Thank you Bunuel! Apologies I do not know the souce of the question. My cousin gave me a pile of printed exercises to practice with and it does not state the source :( I believe it comes from a teacher he had 5 years ago when preparing the GMAT

­
Wow, what a long and winding road for finding practice questions! 😄 Why not take a shortcut with us? Our question bank offers high-quality questions without the headache.­
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Re: For all real numbers x, [x] is defined as the smallest integer that is [#permalink] New post   28 Mar 2024, 01:55
­Will do! I have signed to Gmat Club Quizzes and could not be happier! I am a huge fan of the tool. It is super useful to be able to filter what type of questions to practice with knowing they are quality questions. Then, every once in a while I try some printed paper QQs as I like to take a break from the screen ­
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For all real numbers x, [x] is defined as the smallest integer that is [#permalink] New post   Updated on: 02 Apr 2024, 02:48
 
ruis wrote:
­For all real numbers x, [x] is defined as the smallest integer that is greater than 2x. Is [2x] = 0 ?

(1) [x] = 0
(2) [3x] = 0­

­\(2x\) will equal zero if \(-1<4x<0\) or  \(-\frac{1}{4}<x<0\)

(1) [x] = 0

 Implies   \(-1<x<0\) 

INSUFF.

(2) [3x] = 0­

Hence   \(-1< 6x<0\) 

\(-\frac{1}{6}<x<0\)

Hence our required condition is satisfied.  

SUFF.

Ans B

Hope it helped 
 ­

Originally posted by stne on 31 Mar 2024, 13:13.
Last edited by stne on 02 Apr 2024, 02:48, edited 1 time in total.
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Re: For all real numbers x, [x] is defined as the smallest integer that is [#permalink] New post   31 Mar 2024, 13:50
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stne wrote:
ruis wrote:
­For all real numbers x, [x] is defined as the smallest integer that is greater than 2x. Is [2x] = 0 ?

(1) [x] = 0
(2) [3x] = 0­

­\(2x\) will equal zero if \(-1<4x<0\) or  \(-\frac{1}{4}<x<0\)

(1) [x] = 0

 Implies   \(-1<x<0\) 

INSUFF.

(2) [3x] = 0­

Hence   \(-\frac{1}{3} < x<0\) 

Hence our required condition may or may not be true 

INSUFF.

1+2

INSUFF.

Ans E

However since the OA is given as B, I assume there is a small typo and question should read:

For all real numbers x, [x] is defined as the smallest integer that is greater than x. Is [2x] = 0 ?

In that case B would be SUFF. 

ruis  can you please check. Thank you
 ­

­For all real numbers x, [x] is defined as the smallest integer that is greater than 2x. Is [2x] = 0 ?

For [2x] = 0 to hold true, -1 ≤ 4x < 0 must be true. Hence, the question asks whther -1/4 ≤ x < 0.

(1) [x] = 0

The above implies -1 ≤ 2x < 0, which gives -1/2 ≤ x < 0. Not sufficient.

(2) [3x] = 0­

The above implies -1 ≤ 6x < 0, which gives -1/6 ≤ x < 0. Sufficient.

Answer: B.­
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Re: For all real numbers x, [x] is defined as the smallest integer that is [#permalink] New post   02 Apr 2024, 02:45
Bunuel wrote:
stne wrote:
ruis wrote:
­For all real numbers x, [x] is defined as the smallest integer that is greater than 2x. Is [2x] = 0 ?

(1) [x] = 0
(2) [3x] = 0­

­\(2x\) will equal zero if \(-1<4x<0\) or  \(-\frac{1}{4}<x<0\)

(1) [x] = 0

 Implies   \(-1<x<0\) 

INSUFF.

(2) [3x] = 0­

Hence   \(-\frac{1}{3} < x<0\) 

Hence our required condition may or may not be true 

INSUFF.

1+2

INSUFF.

Ans E

However since the OA is given as B, I assume there is a small typo and question should read:

For all real numbers x, [x] is defined as the smallest integer that is greater than x. Is [2x] = 0 ?

In that case B would be SUFF. 

ruis  can you please check. Thank you
 ­

­For all real numbers x, [x] is defined as the smallest integer that is greater than 2x. Is [2x] = 0 ?

For [2x] = 0 to hold true, -1 ≤ 4x < 0 must be true. Hence, the question asks whther -1/4 ≤ x < 0.

(1) [x] = 0

The above implies -1 ≤ 2x < 0, which gives -1/2 ≤ x < 0. Not sufficient.

(2) [3x] = 0­

The above implies -1 ≤ 6x < 0, which gives -1/6 ≤ x < 0. Sufficient.

Answer: B.­
 

­Correct. Erred in statement 2. Thanks.
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Re: For all real numbers x, [x] is defined as the smallest integer that is [#permalink]
02 Apr 2024, 02:45
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