## inequity 54

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### inequity 54

by magical cook » Sun Dec 23, 2007 11:42 am
If n denotes a numner 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

my way was...
n^2 , 1/100
-1/10 < n < 1/10
since n is negative
-1/10 < n
n needs to be reciprocal
-10 < n

but which is greater than -10 and which is not answer (not even an option)

Could anyone pls take a look at my procedure and give me advise where I got it wrong...

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### Re: inequity 54

by gabriel » Sun Dec 23, 2007 12:34 pm
magical cook wrote:If n denotes a numner 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

my way was...
n^2 , 1/100
-1/10 < n < 1/10
since n is negative
-1/10 < n
Everything until here is fine
magical cook wrote: n needs to be reciprocal
-10 < n
When you take the reciprocal u need to take it on both the sides (this applies to all mathematical operations for example if you multiply one side with -2 then you have to do the same with the other side if you dont then you are changing the relation between the two sides, the same goes for addition, subtraction, division, reciprocals etc.), so the last step should have been -10<1/n.. which basically means n < -10 .. so the answer should be A ..

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by magical cook » Sun Dec 23, 2007 2:08 pm
ahhh, my bad.. thank you !

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### clarification for previous explanation

by Bschool08 » Sun Dec 23, 2007 6:48 pm
magical cook, can you confirm that A is the right answer? i'm not seeing how -10<1/n is actually n<-10---i'm missing something here? if n is actually negative shouldn't taking it over to the other side yield n>10 making the answer E? if you can confirm would appreciate it - thanks

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by magical cook » Sun Dec 23, 2007 7:56 pm
Hi, the answer is A (this is gmatprep question, so OA should be correct )

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by Bschool08 » Sun Dec 23, 2007 9:21 pm
ok- thanks for confirming

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by samirpandeyit62 » Sun Dec 23, 2007 9:32 pm
n^2 < 1/100

i.e n <1> -1/10

since n is to the left of 0, hence n > -1/10

i.e n > -1/10

i.e 10 > -1/n

or 1/n (reciprocal of n)< -10

A
Regards
Samir

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