|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 13 May 2009
Posts: 18
|
If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
 08 Aug 2009, 06:55
1
This post received
KUDOS
3
This post was
BOOKMARKED
D
E
Question Stats:
65% (02:02) correct
35% (01:14) wrong based on 256 sessions
HideShow timer Statistics
If n is not equal to 0, is |n| < 4 ? (1) n^2 > 16 (2) 1/|n| > n OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-not-equal-to-0-is-n-4-1-n-85256.html
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 17 Jul 2014, 01:30, edited 1 time in total.
Edited the question and added the OA.
|
|
|
|
|
|
Director
Joined: 01 Apr 2008
Posts: 881
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
08 Aug 2009, 07:24
lbsgmat wrote: If n is not equal to 0, is |n| < 4 ?
(1) n2 > 16
(2) 1/|n| > n D for me. 1) if n^2 > 16, then we get two possibilities, either n>4 or n<-4. For both cases, absolute value of n will be always > 4. Sufficient. 2) In order for this inequality to be true, n can be anything < 1 (excluding 0 ). So we cant say if the absolute value is < 4. Insufficient.
Last edited by Economist on 08 Aug 2009, 10:02, edited 1 time in total.
|
|
|
|
|
|
Senior Manager
Joined: 17 Jul 2009
Posts: 286
Concentration: Nonprofit, Strategy
GPA: 3.42
WE: Engineering (Computer Hardware)
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
08 Aug 2009, 07:30
2
This post received
KUDOS
I would go for A
statement 1 is sufficient as n^2 > 16 meaning n > 4 or n < -4, either way, |n| > 4
statement 2 1/|n| > n...insufficient, two examples:
when n = -2, 1/2 > -2, |-2| < 4
when n = -5, 1/5 > -5, |-5| > 4
|
|
|
|
|
|
SVP
Joined: 05 Jul 2006
Posts: 1747
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
16 Aug 2009, 00:47
8) If n is not equal to 0, is |n| < 4 ?
(1) n^2 > 16
(2) 1/|n| > n
|
|
|
|
|
|
Senior Manager
Joined: 17 Mar 2009
Posts: 301
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
16 Aug 2009, 03:07
Imo D
given n!= 0, is |n| < 4? which is n^2 < 16?
stmt 1
n^2>16 , so n^2 cannot be < 16.
suffi.
stmt2
1/|n| > n
squaring on both sides
1/(n^2) > n^2
1 > n^4 ( can multiply because n^2 is always +ve independent of the value of n)
n^4<1, then defintely n^2 < 1, so n^2 < 16
suffi.
|
|
|
|
|
|
Director
Joined: 01 Apr 2008
Posts: 881
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
16 Aug 2009, 04:59
Yep D.
stmt 1:
n>4 or n<-4. In either case the magnitude of n (absolute value) will always be >4.
Sufficient.
stmt 2:
1>|n|*n, For this inequality to be true, n<1. Hence, |n| will always be <4.
Sufficient.
Last edited by Economist on 16 Aug 2009, 08:05, edited 1 time in total.
|
|
|
|
|
|
Intern
Joined: 01 Aug 2009
Posts: 29
Location: Australia
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
16 Aug 2009, 07:59
Economist wrote: stmt 2:
1>|n|*n, For this inequality to be true, we have -1<n<0 or 0<n<1. Hence, |n| will always be <4.
Sufficient. I agree with D, but the solution for statement 2 is not \(-1<n<0\) or \(0<n<1\) \(-1<n<0\) or \(0<n<1\) is the solution for \(n^2 < 1\) Solution for \(|n|*n < 1\) is \(n < 1\)
_________________
The three most significant times in your life are:
1. When you fall in love
2. The birth of your first child
3. When you prepare for your GMAT
|
|
|
|
|
|
Director
Joined: 01 Apr 2008
Posts: 881
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
17 Aug 2009, 06:49
yezz wrote: crejoc wrote: Imo D
given n!= 0, is |n| < 4? which is n^2 < 16?
stmt 1
n^2>16 , so n^2 cannot be < 16.
suffi.
stmt2
1/|n| > n
squaring on both sides ( can we do that " what if n is -ve , squaring will hide the sign??)
1/(n^2) > n^2
1 > n^4 ( can multiply because n^2 is always +ve independent of the value of n)
n^4<1, then defintely n^2 < 1, so n^2 < 16
suffi. We cannot do that unless we are sure that n is +ve, else the inequality sign will reverse. Hence we can only derive 1>|n|n, as |n| is always +ve:)
|
|
|
|
|
|
Manager
Joined: 07 Apr 2009
Posts: 145
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
17 Aug 2009, 11:34
Guys the answer is 'A'.
n*|n| < 1 ==> n < 0 it holds good for any negative values so insuff to say if |n| < 4 or not...
|
|
|
|
|
|
SVP
Joined: 29 Aug 2007
Posts: 2473
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
17 Aug 2009, 17:03
yezz wrote: 8) If n is not equal to 0, is |n| < 4 ?
(1) n^2 > 16
(2) 1/|n| > n Thats A. (1) If n^2 > 16, n is either > 4 or < -4. Suff.. (2) If 1/|n| > n, n is smaller than 1 but not 0 i.e. n could be 0.5, -1, -10 etc. not suff.. I was scrolling down for A. Got it............ skpMatcha wrote: Guys the answer is 'A'.
n*|n| < 1 ==> n < 0 it holds good for any negative values so insuff to say if |n| < 4 or not...
_________________
Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html
GT
|
|
|
|
|
|
Senior Manager
Joined: 17 Mar 2009
Posts: 301
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
17 Aug 2009, 17:05
Economist wrote: squaring on both sides ( can we do that " what if n is -ve , squaring will hide the sign??)
We cannot do that unless we are sure that n is +ve, else the inequality sign will reverse. Hence we can only derive 1>|n|n, as |n| is always +ve:) that makes sense economist,.. i thought squaring will hide it.. you are correct it cannot be squared, unless n is always +ve..
|
|
|
|
|
|
Manager
Joined: 05 Jun 2009
Posts: 77
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
17 Aug 2009, 17:29
I dont understand, doesn't statement 2 yield N to be under 1 and statement 1 yields it to be above 4. Can this be a question, N cant be both? Either way, arent both statement sufficient, statement 1 tells you it has to be over 4, statement 2 tells you definitively that its under it?
|
|
|
|
|
|
Senior Manager
Joined: 17 Mar 2009
Posts: 301
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
17 Aug 2009, 18:04
sfeiner wrote: I dont understand, doesn't statement 2 yield N to be under 1 and statement 1 yields it to be above 4. Can this be a question, N cant be both? Either way, arent both statement sufficient, statement 1 tells you it has to be over 4, statement 2 tells you definitively that its under it? i think stmt1 is clear and is sufficient, and you have no doubt with it. consider stmt2 question is |n|< 4? stmt2 given 1/|n|>n case 1: take when n is +ve 1 > |n|* n 1> n^2 n^2<1 so -1<n<1 in this interval for any values |n| is < 4 case 2: when n is -ve 1/|n|> n 1/(-n)>n multiply by -n 1< -n^2 -n^2>1 n^2>-1 since n is negative, and n^2>-1, for all negative values of n this is true, so n can take any negative values say -1,-2..and so on if n=-2 1/|n|>n, 1/2> -2 is true, check |n| < 4, |-2|<4, 2< 4 true, if n= -8 1/|n|>n, 1/8 > -8 , but when you check |n|<4, |-8|<4? , no 8 is not < 4, so insufficient Another easy way is to directly check by plugging numbers stmt2 1/|n|> n for any positive value of n, this statement holds false, so n can take negative values and only fractions. check with negative numbers when n = -2 |n| < 4? , |-2|<4 , yes but when n = -8 |n| < 4?, |-8|is not < 4, so stmt2 insufficient similarly, for fractions also try using n = 1/2, n=1/8 , it is insufficient so answer is A hope this helps..
|
|
|
|
|
|
Manager
Joined: 10 Jul 2009
Posts: 126
Location: Ukraine, Kyiv
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
15 Sep 2009, 02:16
Agree with A. It is the sole choice, which represents a clear answer on the question. In stmt B there is an evidence, that n is negative only. This gives nothing.
_________________
Never, never, never give up
|
|
|
|
|
|
Intern
Joined: 30 May 2008
Posts: 4
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
23 Dec 2009, 17:21
Can somebody breakdown for me how n^2 > 16 is n<-4 or n>4.
As I look at it if n^2 > 16 then n > + or -4.
also I think I understand how |n| > 4 but please breakdown that as well.
Thanks.
|
|
|
|
|
|
Manager
Joined: 09 May 2009
Posts: 205
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
23 Dec 2009, 18:52
1
This post received
KUDOS
sudimba wrote: Can somebody breakdown for me how n^2 > 16 is n<-4 or n>4.
As I look at it if n^2 > 16 then n > + or -4.
also I think I understand how |n| > 4 but please breakdown that as well.
Thanks. n^2>16---->+-n>16---->+n>16 or -n>16---->n<-4(multiplying bth side by -1 reverses the sign) one can try with numbers also as square of(-3)=9<16 therfore n<-4 to satisfy the inequality same with otherone lnl>4--->+n>4 or -n > 4---->n<-4
_________________
GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME
|
|
|
|
|
|
Director
Joined: 03 Sep 2006
Posts: 871
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
24 Dec 2009, 16:38
From (i)
\(n^2>16\)
\(\sqrt{n^2}>\sqrt{16}\)
\(|n|>\sqrt{16}\)
\(|n|>4\)
/* Because \(|n| = \sqrt{n^2}\) applies only for positive square roots of n */
Therefore,
|n|<4 is not TRUE.
From(i) we could find this answer.
From(ii)
\(1/|n|>|n|\)
\(n|n|<1\)
\(|n|<1/n\)
If n>0,
\(n<1/n\)
\(n^2<1\)
\(|n|<1\)
|n|<4 is TRUE.
or If n<0,
\(-n<1/n\)
\(]n>1/n\)
\(n^2>1\)
\(|n|>1\)
|n|<4 may or may not be TRUE.
Therefore from(ii), we can't answer this question.
Thus answer is "A"
|
|
|
|
|
|
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16026
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
17 Jul 2014, 00:05
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 39753
|
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
Show Tags
17 Jul 2014, 01:30
If n is not equal to 0, is |n| < 4 ? Question basically asks is -4<n<4 true. (1) n^2>16 --> n>4 or n<-4, the answer to the question is NO. Sufficient. (2) 1/|n| > n, this is true for all negative values of n, hence we can not answer the question. Not sufficient. Answer: A. As you can see we don't really want the complete range for (2) to see that this statement is not sufficient, but still if interested: 1/|n| > n --> n*|n| < 1. If n<0, then we'll have -n^2<1 --> n^2>-1. Which is true. So, n*|n| < 1 holds true for any negative value of n. If n>0, then we'll have n^2<1 --> -1<n<1. So, n*|n| < 1 also holds true for 0<n<1. Thus 1/|n| > n holds true if n<0 and 0<n<1. OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-not-equal-to-0-is-n-4-1-n-85256.html
_________________
New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!
Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.
Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
|
|
|
|
|
|
|
Re: If n is not equal to 0, is |n| < 4 ?
[#permalink]
17 Jul 2014, 01:30
|
|
|
|
|
|
|
|
|
|
|
|
|
1
