n is a negative number. If n^2 < 1/100 then n<-1/10. Therefore the reciprocal of n, 1/n < -10.

Answer: A

magizhan wrote:n is a negative number. If n^2 < 1/100 then n<-1/10. Therefore the reciprocal of n, 1/n < -10.

Answer: A

Taking reciprocal changes the direction of the inequality. Why the same thing is not applicable here?

papumba2011 wrote:

magizhan wrote:n is a negative number. If n^2 < 1/100 then n<-1/10. Therefore the reciprocal of n, 1/n < -10.

Answer: A

Taking reciprocal changes the direction of the inequality. Why the same thing is not applicable here?

Including a few more steps should answer your question:

n^2 < 1/100

1/n^2 > 100

1/|n| > 10

-1/n > 10

1/n < -10


Remember : the positive square root of n^2 is |n|

|n| = -n if n < 0

a^2 < b^2 implies that |a| < |b|

kevincanspain wrote:

papumba2011 wrote:

magizhan wrote:n is a negative number. If n^2 < 1/100 then n<-1/10. Therefore the reciprocal of n, 1/n < -10.

Answer: A

Taking reciprocal changes the direction of the inequality. Why the same thing is not applicable here?

Including a few more steps should answer your question:

n^2 < 1/100

1/n^2 > 100

1/|n| > 10

-1/n > 10

1/n < -10


Remember : the positive square root of n^2 is |n|

|n| = -n if n < 0

a^2 < b^2 implies that |a| < |b|

I approached in a similar fashion without doing the reciprocality step in the beginning.

i.e n^2 < 1/100
==> (n-1/10)(n+1/10)<0
After doing the above step and given the info from the question I got -1/10<n<0.

What exactly is wrong in this approach. Since n > -1/10.
or 1/n < -10.

Is this fine?.

I just got a bit confused with the -1/10<-n<0 range . Was not sure how eaxctly the reciprocality thing will work here .

papumba2011 wrote:If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be
1) less than -10
2) between -1 and -1/10
3) between -1/10 and 0
4) between 0 and 1/10
5) greater than 10

certainly the fastest way to do this is to pick a number.

We want the square of n to be a very small positive number, so let n = -(1/100000)

To form the reciprocal, we flip, giving us:

-100000

choose (A).