Number Line Word Problem

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Bens4vcobra: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Thu Feb 19, 2009 12:10 pmFollowed by: 2 members; Thanked: 3 times

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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Source: Beat The GMAT — Problem Solving | Tue Jul 05, 2011 6:10 am

testprepDublin: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Fri Jun 03, 2011 6:44 amFollowed by: 1 member; Location: Dublin, Ireland; Thanked: 8 times; GMAT Score:750

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.

Deirdre at testprepdublin.com

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

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!

Things are not what they appear to be... nor are they otherwise

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

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!

Things are not what they appear to be... nor are they otherwise

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Bens4vcobra: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Thu Feb 19, 2009 12:10 pmFollowed by: 2 members; Thanked: 3 times

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.

"It takes no ability to give effort. Toughness is not God-given; it's a choice. The discipline to execute is a habit." - Nick Saban

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finance: Master | Next Rank: 500 Posts; Posts: 150; Joined: Tue Mar 08, 2011 4:38 am; Thanked: 5 times

by finance » Tue Jul 05, 2011 9:21 am

what's the OA?

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

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!

Things are not what they appear to be... nor are they otherwise

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