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..