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If n denotes a number to the left of 0 on the number line

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new [#permalink] New post 07 Mar 2012, 04:14
can you explain why are you flipping sign?

n> - 1/10.

why 1/n<-10 ?

if n=4 for example 4>-1/10 and 1/4>-10. why to flip sign?
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Re: new [#permalink] New post 07 Mar 2012, 05:23
Expert's post
akakhidze wrote:
can you explain why are you flipping sign?

n> - 1/10.

why 1/n<-10 ?

if n=4 for example 4>-1/10 and 1/4>-10. why to flip sign?


Welcome to GMAT Club. Below is an answer to your question.

Since n denotes a number to the left of 0 on the number then n is negative, so it can not be 4 as you assumed.

Next, when you multiply (or divide) an inequality by a negative number you must flip the sign of the inequality.

So, for n>-\frac{1}{10} --> multiply by negative -10 and flip the sign: -10n<1 --> divide by negative n and flip the sign again: -10>\frac{1}{n}.

For a complete solution refer to the posts above, for example: if-n-denotes-a-number-to-the-left-of-0-on-the-number-line-91659.html#p667838

Hope it helps.
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Re: If n denotes a number to the left of 0 on the number line [#permalink] New post 17 Jun 2013, 04:51
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: If n denotes a number to the left of 0 on the number line [#permalink] New post 22 Jun 2013, 06:20
Hi Bunuel
Can it be right if go like the following way?

given (-n)^2<1/100
=>n^2<1/00
=>n<1/10

Now Q ask us to find reciprocal of n
So take the reciprocal on both side simply we get
1/n<10 Ans
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Re: If n denotes a number to the left of 0 on the number line [#permalink] New post 07 Nov 2013, 01:03
Expert's post
prasannajeet wrote:
Hi Bunuel
Can it be right if go like the following way?

given (-n)^2<1/100
=>n^2<1/00
=>n<1/10

Now Q ask us to find reciprocal of n
So take the reciprocal on both side simply we get
1/n<10 Ans


No.
Given: n < 0
n^2 < (1/100)
Note that you will not use -n because n is negative. n already includes the negative sign.
When you take square root, you get |n| < 1/10 (and not n < 1/10). This means -1/10 < n < 1/10. But since n < 0, -1/10 < n < 0.

We need to find the value of reciprocal i.e. 1/n.

n > -1/10
1/n < -10 Note that in an inequality, if both sides of the inequality have the same sign (positive or negative), the sign of inequality (<, >) flips when you take the reciprocal. Here both sides are negative so sign flips.
(Or do what Bunuel did: multiply by -10/n.)
So reciprocal is less than -10.

Instead, I would do this question by thinking of some numbers and figuring out the logic - discussed here: if-n-denotes-a-number-to-the-left-of-0-on-the-number-line-91659.html#p811517
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Re: If n denotes a number to the left of 0 on the number line   [#permalink] 07 Nov 2013, 01:03
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