November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 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. November 17, 2018 November 17, 2018 09:00 AM PST 11:00 AM PST Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.
Author 
Message 
TAGS:

Hide Tags

eGMAT Representative
Joined: 04 Jan 2015
Posts: 2203

Find the range of values of x such that ((x+6) (3x4)^3)/(x+2)^2 > 0
[#permalink]
Show Tags
Updated on: 31 Aug 2018, 00:47
Question Stats:
42% (01:16) correct 58% (01:31) wrong based on 170 sessions
HideShow timer Statistics
Solving inequalities Number Line Method  Practice Question #4Find the range of values of x such that \(\frac{((x+6) (3x4)^3)}{(x+2)^2} >0\) A. x > \(\frac{4}{3}\) B. (6, 4/3) C. (inf, 4/3) U (6, +inf) – {2} D. (inf, 6 ) U(4/3, +inf) E. (inf, 6) U (4/3, +inf) – {2} Previous Question To read the article: Solving inequalities Number Line MethodTo read all our articles:Must Read articles to reach Q51
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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 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



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2203

Find the range of values of x such that ((x+6) (3x4)^3)/(x+2)^2 > 0
[#permalink]
Show Tags
Updated on: 31 Aug 2018, 00:48
Solution Given: An inequality,\(\frac{(x+6) (3x4)^3}{(x+2)^2}\)>0
To find: The range of x, that satisfies the above inequality
Approach and Working: The first step is to multiply the inequality by \((x+2)^2\) Thus, we get,
\(\frac{(x+2)^2 (x+6) (3x4)^3}{(x+2)^2} >0\) Which implies, \((x + 6) * (3x  4)^3 > 0\) and the denominator, x + 2 ≠ 0, implies, x≠ 2 This can be written as \((x + 6) * (3x  4) * (3x  4)^2 > 0\) Since, \((3x4)^2\), is always positive, expect for x = 4/3
We can write the inequality as, (x + 6) * (3x  4) > 0
The zero points of this inequality are, x = 6 and x = 4/3 Plot these points on the number line.
Since, 4/3 > 6, the inequality will be positive, for all the points to the right of 4/3, on the number line And, it is negative, in the region, between 6 and 4/3 It is again positive for all the values less than 6
Therefore, the range of x is x > 4/3 and x < 6 and x ≠ 2 Hence, the correct answer is option D. Answer: D
_________________
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 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



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 930
WE: Supply Chain Management (Energy and Utilities)

Re: Find the range of values of x such that ((x+6) (3x4)^3)/(x+2)^2 > 0
[#permalink]
Show Tags
23 Aug 2018, 05:21
EgmatQuantExpert wrote: Solving inequalities Number Line Method  Practice Question #4
Find the range of values of x such that \(\frac{((x+6) (3x4)^3)}{(x+2)^2} >0\)
A. x > \(\frac{4}{3}\) B. (6, 4/3) C. (inf, 4/3) U (6, +inf) – {2} D. (inf, 6 ) U(4/3, +inf) E. (inf, 6) U (4/3, +inf) – {2}
\(\frac{((x+6) (3x4)^3)}{(x+2)^2} >0\) Critical points: 6, 4/3 Points that to be excluded from the range of x: 2 Using wavy curve method: Range of x: x < 6 or x>4/3 Range of x in interval form: (inf, 6 ) U(4/3, +inf) (Note: x=2 is already excluded) Ans. (D) Seems option (D) is a typo error. It should be inf instead of inf.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2203

Re: Find the range of values of x such that ((x+6) (3x4)^3)/(x+2)^2 > 0
[#permalink]
Show Tags
23 Aug 2018, 10:25



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 930
WE: Supply Chain Management (Energy and Utilities)

Re: Find the range of values of x such that ((x+6) (3x4)^3)/(x+2)^2 > 0
[#permalink]
Show Tags
28 Aug 2018, 20:17
EgmatQuantExpert wrote: Thanks PKN, I have updated the options. Regards, Ashutosh eGMATAmendment done in the answer options: 1) {+2} has been replaced with {2} in answer options C & E. 2) No change in answer option D, it must be ( inf, 6 ) U(4/3, +inf), which makes sense. Now correct answer option can't be E. Reason: 1) As per official explanation the range of x: x > 4/3 and x < 6 and x ≠ 2We always subtract or exclude points(or positions or ranges) when those points of a range are subset of a bigger range of points. For example , If I say , set of real numbers except 2. It can be written as (inf,+inf){2}, since 2 is already present in {inf,inf}, and we want the interval excluding 2. In line with the above reasoning, option E is to be discarded.(how to exclude 2 where the interval (inf, 6) U (4/3, +inf) doesn't possess the point 2. It's already excluded.) I hope with a small correction in option D, we would arrive at the correct answer option. Please correct me. Thanking you. Hi EgmatQuantExpert, Please guide.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2203

Re: Find the range of values of x such that ((x+6) (3x4)^3)/(x+2)^2 > 0
[#permalink]
Show Tags
31 Aug 2018, 00:52



Intern
Joined: 10 Sep 2018
Posts: 6

Re: Find the range of values of x such that ((x+6) (3x4)^3)/(x+2)^2 > 0
[#permalink]
Show Tags
19 Sep 2018, 00:41
PKN wrote: EgmatQuantExpert wrote: Solving inequalities Number Line Method  Practice Question #4
Find the range of values of x such that \(\frac{((x+6) (3x4)^3)}{(x+2)^2} >0\)
A. x > \(\frac{4}{3}\) B. (6, 4/3) C. (inf, 4/3) U (6, +inf) – {2} D. (inf, 6 ) U(4/3, +inf) E. (inf, 6) U (4/3, +inf) – {2}
\(\frac{((x+6) (3x4)^3)}{(x+2)^2} >0\) Critical points: 6, 4/3 Points that to be excluded from the range of x: 2 Using wavy curve method: Range of x: x < 6or x>4/3 Range of x in interval form: (inf, 6 ) U(4/3, +inf) (Note: x=2 is already excluded) Ans. (D) Seems option (D) is a typo error. It should be inf instead of inf. Hi, can you please tell me how x will be less than 6? I think x should be greater than 6. Can you tell me what I'm missing?



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 930
WE: Supply Chain Management (Energy and Utilities)

Find the range of values of x such that ((x+6) (3x4)^3)/(x+2)^2 > 0
[#permalink]
Show Tags
19 Sep 2018, 00:44
srijnasingh wrote: PKN wrote: EgmatQuantExpert wrote: Solving inequalities Number Line Method  Practice Question #4
Find the range of values of x such that \(\frac{((x+6) (3x4)^3)}{(x+2)^2} >0\)
A. x > \(\frac{4}{3}\) B. (6, 4/3) C. (inf, 4/3) U (6, +inf) – {2} D. (inf, 6 ) U(4/3, +inf) E. (inf, 6) U (4/3, +inf) – {2}
\(\frac{((x+6) (3x4)^3)}{(x+2)^2} >0\) Critical points: 6, 4/3 Points that to be excluded from the range of x: 2 Using wavy curve method: Range of x: x < 6or x>4/3 Range of x in interval form: (inf, 6 ) U(4/3, +inf) (Note: x=2 is already excluded) Ans. (D) Seems option (D) is a typo error. It should be inf instead of inf. Hi, can you please tell me how x will be less than 6? I think x should be greater than 6. Can you tell me what I'm missing? Request to furnish your explanation on x>6 so that I can share my reasoning with you. I have used wavy curve method to determine the intervals.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Intern
Joined: 10 Sep 2018
Posts: 6

Re: Find the range of values of x such that ((x+6) (3x4)^3)/(x+2)^2 > 0
[#permalink]
Show Tags
19 Sep 2018, 01:06
PKN wrote: EgmatQuantExpert wrote: Solving inequalities Number Line Method  Practice Question #4
Find the range of values of x such that \(\frac{((x+6) (3x4)^3)}{(x+2)^2} >0\)
A. x > \(\frac{4}{3}\) B. (6, 4/3) C. (inf, 4/3) U (6, +inf) – {2} D. (inf, 6 ) U(4/3, +inf) E. (inf, 6) U (4/3, +inf) – {2}
\(\frac{((x+6) (3x4)^3)}{(x+2)^2} >0\) Critical points: 6, 4/3 Points that to be excluded from the range of x: 2 Using wavy curve method: Range of x: x < 6 or x>4/3 Range of x in interval form: (inf, 6 ) U(4/3, +inf) (Note: x=2 is already excluded) Ans. (D) Seems option (D) is a typo error. It should be inf instead of inf. I used the following reasoning: (x+6) * (3x4)^3 > 0 This means that both the terms, (x+6) and (3x4)^3 should be positive. so, x+6>0 and 3x4>0 (Because only cube of a positive number can be positive) so, x>6 and 3x>4 or x>6 and x>4/3 Is this reasoning incorrect?



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 930
WE: Supply Chain Management (Energy and Utilities)

Re: Find the range of values of x such that ((x+6) (3x4)^3)/(x+2)^2 > 0
[#permalink]
Show Tags
19 Sep 2018, 01:30
srijnasingh wrote: I used the following reasoning:
(x+6) * (3x4)^3 > 0
This means that both the terms, (x+6) and (3x4)^3 should be positive.
so, x+6>0 and 3x4>0 (Because only cube of a positive number can be positive)
so, x>6 and 3x>4
or x>6 and x>4/3
Is this reasoning incorrect?
Hi srijnasingh, a*b>0 , There are 2 cases: a) a>0, b>0 (Your reasoning) b) a<0 , b<0 We have to find out the common interval in which both the cases (a) and (b) are valid. You may check, if x>6 (say x=5) then the expression \((x+6)*(3x4)^3\)=(+ve)*(ve)=(ve), which contradicts question stem. You may try wavycurve method explained thru below link: https://gmatclub.com/forum/wavylineme ... 24319.html
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine




Re: Find the range of values of x such that ((x+6) (3x4)^3)/(x+2)^2 > 0 &nbs
[#permalink]
19 Sep 2018, 01:30






