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

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Jamboree and GMAT Club Contest: [N] denotes the greatest integer less  [#permalink]

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New post 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


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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less  [#permalink]

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New post 14 Nov 2015, 06:25
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[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 1
Therefore Insufficient

S2:
[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, Sufficient

Hence B
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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less  [#permalink]

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New post 08 Nov 2015, 10:35
2
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  [#permalink]

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New post 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  [#permalink]

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New post 08 Nov 2015, 12:52
1
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  [#permalink]

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New post 08 Nov 2015, 16:25
1
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  [#permalink]

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New post 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  [#permalink]

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New post 09 Nov 2015, 23:25
1
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  [#permalink]

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New post 11 Nov 2015, 00:42
1
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 N--Will try to explain with integer and non-integer 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 non-Integer 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 Non-Integer 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  [#permalink]

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New post 11 Nov 2015, 04:27
1
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  [#permalink]

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New post 11 Nov 2015, 09:15
1
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  [#permalink]

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New post 11 Nov 2015, 09:16
1
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  [#permalink]

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New post 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  [#permalink]

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New post 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  [#permalink]

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New post 12 Nov 2015, 14:25
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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  [#permalink]

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New post 12 Nov 2015, 23:20
1
[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  [#permalink]

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New post 13 Nov 2015, 00:35
1
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  [#permalink]

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New post 13 Nov 2015, 05:41
1
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  [#permalink]

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New post 13 Nov 2015, 07:19
1
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  [#permalink]

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New post 13 Nov 2015, 09:21
1
[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.
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Re: Jamboree and GMAT Club Contest: [N] denotes the greatest integer less &nbs [#permalink] 13 Nov 2015, 09:21

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