Author 
Message 
TAGS:

Hide Tags

eGMAT Representative
Joined: 04 Jan 2015
Posts: 2007

Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
[#permalink]
Show Tags
Updated on: 23 Aug 2018, 21:25
Question Stats:
69% (01:15) correct 31% (01:42) wrong based on 93 sessions
HideShow timer Statistics



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2007

Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
[#permalink]
Show Tags
Updated on: 27 Aug 2018, 02:07
Solution Given:• An inequality, \((x+1) (123x)^5 (x+3) (5x) < 0\)
To find:• The range of x, that satisfies the above inequality
Approach and Working: • So, if we observe carefully, the inequality given to us can be written as,
o \((x+1) (123x) (123x)^4 (x+3) (5x) < 0\) • We know that, any number of the form \(N^2\) is always positive, expect for N = 0.
o So, we can say that, \((123x)^4\) is always positive, expect for x = 4, o Thus, the inequality can be written as (x+1) (123x) (x+3) (5x) < 0 • Now, let’s multiply the inequality by 1, twice, to make the coefficients of x, in 123x and 5x, positive
o And, note that the inequality sign does not change as we are multiplying it by 1, twice • Thus, the inequality becomes, (x+1) (3x  12) (x+3) (x  5) < 0 • The zero points of this inequality are x = 1, x = 4, x = 3 and x = 5 • Plot these points on the number line.
o Since, 5 is the greatest among all, the inequality will be positive, for all the points to the right of 5, on the number line o And, it is negative, in the region, between 4 and 5 o It is again positive in the region, between 1 and 4 o And, it is again negative in the region, between 3 and 1 o And, it is positive for all the values of x, less than 3 Therefore, the range of x is 5 < x < 4 and 3 < x < 1 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: 857
WE: Supply Chain Management (Energy and Utilities)

Re: Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
[#permalink]
Show Tags
23 Aug 2018, 06:08
EgmatQuantExpert wrote: Solving inequalities Number Line Method  Practice Question #2
Find the range of values of x such that \((x+1) (123x)^5 (x+3) (5x) < 0.\) A. \(x > 5\) B. \(4 < x < 5\) C. \(3 < x < 2\) D. \((3< x < 1) and (4 < x < 5)\) E. \((x < 3) and (x > 5)\)
\((x+1) (123x)^5 (x+3) (5x) < 0\) Or, \(243\left(x4\right)^5\left(x5\right)\left(x+1\right)\left(x+3\right)<0\) using wavy curve method: \(3<x<1\quad \mathrm{or}\quad \:4<x<5\) Ans. (D)
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Manager
Joined: 18 Apr 2018
Posts: 59

Re: Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
[#permalink]
Show Tags
05 Sep 2018, 05:38
PKN wrote: EgmatQuantExpert wrote: Solving inequalities Number Line Method  Practice Question #2
Find the range of values of x such that \((x+1) (123x)^5 (x+3) (5x) < 0.\) A. \(x > 5\) B. \(4 < x < 5\) C. \(3 < x < 2\) D. \((3< x < 1) and (4 < x < 5)\) E. \((x < 3) and (x > 5)\)
\((x+1) (123x)^5 (x+3) (5x) < 0\) Or, \(243\left(x4\right)^5\left(x5\right)\left(x+1\right)\left(x+3\right)<0\) using wavy curve method: \(3<x<1\quad \mathrm{or}\quad \:4<x<5\) Ans. (D) Hello PKN hope you are having a good day. I attempted this question using the wavy line method as well but didn't answer correctly. To rearrange the expressions in the (xa)(xb) form and i multiplied through by 1 and this changed the inequality sign to >0 but I didn't arrive at the right answer anyway. Could you please elaborate on how you rearranged 5x to x5 without changing the sign of the inequality. Thanks. I'm not a Math guru, just pushing hard for a 700 score. Posted from my mobile device



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 857
WE: Supply Chain Management (Energy and Utilities)

Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
[#permalink]
Show Tags
05 Sep 2018, 11:21
Kem12 wrote: PKN wrote: EgmatQuantExpert wrote: Solving inequalities Number Line Method  Practice Question #2
Find the range of values of x such that \((x+1) (123x)^5 (x+3) (5x) < 0.\) A. \(x > 5\) B. \(4 < x < 5\) C. \(3 < x < 2\) D. \((3< x < 1) and (4 < x < 5)\) E. \((x < 3) and (x > 5)\)
\((x+1) (123x)^5 (x+3) (5x) < 0\) Or, \(243\left(x4\right)^5\left(x5\right)\left(x+1\right)\left(x+3\right)<0\) using wavy curve method: \(3<x<1\quad \mathrm{or}\quad \:4<x<5\) Ans. (D) Hello PKN hope you are having a good day. I attempted this question using the wavy line method as well but didn't answer correctly. To rearrange the expressions in the (xa)(xb) form and i multiplied through by 1 and this changed the inequality sign to >0 but I didn't arrive at the right answer anyway. Could you please elaborate on how you rearranged 5x to x5 without changing the sign of the inequality. Thanks. I'm not a Math guru, just pushing hard for a 700 score. Posted from my mobile deviceHi Kem12, Greetings of the day!! Given f(x)<0. Notice that two of the factors of f(x) are not in the form of \((xa)^n\) rather they are in the form of \((ax)^n\). Our requirement: All factors must present in the form \((xa)^n\), If not, then we have to convert to \((ax)^n\). So, odd forms are: \((123x)^5\) & (5x) 1) \((123x)^5\) can be written as:\(((3x12))^5\) or, \((1)^5*(3x12)^5\) or, \((3)^5*(x4)^5\) Or, \(243(x4)^5\) 2) (5x) can be written as : (x5) Now f(x)= \((x+1) (123x)^5 (x+3) (5x)\)=\((x(1))*{243(x4)^5}*(x(3))*{(x5)}=243(x(1))*(x4)^5*(x(3))*(x5)\) Now simplified expression as per desired form: \(243(x(1))*(x4)^5*(x(3))*(x5)<0\) Or, \((x(1))*(x4)^5*(x(3))*(x5)<0\) Step1critical points: 1, 4,3,5 Step2Arrange the critical points in ascending fashion:3,1,4,5 Step3Draw the curve. Please revert in case of any difficulty in step3. All the best. I am no expert, I am at learning stage.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Manager
Joined: 18 Apr 2018
Posts: 59

Re: Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
[#permalink]
Show Tags
07 Sep 2018, 01:39
Hi PKN, thanks for the explanation. But I just want to confirm whether in the 3rd step, the negative in (x5) and 243(x4)^5 canceled because of even number of negatives, right? If the inequality were just (x+1) (x4) (x5) <0 how will we go about this? Thanks. Posted from my mobile device



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 857
WE: Supply Chain Management (Energy and Utilities)

Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
[#permalink]
Show Tags
07 Sep 2018, 02:17
Kem12 wrote: Hi PKN, thanks for the explanation. But I just want to confirm whether in the 3rd step, the negative in (x5) and 243(x4)^5 canceled because of even number of negatives, right? If the inequality were just (x+1) (x4) (x5) <0 how will we go about this? Thanks. Posted from my mobile deviceHi Kem12, You know , multiplying negative sign an even number of times results positive polarity. 1) ()*()=(+) 2) ()*(+)=() 3) ()*()*()=() flip of sign in inequalities: 1. Whenever you multiply or divide an inequality by a positive number, you must keep the inequality sign. 2. Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign. Refer note(2) above, ' (x+1) (x4) {(x5)} <0 Or, (1)(x+1) (x4) (x5)<0 Or, (1)*(1)(x+1) (x4) (x5) >0*(1) (flip of sign occurs , multiplying both side of inequality by (1)) Or, (x+1) (x4) (x5)>0 ((1)*(1)=+1 and 0*(1)=0) Hope it helps.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Manager
Joined: 18 Apr 2018
Posts: 59

Re: Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
[#permalink]
Show Tags
07 Sep 2018, 05:07
Totally clear now. Thanks PKNPosted from my mobile device



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 857
WE: Supply Chain Management (Energy and Utilities)

Re: Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
[#permalink]
Show Tags
07 Sep 2018, 05:15
Kem12 wrote: Totally clear now. Thanks PKNPosted from my mobile deviceNeed not to mention. (blue color) depicts everything. You are always welcome.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine




Re: Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5 &nbs
[#permalink]
07 Sep 2018, 05:15






