Mar 27 03:00 PM PDT  04:00 PM PDT Join a free live webinar and learn the winning strategy for a 700+ score on GMAT & the perfect application. Save your spot today! Wednesday, March 27th at 3 pm PST Mar 29 10:00 PM PDT  11:00 PM PDT Right now, their GMAT prep, GRE prep, and MBA admissions consulting services are up to $1,100 off. GMAT (Save up to $261): SPRINGEXTRAGMAT GRE Prep (Save up to $149): SPRINGEXTRAGRE MBA (Save up to $1,240): SPRINGEXTRAMBA Mar 30 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Mar 31 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 19 Oct 2012
Posts: 306
Location: India
Concentration: General Management, Operations
GMAT 1: 660 Q47 V35 GMAT 2: 710 Q50 V38
GPA: 3.81
WE: Information Technology (Computer Software)

Which of the following describes all the values of y for whi
[#permalink]
Show Tags
Updated on: 14 Oct 2013, 10:21
Question Stats:
48% (01:45) correct 52% (01:44) wrong based on 332 sessions
HideShow timer Statistics
Which of the following describes all the values of y for which y < y^2 ? A. 1 < y B. −1 < y < 0 C. y < −1 D. 1/y < 1 E. 0 < y < 1 I wanted an algebraic approach to solve this question. Any pointers are welcomed. Kudos if you like the question.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Citius, Altius, Fortius
Originally posted by TheMechanic on 14 Oct 2013, 10:15.
Last edited by Bunuel on 14 Oct 2013, 10:21, edited 1 time in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 53800

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
14 Oct 2013, 10:23




Manager
Joined: 13 Aug 2012
Posts: 93

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
15 Oct 2013, 07:40
Bunuel wrote: vabhs192003 wrote: Which of the following describes all the values of y for which y < y^2 ? A. 1 < y B. −1 < y < 0 C. y < −1 D. 1/y < 1 E. 0 < y < 1 I wanted an algebraic approach to solve this question. Any pointers are welcomed. Kudos if you like the question. From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 > 1/y < 1. Answer: D. Hi bunuel, Your method is really easy but could you look at what i did just to tell me where i'm making a mistake? \(y<y^2\) \(y^2y>0\) \(y(y1)>0\) Two cases arise: Case I: When both are positiveeither\(y>0\) or \(Y>1\), Thus \(y>1\) Case II: When both are negative \(Y<0\) and \(y<1\) thus \(Y<0\) From the above two cases\(Y<0\) and \(Y>1\). Where am I going wrong????



Math Expert
Joined: 02 Sep 2009
Posts: 53800

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
15 Oct 2013, 08:56
mahendru1992 wrote: Bunuel wrote: vabhs192003 wrote: Which of the following describes all the values of y for which y < y^2 ? A. 1 < y B. −1 < y < 0 C. y < −1 D. 1/y < 1 E. 0 < y < 1 I wanted an algebraic approach to solve this question. Any pointers are welcomed. Kudos if you like the question. From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 > 1/y < 1. Answer: D. Hi bunuel, Your method is really easy but could you look at what i did just to tell me where i'm making a mistake? \(y<y^2\) \(y^2y>0\) \(y(y1)>0\) Two cases arise: Case I: When both are positiveeither\(y>0\) or \(Y>1\), Thus \(y>1\) Case II: When both are negative \(Y<0\) and \(y<1\) thus \(Y<0\) From the above two cases\(Y<0\) and \(Y>1\). Where am I going wrong???? Yes, y < y^2 means that either y < 0 or y > 1. If y < 0, then 1/y = negative < 0 < 1. If y > 1, then 1/y < 1. So, D is 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: 13 Aug 2012
Posts: 93

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
15 Oct 2013, 09:00
Oh Thanks! I expected a verbatim answer because usually that is the case. I'll have to be careful in evaluating the choices from now on.



Intern
Joined: 09 Aug 2013
Posts: 2

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
16 Oct 2013, 07:37
Bunuel wrote: vabhs192003 wrote: Which of the following describes all the values of y for which y < y^2 ? A. 1 < y B. −1 < y < 0 C. y < −1 D. 1/y < 1 E. 0 < y < 1 I wanted an algebraic approach to solve this question. Any pointers are welcomed. Kudos if you like the question. From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 > 1/y < 1. Answer: D. Hi Bunnel I got your method of solving the equation. But could you please tell me why answer choice C is incorrect , won't y < 1 lead to all values for which y < y^2 ? Thanks in advance !



Math Expert
Joined: 02 Sep 2009
Posts: 53800

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
16 Oct 2013, 07:38



SVP
Joined: 06 Sep 2013
Posts: 1676
Concentration: Finance

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
01 Jan 2014, 07:27
Bunuel wrote: vabhs192003 wrote: Which of the following describes all the values of y for which y < y^2 ? A. 1 < y B. −1 < y < 0 C. y < −1 D. 1/y < 1 E. 0 < y < 1 I wanted an algebraic approach to solve this question. Any pointers are welcomed. Kudos if you like the question. From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 > 1/y < 1. Answer: D. I also solved it factorizing y^2y>0 y(y1)>0 Two cases: y<0 or y>1 Now if y>0 Then 1/y<1 is y>1, by reciprocal. So we have case 1 checked Then if y<0 We have that 1/y<1, do not flip inequality. y<1<0 So we have second case Therefore D is the correct answer PS. Its fine not to flip inequality in second case no? Just wanted to confirm this Thanks Cheers! J



Manager
Joined: 26 Feb 2012
Posts: 97
Location: India
Concentration: General Management, Finance
WE: Engineering (Telecommunications)

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
14 Mar 2014, 23:42
jlgdr wrote: Bunuel wrote: vabhs192003 wrote: Which of the following describes all the values of y for which y < y^2 ? A. 1 < y B. −1 < y < 0 C. y < −1 D. 1/y < 1 E. 0 < y < 1 I wanted an algebraic approach to solve this question. Any pointers are welcomed. Kudos if you like the question. From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 > 1/y < 1. Answer: D. I also solved it factorizing y^2y>0 y(y1)>0 Two cases: y<0 or y>1 Now if y>0 Then 1/y<1 is y>1, by reciprocal. So we have case 1 checked Then if y<0 We have that 1/y<1, do not flip inequality. y<1<0 So we have second case Therefore D is the correct answer PS. Its fine not to flip inequality in second case no? Just wanted to confirm this Thanks Cheers! J Mr J Could you why did u get Two cases:y<0 or y>1 after factorization .? I did the factorization lets c... Y^2Y>0 =>Y(Y1)>0 =>Y>0 and Y>1 Then i have checked the answer and landed upon D... Rgds Prasannajeet



Manager
Joined: 26 Feb 2012
Posts: 97
Location: India
Concentration: General Management, Finance
WE: Engineering (Telecommunications)

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
14 Mar 2014, 23:43
jlgdr wrote: Bunuel wrote: vabhs192003 wrote: Which of the following describes all the values of y for which y < y^2 ? A. 1 < y B. −1 < y < 0 C. y < −1 D. 1/y < 1 E. 0 < y < 1 I wanted an algebraic approach to solve this question. Any pointers are welcomed. Kudos if you like the question. From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 > 1/y < 1. Answer: D. I also solved it factorizing y^2y>0 y(y1)>0 Two cases: y<0 or y>1 Now if y>0 Then 1/y<1 is y>1, by reciprocal. So we have case 1 checked Then if y<0 We have that 1/y<1, do not flip inequality. y<1<0 So we have second case Therefore D is the correct answer PS. Its fine not to flip inequality in second case no? Just wanted to confirm this Thanks Cheers! J Mr J Could you why did u get Two cases:y<0 or y>1 after factorization .? I did the factorization lets c... Y^2Y>0 =>Y(Y1)>0 =>Y>0 and Y>1 Then i have checked the answer and landed upon D... Rgds Prasannajeet



Math Expert
Joined: 02 Sep 2009
Posts: 53800

Which of the following describes all the values of y for whi
[#permalink]
Show Tags
15 Mar 2014, 05:32
prasannajeet wrote: Could you why did u get Two cases:y<0 or y>1 after factorization .? I did the factorization lets c... Y^2Y>0 =>Y(Y1)>0 =>Y>0 and Y>1 Then i have checked the answer and landed upon D...
Rgds Prasannajeet If you think about it, you should understand that y>0 and y>1 does not make any sense. What could be the values of y in this case? y(y1)>0 > the "roots" are 0 and 1, this gives us 3 ranges: y<0; 0<y<1; y>1. Next, test some extreme value for y: if y is some large enough number, say 10, then both multiples will be positive which gives the positive result for the whole expression, so when y>1 the expression is positive. Now the trick: as in the 3rd range expression is positive then in the 2nd it'll be negative and finally in the 1st it'll be positive again: +  + . So, the ranges when the expression is positive are: y<0 and y>1. Check this for more: x24x94661.html#p731476Hope it helps.
_________________
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



Senior Manager
Joined: 21 Oct 2013
Posts: 416

Which of the following describes all the values of y for
[#permalink]
Show Tags
30 Jun 2014, 03:22
Which of the following describes all the values of y for which y < y^2? A) 1 < y B) −1 < y < 0 C) y < −1 D) 1/y < 1 E) 0 < y < 1



Math Expert
Joined: 02 Sep 2009
Posts: 53800

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
30 Jun 2014, 03:24



Manager
Joined: 27 May 2014
Posts: 79

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
30 Jun 2014, 14:18
What is y = 4. Then y<1 holds true but y>1 does not....



Math Expert
Joined: 02 Sep 2009
Posts: 53800

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
30 Jun 2014, 14:24



Manager
Joined: 27 May 2014
Posts: 79

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
30 Jun 2014, 14:31
If we have two solutions : y<0 and y>1, and the above comment was if y is equal to 2, Y<0 does not hold up. But if y=3 then y>1 does not hold up.... maybe I'm not understanding the explanation completely. I still don't understand why choice C won't work



Math Expert
Joined: 02 Sep 2009
Posts: 53800

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
30 Jun 2014, 14:59
bankerboy30 wrote: If we have two solutions : y<0 and y>1, and the above comment was if y is equal to 2, Y<0 does not hold up. But if y=3 then y>1 does not hold up.... maybe I'm not understanding the explanation completely. I still don't understand why choice C won't work \(y < 0\) and \(y > 1\) are the ranges for which \(y < y^2\) holds true. For any \(y\) from these ranges, \(y\) is less than \(y^2\). Option C is not true because the question asks to find ALL the values of \(y\) for which \(y\) is less than \(y^2\). And while for \(y < 1\), \(y\) is indeed less than \(y^2\), this range (\(y < 1\)) does not cover ALL the values of \(y\) for which \(y\) is less than \(y^2\). Namely it does not cover range \(1\leq{y}<0\) and range \(y>1\). I think you need to brush up fundamentals on inequality: Hope it helps.
_________________
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: 10 Mar 2014
Posts: 187

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
07 Jul 2014, 03:17
Bunuel wrote: vabhs192003 wrote: Which of the following describes all the values of y for which y < y^2 ? A. 1 < y B. −1 < y < 0 C. y < −1 D. 1/y < 1 E. 0 < y < 1 I wanted an algebraic approach to solve this question. Any pointers are welcomed. Kudos if you like the question. From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 > 1/y < 1. Answer: D. Hi Bunnel, I have a query for ans. choice A here it is mentioned y<1 i.e. y >1. if y>1 then always y<y^2. Please clarify this. What is the issue in this logic Thanks.



Math Expert
Joined: 02 Sep 2009
Posts: 53800

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
07 Jul 2014, 03:24



Intern
Joined: 29 Aug 2013
Posts: 39
Location: Bangladesh
GPA: 3.76
WE: Supply Chain Management (Transportation)

Re: Which of the following describes all the values of y for whi
[#permalink]
Show Tags
19 Dec 2015, 11:26
Which of the following describes all the values of y for which y < y^2 ?
A. 1 < y B. −1 < y < 0 C. y < −1 D. 1/y < 1 E. 0 < y < 1I solved it as per below and plucked the wrong answer. Can anyone please explain where i am wrong: y < y^2 Or, y^2>y Or, y^2/y>y/y Or, y>1 Or, 1<y Hereby, I choose "A".
_________________
Appreciate Kudos if the post seems worthwhile!




Re: Which of the following describes all the values of y for whi
[#permalink]
19 Dec 2015, 11:26



Go to page
1 2
Next
[ 26 posts ]



