Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50002

If x^2 − 12 = x, which of the following could be the value of x?
[#permalink]
Show Tags
29 Apr 2016, 02:36
Question Stats:
68% (01:21) correct 32% (01:25) wrong based on 1012 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Aug 2009
Posts: 6961

Re: If x^2 − 12 = x, which of the following could be the value of x?
[#permalink]
Show Tags
29 Apr 2016, 02:46
Bunuel wrote: If x^2 − 12 = x, which of the following could be the value of x?
A. –4 B. –3 C. 1 D. 2 E. 3 Hi, In MODULUS, always be careful of EQUATING two sides.. Here ONE important point is that LHS is positive, so RHS will also be positive, SO x will be +IVE.. A and B are eliminated.. Now try to substitute remaining choices C. 1 x^2 − 12 = x.. 1^212=1.. 11=1.. NO D. 2 x^2 − 12 = x.. 2^212=2.. 7=2.. NO E. 3 x^2 − 12 = x.. 3^212=3.. 3=3.. YES ans E
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor




Manager
Joined: 17 Oct 2015
Posts: 107
Location: India
Concentration: Finance
GMAT 1: 690 Q47 V37 GMAT 2: 700 Q44 V41
WE: Corporate Finance (Commercial Banking)

Re: If x^2 − 12 = x, which of the following could be the value of x?
[#permalink]
Show Tags
29 Apr 2016, 12:14
well, a mod here indicates that x is positive. Eliminate a and b immediately. Now, you may substitute values themselves..none of them except E fits the bill.




Intern
Joined: 11 Aug 2013
Posts: 26
Location: India
Concentration: Finance, General Management
GPA: 3.23
WE: Information Technology (Investment Banking)

Re: If x^2 − 12 = x, which of the following could be the value of x?
[#permalink]
Show Tags
29 Apr 2016, 03:01
Another easy way and timesaver will be to substitute the values directly in the equation. so A: (4)^212=4 ne 4 => FALSE B: (3)^212=3 ne 3 => FALSE C: (1)^212=11 ne 1 => FALSE D: (2)^212=8 ne 2=> FALSE E: (3)^212=3 eq 3 => TRUE
_________________
Thanks Sindbad  Click +1 Kudos if my post helped...



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4094
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If x^2 − 12 = x, which of the following could be the value of x?
[#permalink]
Show Tags
29 Apr 2016, 12:52
Sindbad wrote: Another easy way and timesaver will be to substitute the values directly in the equation. so A: (4)^212=4 ne 4 => FALSE B: (3)^212=3 ne 3 => FALSE C: (1)^212=11 ne 1 => FALSE D: (2)^212=8 ne 2=> FALSE E: (3)^212=3 eq 3 => TRUE Substituting the value works in most of the Problems of GMAT and is a sureshot way... Same opinion , answer will be (E)
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Director
Joined: 04 Jun 2016
Posts: 569

If x^2 − 12 = x, which of the following could be the value of x?
[#permalink]
Show Tags
25 Jul 2016, 02:23
Bunuel wrote: If x^2 − 12 = x, which of the following could be the value of x?
A. –4 B. –3 C. 1 D. 2 E. 3 \(x^2 − 12 = x\) \(x^2 − 12\)cannot be negative; anything that comes out of mod is always positive so \(x^2 − 12>0\) Out of our options A= 4 B= 3 cannot be the right answer because none of them are greater than 0 Now only Option C=1 or D=2 or E=3 are contenders for right answers. A quick Cursory crude calculation will tell you that E is the right choice \(3^212=3\) \(912=3\) \(3=3\) \(3=3\) ANSWER IS E
_________________
Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE : 17th SEPTEMBER 2016. .. 16 March 2017  I am back but for all purposes please consider me semiretired.



VP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1267
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Consulting)

Re: If x^2 − 12 = x, which of the following could be the value of x?
[#permalink]
Show Tags
12 Mar 2018, 05:12
chetan2u wrote: Bunuel wrote: If x^2 − 12 = x, which of the following could be the value of x?
A. –4 B. –3 C. 1 D. 2 E. 3 Hi, In MODULUS, always be careful of EQUATING two sides.. Here ONE important point is that LHS is positive, so RHS will also be positive, SO x will be +IVE.. A and B are eliminated.. Now try to substitute remaining choices C. 1 x^2 − 12 = x.. 1^212=1.. 11=1.. NO D. 2 x^2 − 12 = x.. 2^212=2.. 7=2.. NO E. 3 x^2 − 12 = x.. 3^212=3.. 3=3.. YES ans E Hi chetan2u, Though I know the substitution method, but instinctively I went to solve the the equations given. Can you help me how it can be done with critical value method. I am stuck up.
_________________
"Do not watch clock; Do what it does. KEEP GOING."



VP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1267
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Consulting)

Re: If x^2 − 12 = x, which of the following could be the value of x?
[#permalink]
Show Tags
12 Mar 2018, 10:36
Abhishek009 wrote: Sindbad wrote: Another easy way and timesaver will be to substitute the values directly in the equation. so A: (4)^212=4 ne 4 => FALSE B: (3)^212=3 ne 3 => FALSE C: (1)^212=11 ne 1 => FALSE D: (2)^212=8 ne 2=> FALSE E: (3)^212=3 eq 3 => TRUE Substituting the value works in most of the Problems of GMAT and is a sureshot way... Same opinion , answer will be (E)Can you tell me the algebraic way? I am stuck up a bit. QZ
_________________
"Do not watch clock; Do what it does. KEEP GOING."



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3896
Location: United States (CA)

Re: If x^2 − 12 = x, which of the following could be the value of x?
[#permalink]
Show Tags
13 Mar 2018, 16:57
Bunuel wrote: If x^2 − 12 = x, which of the following could be the value of x?
A. –4 B. –3 C. 1 D. 2 E. 3 Since we see that the left side of the equation must be positive, the right side also must be positive. Thus, A and B cannot be correct since the absolute value of any quantity can’t be negative. Let’s substitute in the remaining answer choices: 1^2  12  = 1 ? We see this is not true. 2^2  12 = 2 ? We see this is not true 3^3  12 = 3 ? We see this is true. Answer: E
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 02 Feb 2017
Posts: 1

Re: If x^2 − 12 = x, which of the following could be the value of x?
[#permalink]
Show Tags
13 Mar 2018, 18:01
QZ wrote: Abhishek009 wrote: Sindbad wrote: Another easy way and timesaver will be to substitute the values directly in the equation. so A: (4)^212=4 ne 4 => FALSE B: (3)^212=3 ne 3 => FALSE C: (1)^212=11 ne 1 => FALSE D: (2)^212=8 ne 2=> FALSE E: (3)^212=3 eq 3 => TRUE Substituting the value works in most of the Problems of GMAT and is a sureshot way... Same opinion , answer will be (E)Can you tell me the algebraic way? I am stuck up a bit. QZ I'll help. First of all, x is the outcome of an absolute value so x=>0 Then we have to analyze the two possible scenarios of what we have inside the absolute value so that we can eliminate the absolute value: 1. X^212=>0, x^2=>12 So that x=<sqrt(12) or x=>sqrt(12) The only possible scenario according to the constraint that x can take any non negative value is the second one so we can say that x has to be greater than or equal to approximately 3.4 Then we would have the quadratic equation x^2x12=0 with roots x=3 or x=4 we eliminate the first one because x can not take negative values. 2. X^212<0, x^2<12 So that sqrt(12)<x<sqrt(12) Then according to the initial constraint 0<x<3.4 Then we would have the quadratic equation x^2+x12=0 with roots x=3 or x=4 We eliminate the second one because x can not take negative values. So from the first scenario x=4 and from the second one x=3, those are the two solutions for the absolute value equation. I hope it is clear. Regards César Orihuela Posted from my mobile device



VP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1267
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Consulting)

Re: If x^2 − 12 = x, which of the following could be the value of x?
[#permalink]
Show Tags
20 Mar 2018, 22:05
Thanks Cesar to clarify. Posted from my mobile device
_________________
"Do not watch clock; Do what it does. KEEP GOING."



VP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1267
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Consulting)

Re: If x^2 − 12 = x, which of the following could be the value of x?
[#permalink]
Show Tags
28 Apr 2018, 00:08
Bunuel wrote: If x^2 − 12 = x, which of the following could be the value of x?
A. –4 B. –3 C. 1 D. 2 E. 3 The algebraic way:
x^2 − 12 = x
Case 1:
x^2  12 = x
x^2  x = 12
x (x  1) = 12
We need two consecutive numbers whose products is 12.
So 4(41) = 12
4*3 = 12
But we don't have "4" in the answer choices.
Case 2:
x^2  12 = x
x^2 + x = 12
x (x + 1) = 12
We need two consecutive numbers whose products is 12.
3 (3 + 1) = 12
3*4 = 12
12 = 12
So x = 3
(E)
_________________
"Do not watch clock; Do what it does. KEEP GOING."



Intern
Joined: 28 Sep 2017
Posts: 4

Re: If x^2 − 12 = x, which of the following could be the value of x?
[#permalink]
Show Tags
23 May 2018, 20:13
chetan2u wrote: Bunuel wrote: If x^2 − 12 = x, which of the following could be the value of x?
A. –4 B. –3 C. 1 D. 2 E. 3 Hi, In MODULUS, always be careful of EQUATING two sides.. Here ONE important point is that LHS is positive, so RHS will also be positive, SO x will be +IVE.. A and B are eliminated.. Now try to substitute remaining choices C. 1 x^2 − 12 = x.. 1^212=1.. 11=1.. NO D. 2 x^2 − 12 = x.. 2^212=2.. 7=2.. NO E. 3 x^2 − 12 = x.. 3^212=3.. 3=3.. YES ans E Hello, is there any algebraic way to solve this? can u plz explain Posted from my mobile device



VP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1267
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Consulting)

Re: If x^2 − 12 = x, which of the following could be the value of x?
[#permalink]
Show Tags
23 May 2018, 20:45
AvinashT2303 wrote: chetan2u wrote: Bunuel wrote: If x^2 − 12 = x, which of the following could be the value of x?
A. –4 B. –3 C. 1 D. 2 E. 3 Hi, In MODULUS, always be careful of EQUATING two sides.. Here ONE important point is that LHS is positive, so RHS will also be positive, SO x will be +IVE.. A and B are eliminated.. Now try to substitute remaining choices C. 1 x^2 − 12 = x.. 1^212=1.. 11=1.. NO D. 2 x^2 − 12 = x.. 2^212=2.. 7=2.. NO E. 3 x^2 − 12 = x.. 3^212=3.. 3=3.. YES ans E Hello, is there any algebraic way to solve this? can u plz explain Posted from my mobile deviceHERE IT IS: https://gmatclub.com/forum/ifx212x ... l#p2052961Please read the complete thread before raising queries. Hope this helps. QZ
_________________
"Do not watch clock; Do what it does. KEEP GOING."




Re: If x^2 − 12 = x, which of the following could be the value of x? &nbs
[#permalink]
23 May 2018, 20:45






