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Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

[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.

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

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20 Feb 2014, 23:58

1

This post received KUDOS

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.

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

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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.

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.

[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.

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

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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.

[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?
_________________

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

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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.

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, ...

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

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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, ...

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?
_________________

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

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08 Feb 2016, 18:20

1

This post was BOOKMARKED

redfield wrote:

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, ...

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.

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.
_________________