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[y] denotes the greatest integer less than or equal to y. Is
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20 Feb 2014, 01:14
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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 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach 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. Thank you!
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Re: [y] denotes the greatest integer less than or equal to y. Is
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Re: [y] denotes the greatest integer less than or equal to y. Is
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20 Feb 2014, 04:00
[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 noninteger say 4.9 then y[y]= 4.94= .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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Re: [y] denotes the greatest integer less than or equal to y. Is
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20 Feb 2014, 23:58
Option D. From S1:d=y[y] For any value of nonintegral 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
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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.



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Re: [y] denotes the greatest integer less than or equal to y. Is
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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 expressionsSymbols Representing Arithmetic OperationRounding FunctionsVarious FunctionsHope it helps.
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Re: [y] denotes the greatest integer less than or equal to y. Is
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01 Oct 2015, 05:41
Quote: [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 SUFFICIENTStatement 2: [d]= 0 The integral part of a number is ) means number is greated than 0 and less than 1. SUFFICIENTOption D



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Re: [y] denotes the greatest integer less than or equal to y. Is
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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: \(y=1.5\) > \(d=1.5[1.5]=1.51=0.5<1\) 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 (55=0), or 1 (54=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
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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: \(y=1.5\) > \(d=1.5[1.5]=1.51=0.5<1\) 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 (55=0), or 1 (54=1) and therefore the statement is insufficient. Where exactly I am thinking wrong. Help please. Please reread 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
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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: \(y=1.5\) > \(d=1.5[1.5]=1.51=0.5<1\) 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 (55=0), or 1 (54=1) and therefore the statement is insufficient. Where exactly I am thinking wrong. Help please. Please reread 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 55 =0 or 54=1.



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Re: [y] denotes the greatest integer less than or equal to y. Is
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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 (55=0), or 1 (54=1) and therefore the statement is insufficient.
Where exactly I am thinking wrong. Help please.
Please reread 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 55 =0 or 54=1. You misunderstood the question. Please reread 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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Re: [y] denotes the greatest integer less than or equal to y. Is
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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
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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, ... 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
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08 Feb 2016, 18:20
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, ... 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
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13 Feb 2017, 07:27
Is it wrong to assume a nonfraction 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
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13 Feb 2017, 07:39
vikasx wrote: Is it wrong to assume a nonfraction 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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Re: [y] denotes the greatest integer less than or equal to y. Is
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07 Nov 2017, 00:38
how can we consider numbers while doing this problem??



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Re: [y] denotes the greatest integer less than or equal to y. Is
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07 Dec 2017, 01:54
i think what is confusing most is this point.
Question states. [y] is the greatest integer less than or equal to Y. Most are also assuming that Y has to be an integer, that stipulation is only for [y]. Only [y] has to be an integer, on other hand Y can be any non integer value.
Therefore if Y = 4.5 then [Y] being an integer only can be 4 at most. because if it is 5 then it will break the parameters set by the question i.e. greatest integer less than or equal to Y.
Hope it helps some folks.



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Re: [y] denotes the greatest integer less than or equal to y. Is
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19 Apr 2018, 13:34
Bunuel wrote: 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 First, let's take a moment to get a good idea of what this strange notation means. A few examples: [5.1] = 5 [3] = 3 [8.9] = 8 [1.4] = 2 [13.6] = 14 IMPORTANT FACT #1: [y] < yIMPORTANT FACT #2: The difference between y and [y] is always less than 1. In other words, y  [y] < 1Target question: Is d < 1? Statement 1: d = y  [y] Take IMPORTANT FACT #1 from above: [y] < ySubtract [y] from both sides to get: 0 < y  [y]Now take IMPORTANT FACT #2 and add it to our inequality to get: 0 < y  [y] < 1Statement 1 tells us that d = y  [y], so let's replace y  [y] with d to get: 0 < d < 1PERFECT, we can now be certain that d < 1Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: [d] = 0 We're going to use IMPORTANT FACT #2 in our solution. Take [d] = 0 and add d to both sides to get: [d] + d = d Subtract [d] from both sides to get: d = d  [d] From IMPORTANT FACT #2, we know that d  [d] < 1Since we just showed that d = d  [d], we can be certain that d < 1Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: D Cheers, Brent
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Re: [y] denotes the greatest integer less than or equal to y. Is
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12 May 2019, 17:10
[y] = y, if y is an int, and [y] rounds down to the lesser value if y is between 2 ints.
(1) d = y  [y] d = 1  [1] d = 1  1 d = 0 If [y] = y then d must be 0
d = 0.999  [0.999] d = 0.999  0 d = 0.999 If [y] rounded down from y then d cannot be equal to or more than 1, Sufficient. Testing more, we can see 1 ≠ 1  [1] and 1 ≠ 1  [1]
(2) [d] = 0 So the range is 0 ≤ d < 1 Sufficient.




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