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

Question

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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Official Answer

B

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arhumsid · Accepted Answer

denotes the greatest integer less than or equal to N. is   = 0?

(1)   = 0
(2)   = 0

S1:
  = 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 
=>    = 0 or 1 
Therefore  Insufficient

S2:
  = 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 
=>    = 0

Therefore,  Sufficient

Hence B

Skywalker18 · Answer

is  =0 ?

1.  =0
if N=.1 
4N=.4
 
= =0
5N=.5
 =0

if N=.2
4N=.8
 =0

= =1
Not sufficient.

2. =0
Since  =0
=> =0

Sufficient.

Answer B

saikiransomala · Answer

Hi,

In case of questions such as these, substitution of values can help us arrive at the solution.

Take N = 0.17 ---   =   = 0,   =   but when N = 0.22 ----   =   = 0,   =   = Either 1 or 0...Hence Insufficient

St 2: Take N = 0.16 ----   =   = 0,   =   = 0 and when N = 0.17   =   = either 0 or 1,   =   = 0 So values are not consistent.

Taking together also we do not arrive at a common solution.

Eg; N = 0.22   =     =     = 1.32 
 N = 0.15   =     =     = 0.90

So the final solution is E

JackH · Answer

Option A - Not sufficient. if N = 0.2 then 4N = 0.8 and   = 0 , but 5N = 1 or   = 1
Option B - Sufficient, if 6N = say < 1 then obviously 5N must be < 1 or   = 0.

kanigmat011 · Answer

IMO B is correct
I] 4 = 0
this is possible when N=0 or 0<N<1
and precisely for 4  0<N<0.25
SO if N =0 .19 then 5  = 0 and if N=0.20 then 5  = 1.0

So clearly insufficient
II] 6 = 0
this is possible when N=0 or 0<N<1
and precisely for 6  0<N<0.166
SO if N be any value between 0 adn 0.166 then 5  <1 and then 5  = 0.0

So clearly sufficient

camlan1990 · Answer

=0, N is integer => N=0
Sufficient 
  =0, N is integer => N=0
Sufficient

Ans D

Kurtosis · Answer

St1:   = 0
Taking the max value of N = 0.24 -->   = 0 and   = 1
But for N = 0.1 -->   = 0 and   = 0
So St1 alone is not sufficient

St2:   = 0
Taking the max value of N = 0.16 -->   = 0 and   = 0. 
St2 is Sufficient as it satisfies the condition for all values of N.

Answer: B

sahil7389 · Answer

N] denotes the greatest integer less than or equal to N. is   = 0?

(1)   = 0 
(2)   = 0

Answer- B
  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  =1 only as  =N when N is an integer.
If N in non-Integer eg. 1/2 then  =0 as  <N but the previous integer only. 
Now taking statements--->
1) says  =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  = =0, Hence Yes,
but when N=2/10, then  =0 but  =1, hence NO
2) Says  =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  =0 will always give  =0 as 6*N is between 0 and 1 so 5*N will be also between 0 and 1.

vickyp7030 · Answer

IMO B

A. As    = 0  ,  0\leq{4N}<1  OR  0\leq{N}< \frac{1}{4} .
 For    , with N< \frac{1}{4} ; 
 Case I : If  N = \frac{1}{5}  then,    = 1  and 
 Case II: If  N > \frac{1}{5}  then,    = 0 , Insufficient.

B. As    = 0  ,  0\leq{6N}< {1}  OR  0\leq{N}<\frac{1}{6} .
 For    , with  N <\frac{1}{6} ;  0\leq{5N}<{1} .
 Thus,    = 0 . Sufficient.

ShristiK · Answer

The question asks us if   =0?
This means that either N =0 or 1/5 <= N < 1
Stmt 1:   = 0. So N can be either 0 or <= 1/4.
If N is 0,   =0
If N is 1/4.5 then   =   =   = 1. So, not sufficient.

Stmt 2:   = 0. So N can be either 0 or <= 1/6.
If N is 0,   =0
If N is 1/6 or lesser, then   =   =   = 0. So, sufficient.

Ans B.

vinod265 · Answer

is  =0?

potion (1)

=0
Here N can be 0.1 then  =  =0

=  =0

N can be 0.2 then  = =0

= = =1

it gives two values, so it is not sufficient

option (2)

=0
Here we cannot take negative values for N

if N=0.16 then   =

=  = =0

if N=0.2 then  = =1 but here condition fails....
 
if N=0.1 then  = =0

= = =0

so it is sufficient

answer is (B)

Nevernevergiveup · Answer

denotes the greatest integer less than or equal to N. is   = 0?

(1)   = 0 
(2)   = 0

Any statement indicates the same. Answer. D

Deepak66 · Answer

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  =0,   would be 0 but not necessarily in case of  =0 for e.g. take N=0.20 then  =0 but  =1.

saunakdey · Answer

Please refer to the uploaded attachment for the solution.

rakshithbabu · Answer

denotes the greatest integer less than or equal to N. is = 0? (1) = 0 (2) = 0 Need is to find if 0<=5N<1 Stmt 1: = 0 This means 0<=4N<1 if 4N=0.72 -> N=0.18 -> 5N=0.9 -> = 0 if 4N=0.96 -> N=0.24 -> 5N=1.2 -> = 1 Not Sufficient. Stmt 2: = 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 -> =0 Sufficient Ans: B

AmoyV · Answer

St 1:
  = 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
  could be 0 or 1

Not Sufficient

St 2:
  = 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
  will be 0

Sufficient

Answer: B

sri1sastra · Answer

1)   =0
which means 0<=4N<1
0<=N<1/4

Is   =0 ?
Lets substitute highest value for N= 0.24 which is 5 * 0.24 =1.2 =  =1 which gives No answer
Lets substitute N= 0.1 which is 5*0.1 =0.5 =  = 0 which gives Yes answer
Statement A is not sufficient.

2)   =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 
Lets substitute lowest possible value for N = 5 * 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.

pksam · Answer

QUESTION #6: denotes the greatest integer less than or equal to N. is = 0? (1) = 0 (2) = 0 Explanation:- 1) = 0 -> 0<=4N<1 ->0<=N<1/4.Now if N=0.2, = 1 OR N=0.15, = 0. Hence insufficient. 2) = 0 -> 0<=6N<1 ->0<=N<1/6.Now for any value of N = 0. Hence sufficient. Correct answer is "B".

prakharsworld · Answer

denotes the greatest integer less than or equal to N. is   = 0?

We need to find out whether   = 0. For this, we need to determine the value of N. Let's analyze the given statements:

(1)   = 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)   = 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.

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

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