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Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
16 Aug 2009, 02:07
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.
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
17 Aug 2009, 05:49
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:)
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
17 Aug 2009, 16:05
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..
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
17 Aug 2009, 16:29
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?
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
17 Aug 2009, 17:04
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..
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
15 Sep 2009, 01:16
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. _________________
Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
23 Dec 2009, 17:52
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 _________________
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Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
16 Jul 2014, 23:05
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Re: If n is not equal to 0, is |n| < 4 ? [#permalink]
17 Jul 2014, 00:30
Expert's post
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.
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