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

Question

Jamboree and GMAT Club Contest Starts

QUESTION #6:

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

(1)   = 0 
(2)   = 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 6-months 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.

Thank you!

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards