January 26, 2019 January 26, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions. January 27, 2019 January 27, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 05 Oct 2008
Posts: 243

reciprocals and negatives
[#permalink]
Show Tags
Updated on: 25 Nov 2011, 21:59
Can someone please explain this:
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 0 D. between 0 and 1/10 E. greater than 10
n^2 < 1/100 1/10 < n < 1/10 n is negative so forget right side of equation multiply both sides by 1/n 1/n * 1/10 < n * 1/n flip signs as n is negative 1/10n > 1 note 1/n * 1/10 = +1/10n now multiply both sides by 10 10 * 1/10n < 1 * 10 Don't flip signs 1/n < 10
Answer is A! Please explain your answers.
Originally posted by study on 25 Nov 2011, 01:02.
Last edited by study on 25 Nov 2011, 21:59, edited 3 times in total.



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1323

Re: reciprocals and negatives
[#permalink]
Show Tags
25 Nov 2011, 04:41
study wrote: n^2 < 1/100 1/10 < n < 1/10 n is negative so forget right side of equation multiply both sides by 1/n 1/n * 1/10 < n * 1/n 1/10n < 1 now multiply both sides by 10 10 * 1/10n < 1 * 10 Flip signs 1/n > 10
Answer E!
First, that is not what E says (E says that 1/n is greater than positive 10, not negative 10), so that might have suggested that your answer wasn't quite right. I've highlighted your mistake in red. When you multiply on both sides of the inequality by 1/n, you must reverse the inequality, because 1/n is negative.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Manager
Joined: 05 Oct 2008
Posts: 243

Re: reciprocals and negatives
[#permalink]
Show Tags
25 Nov 2011, 13:51
Thanks, Ian. I edited the post. That was a typo. Would you please look at the post now and correct my mistake. Thanks.



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1323

Re: reciprocals and negatives
[#permalink]
Show Tags
26 Nov 2011, 06:14
study wrote: Thanks, Ian. I edited the post. That was a typo. Would you please look at the post now and correct my mistake. Thanks. In your edited post, the negative sign vanished  it still needs to be there. You have: 1/10 < n Now if we multiply by 1/n on both sides, we must reverse the inequality, since 1/n is negative: 1/10n > 1 Now we can multiply by 10 on both sides: 1/n > 10 Now we can multiply by 1 on both sides, reversing the inequality since we are multiplying by a negative: 1/n < 10 Note that you can also do this problem very quickly by finding any suitable number for n (say 1/100) and working out the reciprocal of n.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1323

Re: reciprocals and negatives
[#permalink]
Show Tags
26 Nov 2011, 17:22
study wrote: Yes, the negative sign vanished, cuz negative * negative = positive. So a negative 1/n * negative 1/10 = + 1/10n And that is exactly the part I don't understand. Why would you retain a negative after multiplying a negative number by another negative number? Would you please explain To illustrate 2 * 5 = 10. Not 10 so why would 1/n * 1/10 = 1/10n? If you multiply, say, 1 by x, the result is x. It makes no difference if x is positive or negative. If x is negative, then x is a *positive* number, even if it might look negative because of the negative sign in front. There is a second negative sign 'hidden' inside of 'x'. That's the issue with the step you took in your edited post. When you multiply 1/n by 1/10, the result is *always* equal to 1/10n. It makes no difference at all if n is positive or negative. If n is negative, then 1/10n is a positive number, because you have two negatives in the fraction, one in the numerator and one in the denominator (since n is negative). I'd strongly suggest you review this part of algebra, because it's fundamental in many GMAT questions.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Intern
Joined: 09 Feb 2012
Posts: 2

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?



Math Expert
Joined: 02 Sep 2009
Posts: 52431




Math Expert
Joined: 02 Sep 2009
Posts: 52431

Re: If n denotes a number to the left of 0 on the number line
[#permalink]
Show Tags
17 Jun 2013, 04:51



Manager
Joined: 26 Feb 2012
Posts: 99
Location: India
Concentration: General Management, Finance
WE: Engineering (Telecommunications)

Re: If n denotes a number to the left of 0 on the number line
[#permalink]
Show Tags
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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8810
Location: Pune, India

Re: If n denotes a number to the left of 0 on the number line
[#permalink]
Show Tags
07 Nov 2013, 01:03
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: ifndenotesanumbertotheleftof0onthenumberline91659.html#p811517
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 23 Jan 2013
Posts: 138
Concentration: Technology, Other
GMAT Date: 01142015
WE: Information Technology (Computer Software)

Re: If n denotes a number to the left of 0 on the number line
[#permalink]
Show Tags
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



Math Expert
Joined: 02 Sep 2009
Posts: 52431

Re: If n denotes a number to the left of 0 on the number line
[#permalink]
Show Tags
04 Oct 2014, 02:22
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 InequalitiesSolving Quadratic Inequalities  Graphic Approach: solvingquadraticinequalitiesgraphicapproach170528.htmlInequality tips: tipsandhintsforspecificquanttopicswithexamples172096.html#p1379270inequalitiestrick91482.htmldatasuffinequalities109078.htmlrangeforvariablexinagiveninequality109468.htmleverythingislessthanzero108884.htmlgraphicapproachtoproblemswithinequalities68037.html
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 14 Dec 2014
Posts: 19
Concentration: Technology

Re: If n denotes a number to the left of 0 on the number line
[#permalink]
Show Tags
14 Feb 2016, 08:25
These types of problems can be easier to do visually :
Step 1: range of n^2 < 1 /100   0 <.01 
Step 2: range of \sqrt{n^2} = \sqrt{1/100} (question states only to the left of 0) :  (1/10)>0 
* note to see if the range of n is going towards 0 or away test a number of n^2 and see what the sq root gives you i.e. \sqrt{1/10000} = +/ \frac{1}{100} which is smaller.
Step 3: inverse of the range n  < (10)  0 



Manager
Joined: 03 Jan 2017
Posts: 150

Re: If n denotes a number to the left of 0 on the number line
[#permalink]
Show Tags
28 Mar 2017, 09:57
I approached it this way: n is number to the left from 0 n^2<1/100 question asks 1/n? so from the data we know that 1/10<n<1/10 let's flip so 10>1/n>10 As we know that n is to the left from 0, then 1/n<10 Answer is A



Senior Manager
Joined: 26 Dec 2015
Posts: 256
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)

Re: If n denotes a number to the left of 0 on the number line
[#permalink]
Show Tags
08 Jul 2017, 19:13
Bunuel wrote: 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 0 D. between 0 and 1/10 E. greater than 10
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 \(n<0\), then \(\frac{10}{n}>0\), 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 \(\frac{1}{n}<10<0\).
Answer: A. Bunuel, why do you Multiply \(\frac{1}{10}<n<0\) by \(\frac{10}{n}\)? Can you not just take the reciprocal of \(\frac{1}{10}<n<0\) to give you: \(10<\frac{1}{n}<0\)?



Math Expert
Joined: 02 Sep 2009
Posts: 52431

Re: If n denotes a number to the left of 0 on the number line
[#permalink]
Show Tags
09 Jul 2017, 01:28
LakerFan24 wrote: Bunuel wrote: 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 0 D. between 0 and 1/10 E. greater than 10
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 \(n<0\), then \(\frac{10}{n}>0\), 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 \(\frac{1}{n}<10<0\).
Answer: A. Bunuel, why do you Multiply \(\frac{1}{10}<n<0\) by \(\frac{10}{n}\)? Can you not just take the reciprocal of \(\frac{1}{10}<n<0\) to give you: \(10<\frac{1}{n}<0\)? As you can see you are not getting correct inequality, so you cannot do that way. 10 < 5 < 1 but 1/10 < 1/5 < 1 is not correct.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 30 May 2012
Posts: 208
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)

Re: If n denotes a number to the left of 0 on the number line
[#permalink]
Show Tags
10 Jul 2017, 18:39
Math mods and others  Please check my approach:
Given: n is less than 0, implying n is negative.
Also given: \(n^2\) < \(\frac{1}{100}\)
Square rooting both sides:
n< \(\frac{1}{10}\) AND n < \(\frac{1}{10}\)
Reciprocating both the inequalities, \(\frac{1}{n}\) <10 AND \(\frac{1}{n}\) <10
Since, \(\frac{1}{n}\) MUST be less than 10 and 10 at all times, the option that always satisfies this is A.
Is this a right approach? I always falter when removing the squares on both sides of the equation/inequality and I want to make sure my approach is correct so that I can register it in my noggin.



Senior Manager
Joined: 26 Dec 2015
Posts: 256
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)

Re: If n denotes a number to the left of 0 on the number line
[#permalink]
Show Tags
26 Aug 2017, 07:41
experts, please correct me if i'm wrong:
isn't it easy to just take a glance here and eliminate A/C?  You're told the SQUARE of n = fraction meaning n = fraction > The reciprocal of n must therefore b an integer. Elim B, C, D straight away
Between A & E, you know that n = negative, so its reciprocal cannot be positive. Elim E.
Ans: A



Senior Manager
Joined: 29 Jun 2017
Posts: 461
GPA: 4
WE: Engineering (Transportation)

Re: If n denotes a number to the left of 0 on the number line
[#permalink]
Show Tags
17 Dec 2017, 06:37
A n= 1/x (1/x)^2 < 1/100 LHS positive since x is negative and square is positive and RHS is positive cross multiply x^2 >100 (x10)(x+10)>0 (infinity,10) U ( 10,+infinity) positive part is not included as x is negative since n is negative ( left of zero 0) so reciprocal of negative cant be positive answer is x or (1/n) <10
_________________
Give Kudos for correct answer and/or if you like the solution.



VP
Joined: 09 Mar 2016
Posts: 1287

If n denotes a number to the left of 0 on the number line
[#permalink]
Show Tags
06 Jan 2018, 09:41
AKProdigy87 wrote: The answer is A.
We are given two pieces of information:
1) \(n^2 < \frac{1}{100}\)
2) \(n < 0\)
SO:
\(n^2 < \frac{1}{100}\)
\(n < \frac{1}{10}\)
BUT n < 0 SO:
\(n > \frac{1}{10}\)
To determine the conditions on the reciprocal of n:
\(\frac{1}{n} < \frac{10}{1}\)
\(\frac{1}{n} < 10\) Hello Bunuel, could help me to clear my doubts :) according to general rule when variable is under radical sign we square both sides  > for example if \(\sqrt{x}\) = 4 then we need to squae both sides of equation so \(\sqrt{(x)}\) = \((4)^2\) > x= 16 now when it comes to the solution above from this equation \(n^2 < \frac{1}{100}\) we get this \(n < \frac{1}{10}\)  why ? should not we square both sides as I did in my example ? Why are we applying this formula \(\sqrt{x^2}\) = \(x\) if this doesnt look like \(n^2 < \frac{1}{100}\) ? < (here we dont have radical sign) why 100 in denominator is reduced by 10 ? shouldn't 100 be multiplied by itself as in my example ? in my example the number 4 turns into 16 and here it get reduced...so I am confused Also ss there a difference between \(\sqrt{x^2}\) and \(\sqrt{x}\) ? many thanks ! perhaps you friends can help chetan2u , niks18




If n denotes a number to the left of 0 on the number line &nbs
[#permalink]
06 Jan 2018, 09:41



Go to page
Previous
1 2 3
Next
[ 47 posts ]



