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[y] denotes the greatest integer less than or equal to y. Is

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

[y] denotes the greatest integer less than or equal to y. Is d < 1?

(1) d = y - [y]
(2) [d]= 0

Data Sufficiency
Question: 102
Category: Algebra Operations with real numbers
Page: 160
Difficulty: 650


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SOLUTION

[y] denotes the greatest integer less than or equal to y. Is d < 1?

Some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Question: is \(d<1\)?

(1) d = y - [y] --> if y is an integer then \([y]=y\) and \(d=y-[y]=0<1\), if y is not an integer [y] is nearest integer less than y and still \(d=y-[y]<1\) (for example: \(y=1.5\) --> \(d=1.5-[1.5]=1.5-1=0.5<1\) or \(y=-1.5\) --> \(d=-1.5-[-1.5]=-1.5-(-2)=0.5<1\) ). Sufficient.

(2) [d] = 0 --> \(0\leq{d}<1\). Sufficient.

Answer: D.

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[y] denotes the greatest integer less than or equal to y. Is d < 1?

(1) d = y - [y]

if y is an integer than y-[y]=0, if y is non-integer say 4.9 then y-[y]= 4.9-4= .9 in both of these cases d is less than 1 hence sufficient
(2) [d]= 0

[d]=0 means 0<= d< 1. hence sufficient

therefor D

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Option D.
From S1:d=y-[y]
For any value of non-integral y on no. line,y-[y]=0.1,0.2,0.3,...,0.9=d<1
For eg. y=5.9;[y]=5 y-[y]=0.9=d<1
And if y=-5.9;[y]=-6 y-[y]=-5.9 -(-6);d=0.1<1
And for any integral y,y=[y] => [d=0<1].Suff.

From S2:[d]=0
means d=0,0.1,0.2,0.3,...,0.9 only.All these vales are less than 1
Sufficient.

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Re: [y] denotes the greatest integer less than or equal to y. Is [#permalink]

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New post 23 Jul 2014, 17:29
I have a question on this. [d] is not defined in the question stem, only [y] is. Now, I understand how one can infer that statement 2 is sufficient based on the definition of [y] given.

However, I would also not be surprised if the OG solution said that statement 2 is insufficient is not defined because [d] was not defined in the question stem. How should I be thinking about such cases? Thank you.

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New post 23 Jul 2014, 17:59
mattdnb wrote:
I have a question on this. [d] is not defined in the question stem, only [y] is. Now, I understand how one can infer that statement 2 is sufficient based on the definition of [y] given.

However, I would also not be surprised if the OG solution said that statement 2 is insufficient is not defined because [d] was not defined in the question stem. How should I be thinking about such cases? Thank you.


The question does not define [y], it defines function denoted as [], which rounds DOWN a number to the nearest integer.

Check other function questions in our Special Questions Directory:

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions

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Re: [y] denotes the greatest integer less than or equal to y. Is [#permalink]

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[y] denotes the greatest integer less than or equal to y. Is d < 1?

(1) d = y - [y]
(2) [d]= 0


Any number x can be written in the form of I + f
Here I is the integral part or [x], example: 1 , 2, 3 etc.
and f is the fractional part: 0.1, 0.2, 0.001 etc.

Given: [y] is the integral part of a number
Required: Is d < 1

Statement 1: d = y - [y]
We can say y = I + f
Where I = [y]
So, y -[y] means the fractional part of a number.
This would always be between 0 and 1

SUFFICIENT

Statement 2: [d]= 0
The integral part of a number is ) means number is greated than 0 and less than 1.

SUFFICIENT

Option D
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Re: [y] denotes the greatest integer less than or equal to y. Is [#permalink]

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New post 22 Oct 2015, 04:01
Bunuel wrote:
SOLUTION

[y] denotes the greatest integer less than or equal to y. Is d < 1?

Some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Question: is \(d<1\)?

(1) d = y - [y] --> if y is an integer then \([y]=y\) and \(d=y-[y]=0<1\), if y is not an integer [y] is nearest integer less than y and still \(d=y-[y]<1\) (for example: \(y=1.5\) --> \(d=1.5-[1.5]=1.5-1=0.5<1\) or \(y=-1.5\) --> \(d=-1.5-[-1.5]=-1.5-(-2)=0.5<1\) ). Sufficient.

(2) [d] = 0 --> \(0\leq{d}<1\). Sufficient.

Answer: D.

Hope it helps.


Why we are not considering Y = an integer as well? i.e. y=5,6,7 etc...

Question stem says: [y] denotes the greatest integer less than or equal to y.

If I am not wrong, the above question stem doesn't imply that Y should only take fractional forms such as: 1.5, -1.5 etc... and y is not an integer.

So I took y=5 so in 1 d = y - [y], d = 0 (5-5=0), or 1 (5-4=1) and therefore the statement is insufficient.

Where exactly I am thinking wrong. Help please.

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Re: [y] denotes the greatest integer less than or equal to y. Is [#permalink]

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New post 23 Oct 2015, 04:55
gauraku wrote:
Bunuel wrote:
SOLUTION

[y] denotes the greatest integer less than or equal to y. Is d < 1?

Some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Question: is \(d<1\)?

(1) d = y - [y] --> if y is an integer then \([y]=y\) and \(d=y-[y]=0<1\), if y is not an integer [y] is nearest integer less than y and still \(d=y-[y]<1\) (for example: \(y=1.5\) --> \(d=1.5-[1.5]=1.5-1=0.5<1\) or \(y=-1.5\) --> \(d=-1.5-[-1.5]=-1.5-(-2)=0.5<1\) ). Sufficient.

(2) [d] = 0 --> \(0\leq{d}<1\). Sufficient.

Answer: D.

Hope it helps.


Why we are not considering Y = an integer as well? i.e. y=5,6,7 etc...

Question stem says: [y] denotes the greatest integer less than or equal to y.

If I am not wrong, the above question stem doesn't imply that Y should only take fractional forms such as: 1.5, -1.5 etc... and y is not an integer.

So I took y=5 so in 1 d = y - [y], d = 0 (5-5=0), or 1 (5-4=1) and therefore the statement is insufficient.

Where exactly I am thinking wrong. Help please.


Please re-read the explanation. We are NOT considering y as fraction only.

If y = 5, then d = y - [y] = 5 - 5 = 0 < 1. HOW can it be 1?
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[y] denotes the greatest integer less than or equal to y. Is [#permalink]

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New post 23 Oct 2015, 19:53
Bunuel wrote:
gauraku wrote:
Bunuel wrote:
SOLUTION

[y] denotes the greatest integer less than or equal to y. Is d < 1?

Some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Question: is \(d<1\)?

(1) d = y - [y] --> if y is an integer then \([y]=y\) and \(d=y-[y]=0<1\), if y is not an integer [y] is nearest integer less than y and still \(d=y-[y]<1\) (for example: \(y=1.5\) --> \(d=1.5-[1.5]=1.5-1=0.5<1\) or \(y=-1.5\) --> \(d=-1.5-[-1.5]=-1.5-(-2)=0.5<1\) ). Sufficient.

(2) [d] = 0 --> \(0\leq{d}<1\). Sufficient.

Answer: D.

Hope it helps.


Why we are not considering Y = an integer as well? i.e. y=5,6,7 etc...

Question stem says: [y] denotes the greatest integer less than or equal to y.

If I am not wrong, the above question stem doesn't imply that Y should only take fractional forms such as: 1.5, -1.5 etc... and y is not an integer.

So I took y=5 so in 1 d = y - [y], d = 0 (5-5=0), or 1 (5-4=1) and therefore the statement is insufficient.

Where exactly I am thinking wrong. Help please.


Please re-read the explanation. We are NOT considering y as fraction only.

If y = 5, then d = y - [y] = 5 - 5 = 0 < 1. HOW can it be 1?


Statement says that [Y] denotes either the greatest integer less than or equal to y. So if y =5, [Y] = either 5 (equal to y) or 4 (greatest integer less than y) So d will be equal to either 5-5 =0 or 5-4=1.

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Re: [y] denotes the greatest integer less than or equal to y. Is [#permalink]

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New post 24 Oct 2015, 02:21
gauraku wrote:
Bunuel wrote:
gauraku wrote:

Why we are not considering Y = an integer as well? i.e. y=5,6,7 etc...

Question stem says: [y] denotes the greatest integer less than or equal to y.

If I am not wrong, the above question stem doesn't imply that Y should only take fractional forms such as: 1.5, -1.5 etc... and y is not an integer.

So I took y=5 so in 1 d = y - [y], d = 0 (5-5=0), or 1 (5-4=1) and therefore the statement is insufficient.

Where exactly I am thinking wrong. Help please.


Please re-read the explanation. We are NOT considering y as fraction only.

If y = 5, then d = y - [y] = 5 - 5 = 0 < 1. HOW can it be 1?


Statement says that [Y] denotes either the greatest integer less than or equal to y. So if y =5, [Y] = either 5 (equal to y) or 4 (greatest integer less than y) So d will be equal to either 5-5 =0 or 5-4=1.


You misunderstood the question. Please re-read the solutions above and follow the links provided.

[y] can take only one value, which will be the greatest integer less than or equal to y. Function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Check more questions in Rounding Functions Questions.
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New post 24 Oct 2015, 05:29
Thanks a lot for the explanation. I got it now and made a note of it.

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Re: [y] denotes the greatest integer less than or equal to y. Is [#permalink]

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New post 08 Feb 2016, 18:14
Bunuel wrote:

[y] can take only one value, which will be the greatest integer less than or equal to y. Function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Check more questions in Rounding Functions Questions.


I shared a similar confusion as Garauku; it saying "greatest integer less than or equal to" seemed to me it was saying any integer <= y, which could be as garauku suggested y = 5 [y] = 5, 4, etc. How would it have been phrased if this was the intended meaning rather than that the function rounds down?
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[y] denotes the greatest integer less than or equal to y. Is [#permalink]

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New post 08 Feb 2016, 18:20
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Bunuel wrote:

[y] can take only one value, which will be the greatest integer less than or equal to y. Function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Check more questions in Rounding Functions Questions.


I shared a similar confusion as Garauku; it saying "greatest integer less than or equal to" seemed to me it was saying any integer <= y, which could be as garauku suggested y = 5 [y] = 5, 4, etc. How would it have been phrased if this was the intended meaning rather than that the function rounds down?


Couple of points:

1. This is an official question, so do not question the OA or the language, it will only be a waste of time and energy.

2. The question as such is completely clear. If y=5, then [y] can only be = 5 and NOT 4 as you need the GREATEST integer less or equal to y. What this means is that you must take the greatest integer of <y or =y to be that particular integer. There is no ambiguity here.

For y=1.5, [y] = 1, for y=4.1, [y]=4 etc.

Hope this helps.

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Re: [y] denotes the greatest integer less than or equal to y. Is [#permalink]

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New post 13 Feb 2017, 07:27
Is it wrong to assume a non-fraction as the value of y, say y=5 & [y] will be 4 ?

Pls clarify as the answer choice will change in this case...

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Re: [y] denotes the greatest integer less than or equal to y. Is [#permalink]

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New post 13 Feb 2017, 07:39
vikasx wrote:
Is it wrong to assume a non-fraction as the value of y, say y=5 & [y] will be 4 ?

Pls clarify as the answer choice will change in this case...


Actually this is clarified several times above.

Function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

[y] denotes the greatest integer less than or equal to y. Thus if y = 5, then [5] = 5, because 5 is the greatest integer less than or equal to 5.
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Kudos [?]: 7 [0], given: 13

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Re: [y] denotes the greatest integer less than or equal to y. Is [#permalink]

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New post 07 Nov 2017, 00:38
how can we consider numbers while doing this problem??

Kudos [?]: 7 [0], given: 13

Re: [y] denotes the greatest integer less than or equal to y. Is   [#permalink] 07 Nov 2017, 00:38
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[y] denotes the greatest integer less than or equal to y. Is

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