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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
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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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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] New post 03 Oct 2014, 18:39
Bunuel wrote:
hardnstrong wrote:
i dont get your point bangolarian
we have n^2 < 100 so -1/10 < n < 1/10
how you got n < - 1/10

Can somebody please explain if n > -1/10. does that mean its reciprocal is 1/n < -10 . Do we change less than and greater than sign with reciprocal of any interger? :?:


Refer to my previous post:

We have n<0 and n^2<\frac{1}{100}

n^2<\frac{1}{100} --> -\frac{1}{10}<n<\frac{1}{10}, but as n<0 --> -\frac{1}{10}<n<0.

Multiply the inequality by -\frac{10}{n}, (note as n<0 expression -\frac{10}{n}>0, and we don't have to switch signs) --> (-\frac{1}{10})*(-\frac{10}{n})<n*(-\frac{10}{n})<0*(-\frac{10}{n}) --> so finally we'll get \frac{1}{n}<-10<0. OR \frac{1}{n}<-10.

Answer: A.

Hope it helps.







Hi Bunnel ,

I am weak with inequalities and flipping of signs , where could i get theory for it / additional similar practice questions ?

Thanks and Regards ,
Sheldon Rodrigues
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Re: If n denotes a number to the left of 0 on the number line [#permalink] New post 04 Oct 2014, 02:22
Expert's post
shelrod007 wrote:
Bunuel wrote:
hardnstrong wrote:
i dont get your point bangolarian
we have n^2 < 100 so -1/10 < n < 1/10
how you got n < - 1/10

Can somebody please explain if n > -1/10. does that mean its reciprocal is 1/n < -10 . Do we change less than and greater than sign with reciprocal of any interger? :?:


Refer to my previous post:

We have n<0 and n^2<\frac{1}{100}

n^2<\frac{1}{100} --> -\frac{1}{10}<n<\frac{1}{10}, but as n<0 --> -\frac{1}{10}<n<0.

Multiply the inequality by -\frac{10}{n}, (note as n<0 expression -\frac{10}{n}>0, and we don't have to switch signs) --> (-\frac{1}{10})*(-\frac{10}{n})<n*(-\frac{10}{n})<0*(-\frac{10}{n}) --> so finally we'll get \frac{1}{n}<-10<0. OR \frac{1}{n}<-10.

Answer: A.

Hope it helps.







Hi Bunnel ,

I am weak with inequalities and flipping of signs , where could i get theory for it / additional similar practice questions ?

Thanks and Regards ,
Sheldon Rodrigues


Theory on Inequalities
Solving Quadratic Inequalities - Graphic Approach: solving-quadratic-inequalities-graphic-approach-170528.html
Inequality tips: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1379270

inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html
everything-is-less-than-zero-108884.html
graphic-approach-to-problems-with-inequalities-68037.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If n denotes a number to the left of 0 on the number line   [#permalink] 04 Oct 2014, 02:22
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