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If [z] denotes the greatest integer less than or equal to z and [z] =

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If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post Updated on: 06 Nov 2017, 20:51
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If [z] denotes the greatest integer less than or equal to z and [z] = -1 which of the following statements must be true?

A. z = -1
B. -2 <= z < -1
C. -2 < z <= -1
D. -1 <= z < 0
E. -1 < z <= 0


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Originally posted by sguptashared on 23 Oct 2013, 19:50.
Last edited by Bunuel on 06 Nov 2017, 20:51, edited 3 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 24 Oct 2013, 00:03
9
15
sguptashared wrote:
If [z] denotes the greatest integer less than or equal to z and [z] = -1 which of the following statements must be true?

A. z = -1
B. -2 <= z < -1
C. -2 < z <= -1
D. -1 <= z < 0
E. -1 < z <= 0


[z] is the greatest integer less than or equal to z means that some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Now, since [z] = -1, then \(-1\leq{z}<0\) --> ANY number from this range when rounded down to the nearest integer is -1.

Answer: D.

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Hope it helps.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you,
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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 14 Sep 2014, 12:31
Bunuel wrote:
sguptashared wrote:
If [z] denotes the greatest integer less than or equal to z and [z] = -1 which of the following statements must be true?

A. z = -1
B. -2 <= z < -1
C. -2 < z <= -1
D. -1 <= z < 0
E. -1 < z <= 0


[z] is the greatest integer less than or equal to z means that some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Now, since [z] = -1, then \(-1\leq{z}<0\) --> ANY number from this range when rounded down to the nearest integer is -1.

Answer: D.

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Hope it helps.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you,


If question asks " [z] denotes the greatest integer less than or equal to z and [z] = 0", then can we say 0<=Z<1 ?

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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 14 Sep 2014, 17:06
1
ammuseeru wrote:
Bunuel wrote:
sguptashared wrote:
If [z] denotes the greatest integer less than or equal to z and [z] = -1 which of the following statements must be true?

A. z = -1
B. -2 <= z < -1
C. -2 < z <= -1
D. -1 <= z < 0
E. -1 < z <= 0


[z] is the greatest integer less than or equal to z means that some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Now, since [z] = -1, then \(-1\leq{z}<0\) --> ANY number from this range when rounded down to the nearest integer is -1.

Answer: D.

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Hope it helps.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you,


If question asks " [z] denotes the greatest integer less than or equal to z and [z] = 0", then can we say 0<=Z<1 ?

Regards,
Ammu


Yes. [z] = 0, would mean that \(0\leq{z}<1\) --> ANY number from this range when rounded down to the nearest integer is 0.

Check other Rounding Functions Questions in our Special Questions Directory.

Hope it helps.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 08 Oct 2014, 17:44
Bunuel wrote:
sguptashared wrote:
If [z] denotes the greatest integer less than or equal to z and [z] = -1 which of the following statements must be true?

A. z = -1
B. -2 <= z < -1
C. -2 < z <= -1
D. -1 <= z < 0
E. -1 < z <= 0


[z] is the greatest integer less than or equal to z means that some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Now, since [z] = -1, then \(-1\leq{z}<0\) --> ANY number from this range when rounded down to the nearest integer is -1.

Answer: D.

Similar questions to practice:
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denotes-to-be-the-least-integer-no-less-than-x-is-130841.html
is-the-greatest-integer-less-than-or-equal-to-the-real-n-154006.html

Hope it helps.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you,


Hi Bunuel,

Just a question. Why do you think it could not be A?
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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 09 Oct 2014, 00:51
1
gbascurs wrote:
Bunuel wrote:
sguptashared wrote:
If [z] denotes the greatest integer less than or equal to z and [z] = -1 which of the following statements must be true?

A. z = -1
B. -2 <= z < -1
C. -2 < z <= -1
D. -1 <= z < 0
E. -1 < z <= 0


[z] is the greatest integer less than or equal to z means that some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Now, since [z] = -1, then \(-1\leq{z}<0\) --> ANY number from this range when rounded down to the nearest integer is -1.

Answer: D.

Similar questions to practice:
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Hope it helps.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you,


Hi Bunuel,

Just a question. Why do you think it could not be A?


Because z is not necessarily -1, it could be any number from -1 to 0 (\(-1\leq{z}<0\) ), for example, -1/2.

Check other Rounding Functions Questions in our Special Questions Directory.

Hope it helps.
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Collection of Questions:
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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 09 Oct 2014, 04:21
But the question states that it is an integer... What do I missing?
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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 09 Oct 2014, 04:43
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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 09 Oct 2014, 05:53
Bunuel wrote:
gbascurs wrote:
But the question states that it is an integer... What do I missing?


The questions says that [z] is an integer, not z.

Please re-read the question and solution and follow the links to the similar problems to understand better.



Thanks for your reply, I get it.
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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 30 Oct 2014, 22:55
Dear Bunuel,

Although I completely agree that the answer is indeed option D here, however option A is not wrong also. If we plug in the value given in option A, we indeed satisfy the condition given.
Does the inclusion of option A not make choosing the correct answer slightly ambiguous. I mean why give an option such as A at all in the exam.
What trick am I missing here?

Thanks in advance,

Madhav
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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 31 Oct 2014, 04:05
madhavmarda wrote:
Dear Bunuel,

Although I completely agree that the answer is indeed option D here, however option A is not wrong also. If we plug in the value given in option A, we indeed satisfy the condition given.
Does the inclusion of option A not make choosing the correct answer slightly ambiguous. I mean why give an option such as A at all in the exam.
What trick am I missing here?

Thanks in advance,

Madhav


The question asks which of the following statements MUST be true, not could be true. z could be -1, but it could also be, for example, -1/2. Thus A is not a statement which must be true.

Check other Rounding Functions Questions in our Special Questions Directory.

Hope it helps.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 31 Jul 2015, 13:21
Bunuel wrote:
madhavmarda wrote:
Dear Bunuel,

Although I completely agree that the answer is indeed option D here, however option A is not wrong also. If we plug in the value given in option A, we indeed satisfy the condition given.
Does the inclusion of option A not make choosing the correct answer slightly ambiguous. I mean why give an option such as A at all in the exam.
What trick am I missing here?

Thanks in advance,

Madhav


The question asks which of the following statements MUST be true, not could be true. z could be -1, but it could also be, for example, -1/2. Thus A is not a statement which must be true.

Check other Rounding Functions Questions in our Special Questions Directory.

Hope it helps.


I really cannot understand why A cannot be the answer.

Z=-1

[Z] = -1

Condition satisfies.

I have read the theory and solved all the questions in the link, I don't know what am I missing
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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 31 Jul 2015, 13:39
1
anewbeginning wrote:
Bunuel wrote:
madhavmarda wrote:
Dear Bunuel,

Although I completely agree that the answer is indeed option D here, however option A is not wrong also. If we plug in the value given in option A, we indeed satisfy the condition given.
Does the inclusion of option A not make choosing the correct answer slightly ambiguous. I mean why give an option such as A at all in the exam.
What trick am I missing here?

Thanks in advance,

Madhav


The question asks which of the following statements MUST be true, not could be true. z could be -1, but it could also be, for example, -1/2. Thus A is not a statement which must be true.

Check other Rounding Functions Questions in our Special Questions Directory.

Hope it helps.


I really cannot understand why A cannot be the answer.

Z=-1

[Z] = -1

Condition satisfies.

I have read the theory and solved all the questions in the link, I don't know what am I missing


The question is a MUST BE TRUE for ALL values. Not a could be true. Had this question been a 'could be true" question, then you would have stopped at option A itself and moved to the next question.

But as this is a MUST BE TRUE question, you need to make sure that [z] =-1 is ONLY satisfied by z =-1 from the given options (and not by any other option). The correct answer to a MUST BE TRUE question, will nullify all other options. This is a very important point to remember. We are not denying that z = -1 is not true but what we are mentioning is that is it the ONLY possible choice ? Not necessarily z = -0.5 also satisfies the given condition.

So if z = -0.5 also satisfies the given condition, then option D is true as well (along with option A, per your statement). A question can not have 2 correct answers.

As I said before, in a MUST BE TRUE question,

1. Get the option(s) that satisfy a given condition
2. Eliminate all but 1 options. The remaining option will be the correct answer. There will always be concrete reasons to eliminate other options. If you are not able to eliminate options, then you are missing some important information.

Unless you take care of both the options, you can not be sure of your answer.

For this question, I adopted the following method:

1. Used z =-0.5 to eliminate options A-C
2. Used z = 0 to eliminate option E. If z =0 then [z] = 0 and \(\neq\) -1

The only option remaining after the 2 steps above was D and is the correct answer.
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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post Updated on: 21 Aug 2016, 15:05
Engr2012 wrote:
Dear Bunuel,

The question is a MUST BE TRUE for ALL values. Not a could be true. Had this question been a 'could be true" question, then you would have stopped at option A itself and moved to the next question.

But as this is a MUST BE TRUE question, you need to make sure that [z] =-1 is ONLY satisfied by z =-1 from the given options (and not by any other option). The correct answer to a MUST BE TRUE question, will nullify all other options. This is a very important point to remember. We are not denying that z = -1 is not true but what we are mentioning is that is it the ONLY possible choice ? Not necessarily z = -0.5 also satisfies the given condition. - This helped

So if z = -0.5 also satisfies the given condition, then option D is true as well (along with option A, per your statement). A question can not have 2 correct answers.

As I said before, in a MUST BE TRUE question,

1. Get the option(s) that satisfy a given condition
2. Eliminate all but 1 options. The remaining option will be the correct answer. There will always be concrete reasons to eliminate other options. If you are not able to eliminate options, then you are missing some important information.

Unless you take care of both the options, you can not be sure of your answer.

For this question, I adopted the following method:

1. Used z =-0.5 to eliminate options A-C
2. Used z = 0 to eliminate option E. If z =0 then [z] = 0 and \(\neq\) -1

The only option remaining after the 2 steps above was D and is the correct answer.


Great explanation. I am fully satisfied with the explanation. Thanks a lot :)

Originally posted by keats on 01 Aug 2015, 06:49.
Last edited by keats on 21 Aug 2016, 15:05, edited 2 times in total.
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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 01 Aug 2015, 06:54
anewbeginning wrote:
Engr2012 wrote:
Dear Bunuel,

The question is a MUST BE TRUE for ALL values. Not a could be true. Had this question been a 'could be true" question, then you would have stopped at option A itself and moved to the next question.

But as this is a MUST BE TRUE question, you need to make sure that [z] =-1 is ONLY satisfied by z =-1 from the given options (and not by any other option). The correct answer to a MUST BE TRUE question, will nullify all other options. This is a very important point to remember. We are not denying that z = -1 is not true but what we are mentioning is that is it the ONLY possible choice ? Not necessarily z = -0.5 also satisfies the given condition. - This helped

So if z = -0.5 also satisfies the given condition, then option D is true as well (along with option A, per your statement). A question can not have 2 correct answers.

As I said before, in a MUST BE TRUE question,

1. Get the option(s) that satisfy a given condition
2. Eliminate all but 1 options. The remaining option will be the correct answer. There will always be concrete reasons to eliminate other options. If you are not able to eliminate options, then you are missing some important information.

Unless you take care of both the options, you can not be sure of your answer.

For this question, I adopted the following method:

1. Used z =-0.5 to eliminate options A-C
2. Used z = 0 to eliminate option E. If z =0 then [z] = 0 and \(\neq\) -1

The only option remaining after the 2 steps above was D and is the correct answer.
[/quote]

Awesome explanation.

I am not satisfied with the explanation. Thanks a lot :-D

A lot of Kudos to you[/quote]

So are you or are you not satisfied with the explanation?
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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 01 Aug 2015, 13:31
I'm sorry that was a TYPO Engr2012

I apologise for the same

Cheers
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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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New post 06 Dec 2016, 18:52
Bunuel wrote:
sguptashared wrote:
If [z] denotes the greatest integer less than or equal to z and [z] = -1 which of the following statements must be true?

A. z = -1
B. -2 <= z < -1
C. -2 < z <= -1
D. -1 <= z < 0
E. -1 < z <= 0


[z] is the greatest integer less than or equal to z means that some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Now, since [z] = -1, then \(-1\leq{z}<0\) --> ANY number from this range when rounded down to the nearest integer is -1.

Answer: D.

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P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you,


Thank you for the links.
It helps as always!!
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Re: If [z] denotes the greatest integer less than or equal to z and [z] =  [#permalink]

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