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Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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08 Nov 2015, 09:35
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Jamboree and GMAT Club Contest Starts QUESTION #6:[N] denotes the greatest integer less than or equal to N. is [5N] = 0? (1) [4N] = 0 (2) [6N] = 0 Check conditions below: For the following two weekends we'll be publishing 4 FRESH math questions and 4 FRESH verbal questions per weekend. To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific. Then a week later, respective forum moderators will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6months access to GMAT Club Tests. PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize. He/She can opt for one of the following as a Grand Prize. It will be a choice for the winner:  GMAT Online Comprehensive ( If the student wants an online GMAT preparation course)  GMAT Classroom Program ( Only if he/she has a Jamboree center nearby and is willing to join the classroom program) Bookmark this post to come back to this discussion for the question links  there will be 2 on Saturday and 2 on Sunday! There is only one Grand prize and student can choose out of the above mentioned too options as per the conditions mentioned in blue font.All announcements and winnings are final and no whining GMAT Club reserves the rights to modify the terms of this offer at any time. NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.
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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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14 Nov 2015, 06:25
[N] denotes the greatest integer less than or equal to N. is [5N] = 0? (1) [4N] = 0 (2) [6N] = 0 S1: [4N] = 0 => 4N can range from 0 to 0.9 inclusive. => N can range from 0 to \(\frac{0.9}{4}\) inclusive. => 5N can range from 0 to \(\frac{5*0.9}{4}=1.125\) => [5N] = 0 or 1Therefore InsufficientS2: [6N] = 0 => 6N can range from 0 to 0.9 inclusive. => N can range from 0 to \(\frac{0.9}{6}\) inclusive. => 5N can range from 0 to \(\frac{5*0.9}{6}=0.15\) => [5N] = 0 Therefore, SufficientHence B
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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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08 Nov 2015, 10:35
is [5N]=0 ? 1. [4N]=0 if N=.1 4N=.4 [4N] =[.4]=0 5N=.5 [.5]=0 if N=.2 4N=.8 [4N]=0 [5N]=[.2*5]=1 Not sufficient. 2.[6N]=0 Since [6N]=0 =>[5N]=0 Sufficient. Answer B
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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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08 Nov 2015, 12:25
Hi,
In case of questions such as these, substitution of values can help us arrive at the solution.
Take N = 0.17  [4N] = [0.68] = 0, [5N] = [0.85] but when N = 0.22  [4N] = [0.88] = 0, [5N] = [1.10] = Either 1 or 0...Hence Insufficient
St 2: Take N = 0.16  [6N] = [0.96] = 0, [5N] = [0.9] = 0 and when N = 0.17 [6N] = [1.02] = either 0 or 1, [5N] = [0.85] = 0 So values are not consistent.
Taking together also we do not arrive at a common solution.
Eg; N = 0.22 [4N] = [0.88] [5N] = [1.10] [6N] = 1.32 N = 0.15 [4N] = [0.60] [5N] = [0.75] [6N] = 0.90
So the final solution is E



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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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08 Nov 2015, 12:52
Option A  Not sufficient. if N = 0.2 then 4N = 0.8 and [4N] = 0 , but 5N = 1 or [5N] = 1 Option B  Sufficient, if 6N = say < 1 then obviously 5N must be < 1 or [5N] = 0.



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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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08 Nov 2015, 16:25
IMO B is correct I] 4[N]= 0 this is possible when N=0 or 0<N<1 and precisely for 4[N] 0<N<0.25 SO if N =0 .19 then 5[N] = 0 and if N=0.20 then 5[N] = 1.0
So clearly insufficient II] 6[N]= 0 this is possible when N=0 or 0<N<1 and precisely for 6[N] 0<N<0.166 SO if N be any value between 0 adn 0.166 then 5[N] <1 and then 5[N] = 0.0
So clearly sufficient



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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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09 Nov 2015, 12:21
[4N]=0, N is integer => N=0 Sufficient [6N] =0, N is integer => N=0 Sufficient
Ans D



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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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09 Nov 2015, 23:25
St1: [4N] = 0 Taking the max value of N = 0.24 > [4*0.24] = 0 and [5*0.24] = 1 But for N = 0.1 > [4*0.1] = 0 and [5*0.1] = 0 So St1 alone is not sufficient
St2: [6N] = 0 Taking the max value of N = 0.16 > [6*0.16] = 0 and [5*0.16] = 0. St2 is Sufficient as it satisfies the condition for all values of N.
Answer: B



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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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11 Nov 2015, 00:42
N] denotes the greatest integer less than or equal to N. is [5N] = 0? (1) [4N] = 0 (2) [6N] = 0 Answer B [N] denotes greatest integer less than or equal to NWill try to explain with integer and noninteger value of N If N is an integer eg. 1 then [N]=1 only as [N]=N when N is an integer. If N in nonInteger eg. 1/2 then [N]=0 as [N]<N but the previous integer only. Now taking statements> 1) says [4N]=0 that means 4*N is less than 1 but greater than 0. So we get both yes and No in this case. As when N=1/10 then [4N]=[5N]=0, Hence Yes, but when N=2/10, then [4N]=0 but [5N]=1, hence NO 2) Says [6N]=0 that means 6*N is less than 1 but greater than 0. So we have only YES. whatever positive NonInteger multiplied by 6 gives [6N]=0 will always give [5N]=0 as 6*N is between 0 and 1 so 5*N will be also between 0 and 1.
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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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11 Nov 2015, 04:27
IMO B
A. As \([4N] = 0\) , \(0\leq{4N}<1\) OR \(0\leq{N}< \frac{1}{4}\). For \([5N]\), with N<\(\frac{1}{4}\); Case I : If \(N = \frac{1}{5}\) then, \([5N] = 1\) and Case II: If \(N > \frac{1}{5}\) then, \([5N] = 0\), Insufficient.
B. As \([6N] = 0\) , \(0\leq{6N}< {1}\) OR \(0\leq{N}<\frac{1}{6}\). For \([5N]\), with \(N <\frac{1}{6}\); \(0\leq{5N}<{1}\). Thus, \([5N] = 0\). Sufficient.



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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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11 Nov 2015, 09:15
The question asks us if [5N] =0? This means that either N =0 or 1/5 <= N < 1 Stmt 1: [4N] = 0. So N can be either 0 or <= 1/4. If N is 0, [5N] =0 If N is 1/4.5 then [5N] = [5/4.5] = [(greater than 1)] = 1. So, not sufficient.
Stmt 2: [6N] = 0. So N can be either 0 or <= 1/6. If N is 0, [5N] =0 If N is 1/6 or lesser, then [5N] = [5/6] = [(slightly greater than 0)] = 0. So, sufficient.
Ans B.



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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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11 Nov 2015, 09:16
is [5N]=0?
potion (1)
[4N]=0 Here N can be 0.1 then [4*0.1]=[0.4] =0
[5*0.1]= [0.5]=0
N can be 0.2 then [4*0.2]=[0.8]=0
[5N]=[5*0.2]=[1]=1
it gives two values, so it is not sufficient
option (2)
[6N]=0 Here we cannot take negative values for N
if N=0.16 then [6*0.16] =[0.96]
[5N]=[5 *0.16] =[0.8]=0
if N=0.2 then [6*0.2]=[1.2]=1 but here condition fails.... if N=0.1 then [6*0.1]=[0.6]=0
[5N]=[5*0.1]=[0.5]=0
so it is sufficient
answer is (B)



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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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11 Nov 2015, 12:06
[N] denotes the greatest integer less than or equal to N. is [5N] = 0? (1) [4N] = 0 (2) [6N] = 0 Any statement indicates the same. Answer. D
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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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12 Nov 2015, 11:38
Assuming that it is a Data Sufficiency question answer would be B i.e. only II statement is sufficient to answer the question but not statement I because whenever [6N]=0, [5N] would be 0 but not necessarily in case of [4N]=0 for e.g. take N=0.20 then [4N]=0 but [5N]=1.



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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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12 Nov 2015, 14:25
Please refer to the uploaded attachment for the solution.
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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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12 Nov 2015, 23:20
[N] denotes the greatest integer less than or equal to N. is [5N] = 0?
(1) [4N] = 0 (2) [6N] = 0
Need is to find if 0<=5N<1
Stmt 1: [4N] = 0 This means 0<=4N<1
if 4N=0.72 > N=0.18 > 5N=0.9 > [5N] = 0 if 4N=0.96 > N=0.24 > 5N=1.2 > [5N] = 1
Not Sufficient.
Stmt 2: [6N] = 0 This means 0<=6N<1
For all values of 6N satisfying above condition> 0<=N<1 And 5N<=6N (= when N=0)
Hence 0<=5N<=6N<1
Hence 0<=5N<1 > [5N] =0
Sufficient
Ans: B



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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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13 Nov 2015, 00:35
St 1: [4N] = 0 4N could be from 0 to 0.99 N could be from 0 to 0.2475 5N could be from 0 to 1.2375 [5N] could be 0 or 1
Not Sufficient
St 2: [6N] = 0 6N could be from 0 to 0.99 N could be from 0 to 0.1317 5N could be from 0 to 0.6585 [5N] will be 0
Sufficient
Answer: B



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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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13 Nov 2015, 05:41
1) [4N] =0 which means 0<=4N<1 0<=N<1/4
Is [5N] =0 ? Lets substitute highest value for N= 0.24 which is 5 * 0.24 =1.2 =[1.2] =1 which gives No answer Lets substitute N= 0.1 which is 5*0.1 =0.5 =[0.5] = 0 which gives Yes answer Statement A is not sufficient.
2) [6N] =0 which means 0<=6N<1 > 0<=N<1/6 Lets substitute highest possible value for N =0.166 5*01.66 = 0.83 =[0.83] =0 Lets substitute lowest possible value for N = 5 * 0 = 0 = [0] =0 Since all values for N will be between 0 and 1/6 for this statement, this statement B is sufficient.
So answer is B.



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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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13 Nov 2015, 07:19
QUESTION #6:
[N] denotes the greatest integer less than or equal to N. is [5N] = 0?
(1) [4N] = 0 (2) [6N] = 0 Explanation: 1) [4N] = 0 > 0<=4N<1 >0<=N<1/4.Now if N=0.2,[5N] = 1 OR N=0.15,[5N] = 0. Hence insufficient. 2)[6N] = 0 > 0<=6N<1 >0<=N<1/6.Now for any value of N [5N] = 0. Hence sufficient.
Correct answer is "B".



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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less
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13 Nov 2015, 09:21
[N] denotes the greatest integer less than or equal to N. is [5N] = 0?
We need to find out whether [5N] = 0. For this, we need to determine the value of N. Let's analyze the given statements:
(1) [4N] = 0 This implies that 0 <= 4N < 1 Dividing by 4, we get 0 <= N < 1/4 Now multiplying by 5, we get 0 <= 5N < 5/4 Let's assume 5N is a tiny bit less than 5/4 (say, 1.24), then the greatest integer less than or equal to 1.24 will be 1. On the other hand, if we assume 5N to be anything between 0 and 0.9, then the greatest integer less than or equal to it will be 0.
Since we get two contradictory answers, statement (1) alone is not sufficient.
(2) [6N] = 0 This implies that 0 <= 6N < 1 Dividing by 6, we get 0 <= N < 1/6 Now multiplying by 5, we get 0 <= 5N < 5/6 5/6 is less than 1, hence the greatest integer less than or equal to 5/6 will always be 0. Thus statement (2) alone is sufficient.
Correct answer is b.




Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less &nbs
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