Number Line Word Problem

[Bens4vcobra]

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

A) less than -10

B) Between -1 and -1/10

C) between -1/10 and 10

D) between 0 and 1/10

E) Greater than 10


I understand the problem fairly well. n must be at least -1/11. But here's where I am confused: doesn't the reciprocal also mean the sign changes? So -1/11 becomes 11 so E should be the answer, but A is the answer. The only way A is correct is if the sign doesn't change. But when dealing with reciprocals of negative exponents, the sign changes. This is causing confusion for me.

[testprepDublin]

If the square of n < 1/100 and n < 0, then -1/10 < n < 0. (square root of 1/100 is +/-1/10)

Since a reciprocal multiplies a number into 1, the reciprocal < 1/(-1/10) => < -10.

The answer is A.

[Frankenstein]

I understand the problem fairly well. n must be at least -1/11. But here's where I am confused: doesn't the reciprocal also mean the sign changes? So -1/11 becomes 11 so E should be the answer, but A is the answer. The only way A is correct is if the sign doesn't change. But when dealing with reciprocals of negative exponents, the sign changes. This is causing confusion for me.

Hi,
I don't know where you read this. Reciprocal doesn't change sign(never). So, I think this resolves your confusion.

[Frankenstein]

If the square of n < 1/100 and n < 0, then n < -1/10. (square root of 1/100 is +/-1/10)

Since a reciprocal multiplies a number into 1, the reciprocal < 1/(-1/10) => < -10.

The answer is A.

Hi,
Can you edit this. It should be -1/10 < n < 0.

[Bens4vcobra]

I understand the problem fairly well. n must be at least -1/11. But here's where I am confused: doesn't the reciprocal also mean the sign changes? So -1/11 becomes 11 so E should be the answer, but A is the answer. The only way A is correct is if the sign doesn't change. But when dealing with reciprocals of negative exponents, the sign changes. This is causing confusion for me.

Hi,
I don't know where you read this. Reciprocal doesn't change sign(never). So, I think this resolves your confusion.

Well, in dealing with negative exponents, it does.

4^-3 reciprocal = 1/4^3 = 1/64

Generally speaking though, a number multiplied by its reciprocal must be 1.

[finance]

what's the OA?

[Frankenstein]

I understand the problem fairly well. n must be at least -1/11. But here's where I am confused: doesn't the reciprocal also mean the sign changes? So -1/11 becomes 11 so E should be the answer, but A is the answer. The only way A is correct is if the sign doesn't change. But when dealing with reciprocals of negative exponents, the sign changes. This is causing confusion for me.

Hi,
I don't know where you read this. Reciprocal doesn't change sign(never). So, I think this resolves your confusion.

Well, in dealing with negative exponents, it does.

4^-3 reciprocal = 1/4^3 = 1/64

Generally speaking though, a number multiplied by its reciprocal must be 1.

Hi,
Exponent being negative is different from number itself being negative.
We are dealing with number being negative here.
So, reciprocal of -1/11 is -11 only, not +11.