January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

eGMAT Representative
Joined: 04 Jan 2015
Posts: 2447

If x is an integer and it satisfies the inequalities, x^2 – 6x  7...
[#permalink]
Show Tags
Updated on: 31 Oct 2018, 22:40
Question Stats:
74% (01:36) correct 26% (01:12) wrong based on 101 sessions
HideShow timer Statistics



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2723
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: If x is an integer and it satisfies the inequalities, x^2 – 6x  7...
[#permalink]
Show Tags
31 Oct 2018, 04:59
EgmatQuantExpert wrote: If x is an integer and it satisfies the inequalities, \(x^2 – 6x  7 < 0\) and \(2x – x^2 + 3 < 0\), then which of the following can be the value of x? \(x^2 – 6x  7 < 0\) i.e. \(x^2 – 7x + x  7 < 0\) i.e.\((x7)*(x+1) < 0\) Product of two things is less than zero i.e. one of them must be positive and other must be Negative. Also since (X7) is smaller than (x+1) therefore (X7) must be negativei.e. \((x7) < 0\) and \((x+1) > 0\) i.e. \(1 < x < 7\)Now, \(2x – x^2 + 3 < 0\) i.e. \(x^2  2x  3 > 0\) i.e. \(x^2  3x +x  3 > 0\) i.e. \((x3)*(x+1) > 0\) i.e. \(x > 3 or x < 1\)Looking at both blue results we can infer that \(3 < x < 7\) i.e. x can only be 5 out of given option choices Answer: Option E
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Manager
Joined: 04 Jun 2018
Posts: 121

Re: If x is an integer and it satisfies the inequalities, x^2 – 6x  7...
[#permalink]
Show Tags
31 Oct 2018, 05:19
While I could solve the question by finding out the range of individual equations and then finding out the common value, I have a doubt. Why can't I add the equations and still get the same result? If we were to try add these equations ,we would get: 4x4<0 i.e x<1 Why would this method not work? I know there is a conceptual gap here because x<1 is not a valid range. Can some expert help out? gmatbustersEgmatQuantExpertGladiator59



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2723
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: If x is an integer and it satisfies the inequalities, x^2 – 6x  7...
[#permalink]
Show Tags
31 Oct 2018, 06:30
nitesh50 wrote: While I could solve the question by finding out the range of individual equations and then finding out the common value, I have a doubt. Why can't I add the equations and still get the same result? If we were to try add these equations ,we would get: 4x4<0 i.e x<1 Why would this method not work? I know there is a conceptual gap here because x<1 is not a valid range. Can some expert help out? gmatbustersEgmatQuantExpertGladiator59 nitesh50Addition of inequalities is valid for Linear inequalities with same inequation signs.Here we are dealing with quadratic inequations hence we can not simply add to get the solution I hope this helps!!!
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1195
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: If x is an integer and it satisfies the inequalities, x^2 – 6x  7...
[#permalink]
Show Tags
31 Oct 2018, 06:50
Dear nitesh50Adding the quadratic inequalities/equations might lead to loss of some roots, and you can get a larger Set as other conditions get lost with the loss of quadratic term.Please note that there is a mistake in your solution which seems to show invalid range Adding you get, 4x4<0 or, 4<4x or x>1 note that the actual answer x = 5 also satisfy this condition. nitesh50 wrote: While I could solve the question by finding out the range of individual equations and then finding out the common value, I have a doubt. Why can't I add the equations and still get the same result? If we were to try add these equations ,we would get: 4x4<0 i.e x<1 Why would this method not work? I know there is a conceptual gap here because x<1 is not a valid range. Can some expert help out? gmatbustersEgmatQuantExpertGladiator59
_________________
Win GMAT CLUB Test Weekly Quant Quiz Contest Weekly Quant Quiz Questions Direct Download SC: Confusable words All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory Error log/Key Concepts Combination Concept: Division into groups Question of the Day (QOTD) Free GMAT CATS



Manager
Joined: 04 Jun 2018
Posts: 121

Re: If x is an integer and it satisfies the inequalities, x^2 – 6x  7...
[#permalink]
Show Tags
31 Oct 2018, 07:38
gmatbusters wrote: Dear nitesh50Adding the quadratic inequalities/equations might lead to loss of some roots, and you can get a larger Set as other conditions get lost with the loss of quadratic term.Please note that there is a mistake in your solution which seems to show invalid range Adding you get, 4x4<0 or, 4<4x or x>1 note that the actual answer x = 5 also satisfy this condition. nitesh50 wrote: While I could solve the question by finding out the range of individual equations and then finding out the common value, I have a doubt. Why can't I add the equations and still get the same result? If we were to try add these equations ,we would get: 4x4<0 i.e x<1 Why would this method not work? I know there is a conceptual gap here because x<1 is not a valid range. Can some expert help out? gmatbustersEgmatQuantExpertGladiator59Hi gmatbustersThank you for correcting my mistake. this might be a stupid question, but Why is that when we are adding 2 inequalities, it leads to loss of a certain range. I guess What I am still looking for is a bit of a conceptual understanding to it. Looking forward to you reply! Regards Nitesh



Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1195
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: If x is an integer and it satisfies the inequalities, x^2 – 6x  7...
[#permalink]
Show Tags
31 Oct 2018, 07:44
Hi Since on adding you are loosing the quadratic term, leads to loss of roots/a certain range.See this example if x^2 = 2x and we cancel out x from both sides ( it leads to loss of root, x = 0) We get x = 2. Whereas, x^2 = 2x or, x(x2) = 0 or x = 0 or 2 By cancelling some terms you are loosing roots. nitesh50 wrote: gmatbusters wrote: Dear nitesh50Adding the quadratic inequalities/equations might lead to loss of some roots, and you can get a larger Set as other conditions get lost with the loss of quadratic term.Please note that there is a mistake in your solution which seems to show invalid range Adding you get, 4x4<0 or, 4<4x or x>1 note that the actual answer x = 5 also satisfy this condition. nitesh50 wrote: While I could solve the question by finding out the range of individual equations and then finding out the common value, I have a doubt. Why can't I add the equations and still get the same result? If we were to try add these equations ,we would get: 4x4<0 i.e x<1 Why would this method not work? I know there is a conceptual gap here because x<1 is not a valid range. Can some expert help out? gmatbustersEgmatQuantExpertGladiator59Hi gmatbustersThank you for correcting my mistake. this might be a stupid question, but Why is that when we are adding 2 inequalities, it leads to loss of a certain range. I guess What I am still looking for is a bit of a conceptual understanding to it. Looking forward to you reply! Regards Nitesh
_________________
Win GMAT CLUB Test Weekly Quant Quiz Contest Weekly Quant Quiz Questions Direct Download SC: Confusable words All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory Error log/Key Concepts Combination Concept: Division into groups Question of the Day (QOTD) Free GMAT CATS



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2447

If x is an integer and it satisfies the inequalities, x^2 – 6x  7...
[#permalink]
Show Tags
02 Nov 2018, 03:50
Solution Given:• We are given that x is an integer, and • We are also given two inequalities,
o \(x^2 – 6x  7 < 0\) o \(2x – x^2 + 3 < 0\) To find:• We need to find out which among the given answer choices can be a possible value of x that satisfies the given information Approach and Working: • We need to solve both the quadratic inequalities to arrive at the answer. • Let’s solve the first inequality, \(x^2  6x – 7 < 0\)
o Implies, (x  7)(x + 1) < 0 Approach 1: Wavyline method• Thus, the expression is negative for 1 < x < 7 • The values of x that satisfy this inequality are, x = {0, 1, 2, 3, 4, 5, 6} Now, let’s solve the second inequality, \(2x  x^2  3 < 0\) o Multiplying by 1, we get, \(x^2 – 2x  3 > 0\) o Implies, (x  3)(x + 1) > 0 • Thus, the expression is positive for x < 1 and x > 3 Combining both the results, 1 < x < 7, and (x < 1 or x > 3), we can say that the values of x that satisfy this inequality are, 3 < x < 7 • Since, x is an integer, x = {4 , 5 , 6} Approach 2: Numberline methodNumber line for the expression (x + 1)(x  7) < 0 is, • Thus, the expression is negative for 1 < x < 7 Now, let’s draw the numberline for the expression, (x + 1)(x  3) > 0 • Thus, the expression is positive for x < 1 or x > 3 Combining both these results, we get, 3 < x < 7 • Since, x is an integer, the values of x that satisfy the given expression are {4, 5, 6} Hence, the correct answer is option E. Answer: E
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2  Remainders1  Remainders2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Intern
Joined: 12 Sep 2017
Posts: 45

If x is an integer and it satisfies the inequalities, x^2 – 6x  7...
[#permalink]
Show Tags
15 Jan 2019, 20:03
GMATinsight wrote: EgmatQuantExpert wrote: If x is an integer and it satisfies the inequalities, \(x^2 – 6x  7 < 0\) and \(2x – x^2 + 3 < 0\), then which of the following can be the value of x? \(x^2 – 6x  7 < 0\) i.e. \(x^2 – 7x + x  7 < 0\) i.e.\((x7)*(x+1) < 0\) Product of two things is less than zero i.e. one of them must be positive and other must be Negative. Also since (X7) is smaller than (x+1) therefore (X7) must be negativei.e. \((x7) < 0\) and \((x+1) > 0\) i.e. \(1 < x < 7\)Now, \(2x – x^2 + 3 < 0\) i.e. \(x^2  2x  3 > 0\) i.e. \(x^2  3x +x  3 > 0\) i.e. \((x3)*(x+1) > 0\) i.e. \(x > 3 or x < 1\)Looking at both blue results we can infer that \(3 < x < 7\) i.e. x can only be 5 out of given option choices Answer: Option E Good night GMATinsight I understood the whole method but I am struggling with on doubt: i.e.\((x7)*(x+1) < 0\) If I want to solve it algebraically, isn't the following correct? x < 7 x < 1 What am I doing wrong?, I mean I understand the concept but why does the < sign change here if we are just adding/subtracting? Kind regards!




If x is an integer and it satisfies the inequalities, x^2 – 6x  7... &nbs
[#permalink]
15 Jan 2019, 20:03






