inequity 54

[magical cook]

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...

[gabriel]

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

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 ..

[magical cook]

ahhh, my bad.. thank you !

[Bschool08]

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

[magical cook]

Hi, the answer is A (this is gmatprep question, so OA should be correct )

[Bschool08]

ok- thanks for confirming

[samirpandeyit62]

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