Jun 16 07:00 AM PDT  09:00 AM PDT Get personalized insights and an accurate assessment of your current quant score to achieve your Target Quant Score. Jun 16 09:00 PM PDT  10:00 PM PDT For a score of 4951 (from current actual score of 40+). AllInOne Standard & 700+ Level Questions (150 questions) Jun 18 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, June 18th at 9 pm ET Jun 18 10:00 PM PDT  11:00 PM PDT Send along your receipt from another course or book to info@empowergmat.com and EMPOWERgmat will give you 50% off the first month of access OR $50 off the 3 Month Plan Only available to new students Ends: June 18th Jun 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Jun 22 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.
Author 
Message 
TAGS:

Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7456
GPA: 3.82

Question Stats:
49% (01:21) correct 51% (01:24) wrong based on 69 sessions
HideShow timer Statistics
[ Math Revolution GMAT math practice question] \(x=?\) \(1) x^3+x^2+x=0\) \(2) x=2x\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $149 for 3 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 936

arvind910619 wrote: fskilnik wrote: MathRevolution wrote: [ Math Revolution GMAT math practice question] \(x=?\) \(1) x^3+x^2+x=0\) \(2) x=2x\) \(? = x\) \(\left( 1 \right)\,\,\,x\left( {{x^2} + x + 1} \right) = 0\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \begin{gathered} x = 0 \hfill \\ \,\,\,{\text{OR}} \hfill \\ {x^2} + x + 1 = 0 \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\mathop {\, \Rightarrow }\limits^{\left( * \right)} \,\,\,\,\,x = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.\) \(\left( * \right)\,\,\,\,{x^2} + x + 1 = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\Delta = {\left( 1 \right)^2}  4 \cdot 1 \cdot 1 < 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{x^2} + x + 1 > 0\,\,\,\,{\text{for}}\,\,{\text{all}}\,\,\,\,x\,\,\,\,\,\,\,\,\,\,\,\) \(\left( 2 \right)\,\,\,x =  2x\,\,\,\,\, \Rightarrow \,\,\,\,3x = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. Sir how did you reach the second statement? If the discriminant is negative then the equation involves complex numbers but how to arrive at the equation x^3+x^2+x>1. Can you please explain this concept with diagram. Thanks in advance . Hi arvind910619! Thank you for your interest in my solution. 01. The expression \({x^3} + {x^2} + x\) may be written in the form \(x\left( {{x^2} + x + 1} \right)\) and this last "factorized version" is better for our purposes, because a product is zero if and only if (at least) one of the factors is zero, therefore: \(x\left( {{x^2} + x + 1} \right) = 0\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,x = 0\,\,\,\,{\text{or}}\,\,\,{x^2} + x + 1 = 0\) 02. The equation \({x^2} + x + 1 = 0\) has no real solutions, because its discriminant ("delta") is negative. Therefore the curve (parabola) does not intercept the horizontal axis. From the fact that the parabola is concave upward (see image attached), we are sure \({x^2} + x + 1\) is always positive, by the way. 03. Finally, from the fact that \(x\left( {{x^2} + x + 1} \right) = 0\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,x = 0\,\,\,\,{\text{or}}\,\,\,{x^2} + x + 1 = 0\) and also \({x^2} + x + 1 \ne 0\) for all real values of \(x\), we are sure we must have \(x = 0\) , as mentioned. I hope you got all details! Regards and success in your studies, Fabio. P.S.: If you would like to understand things deeply to be able to perform in the exam in a much higherlevel... try our test drive!
Attachments
12Set18_5t.gif [ 15.5 KiB  Viewed 766 times ]
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



Retired Moderator
Joined: 11 Aug 2016
Posts: 376

MathRevolution wrote: [ Math Revolution GMAT math practice question] \(x=?\) \(1) x^3+x^2+x=0\) \(2) x=2x\) Statement 1: \(x^3+x^2+x=0\) \(x(x^2+x+1)=0\) Now the lease value of\(x^2+x+1\) is \(+\frac{3}{4}\) therefore x must be equal to 0 Sufficient.Statement 2: x=2x 3x=0 x=0 Sufficient.Answer: D
_________________
~R. If my post was of any help to you, You can thank me in the form of Kudos!! Applying to ISB ? Check out the ISB Application Kit.



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 936

MathRevolution wrote: [ Math Revolution GMAT math practice question] \(x=?\) \(1) x^3+x^2+x=0\) \(2) x=2x\) \(? = x\) \(\left( 1 \right)\,\,\,x\left( {{x^2} + x + 1} \right) = 0\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \begin{gathered} x = 0 \hfill \\ \,\,\,{\text{OR}} \hfill \\ {x^2} + x + 1 = 0 \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\mathop {\, \Rightarrow }\limits^{\left( * \right)} \,\,\,\,\,x = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.\) \(\left( * \right)\,\,\,\,{x^2} + x + 1 = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\Delta = {\left( 1 \right)^2}  4 \cdot 1 \cdot 1 < 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{x^2} + x + 1 > 0\,\,\,\,{\text{for}}\,\,{\text{all}}\,\,\,\,x\,\,\,\,\,\,\,\,\,\,\,\) \(\left( 2 \right)\,\,\,x =  2x\,\,\,\,\, \Rightarrow \,\,\,\,3x = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



Senior Manager
Joined: 15 Oct 2017
Posts: 309
GMAT 1: 560 Q42 V25 GMAT 2: 570 Q43 V27 GMAT 3: 710 Q49 V39

IMO D.
1) This gives us x(x^2 + x + 1) = 0, so either x=0 or x^2 + x + 1. But there is no value of x that fits the equation as x^2 can either be +ve or 0, therefore the only value possible for x=0. Sufficient.
2) The only value that fits the equation is x=0. Sufficient.



VP
Status: Learning
Joined: 20 Dec 2015
Posts: 1007
Location: India
Concentration: Operations, Marketing
GPA: 3.4
WE: Engineering (Manufacturing)

fskilnik wrote: MathRevolution wrote: [ Math Revolution GMAT math practice question] \(x=?\) \(1) x^3+x^2+x=0\) \(2) x=2x\) \(? = x\) \(\left( 1 \right)\,\,\,x\left( {{x^2} + x + 1} \right) = 0\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \begin{gathered} x = 0 \hfill \\ \,\,\,{\text{OR}} \hfill \\ {x^2} + x + 1 = 0 \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\mathop {\, \Rightarrow }\limits^{\left( * \right)} \,\,\,\,\,x = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.\) \(\left( * \right)\,\,\,\,{x^2} + x + 1 = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\Delta = {\left( 1 \right)^2}  4 \cdot 1 \cdot 1 < 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{x^2} + x + 1 > 0\,\,\,\,{\text{for}}\,\,{\text{all}}\,\,\,\,x\,\,\,\,\,\,\,\,\,\,\,\) \(\left( 2 \right)\,\,\,x =  2x\,\,\,\,\, \Rightarrow \,\,\,\,3x = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. Sir how did you reach the second statement? If the discriminant is negative then the equation involves complex numbers but how to arrive at the equation x^3+x^2+x>1. Can you please explain this concept with diagram. Thanks in advance .
_________________
Please give kudos if you found my answers useful



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7456
GPA: 3.82

=> Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first. Condition 1) \(x^3+x^2+x=0\) \(=> x(x^2+x+1)=0\) \(=> x = 0\) since \(x^2+x+1 ≠ 0\) Condition 1) is sufficient. Condition 2) \(x = 2x\) \(=> 3x = 0\) \(=> x = 0\) Condition 2) is sufficient. Therefore, D is the answer. Answer: D If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $149 for 3 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



Intern
Joined: 22 Mar 2012
Posts: 3

This Question should mention that x is real, then only Statement 1 is sufficient.
Otherwise x = 0 or complex number. It indicates that Statement 1 is not sufficient.










