Number Line Word Problem

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Number Line Word Problem

by Bens4vcobra » Tue Jul 05, 2011 6:10 am
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.
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by testprepDublin » Tue Jul 05, 2011 6:27 am
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.
Last edited by testprepDublin on Tue Jul 05, 2011 6:43 am, edited 1 time in total.
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by Frankenstein » Tue Jul 05, 2011 6:27 am
Bens4vcobra wrote: 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.
Cheers!

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by Frankenstein » Tue Jul 05, 2011 6:29 am
testprepDublin wrote: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.
Cheers!

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by Bens4vcobra » Tue Jul 05, 2011 9:09 am
Frankenstein wrote:
Bens4vcobra wrote: 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.
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by finance » Tue Jul 05, 2011 9:21 am
what's the OA?

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by Frankenstein » Tue Jul 05, 2011 9:22 am
Bens4vcobra wrote:
Frankenstein wrote:
Bens4vcobra wrote: 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.
Cheers!

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