Author 
Message 
TAGS:

Hide Tags

Director
Joined: 25 Oct 2008
Posts: 596
Location: Kolkata,India

What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
29 Oct 2009, 02:30
5
This post received KUDOS
53
This post was BOOKMARKED
Question Stats:
52% (03:05) correct
48% (02:08) wrong based on 626 sessions
HideShow timer Statistics
What is the sum of all possible solutions of the equation x + 4^2  10x + 4 = 24? A. 16 B. 14 C. 12 D. 8 E. 6 Please help me find my mistake: Let \(x+4=y\) Now we get two cases, Case1: \(y^210y24=0\) Solving we get 2,12 Case2: \(y^2+10y24=0\) where we get 6,4
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
http://gmatclub.com/forum/countdownbeginshasended8548340.html#p649902



Math Expert
Joined: 02 Sep 2009
Posts: 39609

What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
29 Oct 2009, 03:11
11
This post received KUDOS
Expert's post
11
This post was BOOKMARKED
tejal777 wrote: What is the sum of all roots of the equation \(x + 4^2  10x + 4 = 24?\)
Please help me find my mistake: Let \(x+4=y\) Now we get two cases, Case1: \(y^210y24=0\) Solving we get 2,12
Case2: \(y^2+10y24=0\) where we get 6,4 This is a good question. Let me show you how I've solved, maybe it'll help: APPROACH #1:We have x + 4^2  10x + 4 = 24 x + 4 flip sign at x=4, so we should check two ranges: 1. x<=4 (x+4)^2 + 10x+40=24 ((x+4)^2 as it's square will be the same in both ranges) x^2+8x+16+10x+16=0 > x^2+18x+32=0. Solving for x: x=16 or x=2. x=2 won't work as x<=4 (see the defined range), hence we have only one solution for this range x=16. 2. x>4 (x+4)^2  10x40=24 > x^22x48=0. Solving for x: x=6 or x=8. x=6 wont work as x>4, hence we have only one root for this range x=8. 16+8=8. APPROACH #2:x + 4^2  10x + 4 = 24 Solve for \(x+4 \) > \(x+4 =12\) OR \(x+4 =2\), BUT as absolute value never negative thus 2 is out. Solving \(x+4 =12\) > \(x_1=8\) or \(x_2=16\) > \(x_1+x_2=816=8\). Answer: the sum of all roots of the equation is 8.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Affiliations: CA  India
Joined: 27 Oct 2009
Posts: 45
Location: India
Schools: ISB  Hyderabad, NSU  Singapore

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
29 Oct 2009, 06:37
3
This post received KUDOS
Correct me:
I solved from where the author of the problem left it. that is: y = 2 or 12 Hence, considereding + values of x+4, i.e. x+4 = 2 or 12, which gives us x = 6 or 8
Considering  values of x+4, i.e. x4 = 6 or 4, which gives us x = 2 or 8.
Sum of all, 6+82+8 = 8.



Current Student
Joined: 14 Aug 2009
Posts: 112
Schools: MIT Sloan 2012

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
29 Oct 2009, 13:32
23
This post received KUDOS
4
This post was BOOKMARKED
I solve it by replacing x+4 as k
so k^210k24=0 (k12)(k+2) = 0 k = 12 or 2 k can not be 2 because it is an absolute value so k = 12 = x+4 then x+4 = 12, x = 8 x+4 = 12, x = 16 sum is 8



Director
Joined: 01 Apr 2008
Posts: 881
Name: Ronak Amin
Schools: IIM Lucknow (IPMX)  Class of 2014

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
31 Oct 2009, 05:11
IMO 16.
Take y = x+4  and solve for y, then solve for x+4 , we get x=16,8,2,6, sum = 16. OA?



Math Expert
Joined: 02 Sep 2009
Posts: 39609

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
31 Oct 2009, 21:59
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Economist wrote: IMO 16. Take y = x+4  and solve for y, then solve for x+4 , we get x=16,8,2,6, sum = 16. OA? Economist the problem is that 2 and 6 doesn't satisfy the equation. Thus only two values of x are left 16 and 8: 16+8=8. Consider this: x + 4^2  10x + 4 = 24 Solve for \(x+4 \) > \(x+4 =12\) OR \(x+4 =2\), BUT as absolute value never negative thus 2 is out. Solving \(x+4 =12\) > \(x_1=8\) or \(x_2=16\) > \(x_1+x_2=816=8\). Hope it's clear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Retired Moderator
Joined: 02 Sep 2010
Posts: 803
Location: London

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
07 Oct 2010, 12:19
mxgms wrote: jzd wrote: I solve it by replacing x+4 as k
so k^210k24=0 (k12)(k+2) = 0 k = 12 or 2 k can not be 2 because it is an absolute value so k = 12 = x+4 then x+4 = 12, x = 8 x+4 = 12, x = 16 sum is 8 I liked that approach, is this always true? thanks. Not sure what part you are questioning about (1) You can always do a variable switch in an equation (x+4=y) (2) Any expression is always greater than or equal to 0
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings



Manager
Status: ISB, Hyderabad
Joined: 25 Jul 2010
Posts: 173
WE 1: 4 years Software Product Development
WE 2: 3 years ERP Consulting

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
08 Oct 2010, 01:56
8 for me. Once you solve the QE you get x+4 = 6 or 4. 4 is not possible so take the case x+4 = 6 which means x = 10 or 2. So the sum is 8.
_________________
AD



Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 326

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
08 Dec 2010, 09:38
shrouded1 wrote: mxgms wrote: jzd wrote: I solve it by replacing x+4 as k
so k^210k24=0 (k12)(k+2) = 0 k = 12 or 2 k can not be 2 because it is an absolute value so k = 12 = x+4 then x+4 = 12, x = 8 x+4 = 12, x = 16 sum is 8 I liked that approach, is this always true? thanks. Not sure what part you are questioning about (1) You can always do a variable switch in an equation (x+4=y) (2) Any expression is always greater than or equal to 0 Shrouded: can we do this question by the approach you have mentioned in the walker post. .i.e xa<b => ab<x<a+b or this approach is for specific questions. Thanks
_________________
I'm the Dumbest of All !!



VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1327

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
14 Jun 2011, 02:24
3
This post received KUDOS
x+4 = y gives y^2 10y 24 = 0 y = 2 and 12 x+4 = 12 gives x = 8 and 16. sum is 8.
_________________
Visit  http://www.sustainablesphere.com/ Promote Green Business,Sustainable Living and Green Earth !!



Manager
Status: Do till 740 :)
Joined: 13 Jun 2011
Posts: 110
Concentration: Strategy, General Management
GPA: 3.6
WE: Consulting (Computer Software)

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
17 Apr 2012, 07:04
Hi Buneuel,
Please help me with the basic understanding of the mod probs
when we have
x+4= x5
We can two solutions
x+4= x5 and x+4=x+5
but in this problem why do we check for ranges. I mean what s the step by step approach to attack a modulus question? a few examples would be grateful



Math Expert
Joined: 02 Sep 2009
Posts: 39609

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
18 Apr 2012, 04:12



Intern
Status: That which doesn't break me, makes me stronger.
Joined: 27 Aug 2012
Posts: 31
Location: India
Concentration: Economics
GPA: 3.33
WE: Project Management (Consulting)

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
08 Sep 2012, 01:10
2
This post received KUDOS
tejal777 wrote: What is the sum of all roots of the equation \(x + 4^2  10x + 4 = 24?\)
Please help me find my mistake: Let \(x+4=y\) Now we get two cases, Case1: \(y^210y24=0\) Solving we get 2,12
Case2: \(y^2+10y24=0\) where we get 6,4 Let's try this with number line. x+4 = y ==> y^210y24=0 ==> y = 12 or y = 2 Substitute the value of y we have x+4=12 or x+4= 2 Hmm.. can mod be a negative number? NO ==> Eliminate x+4= 2 Now we are left only with x+4=12 Lets draw a number line .................................x+4 ................................. <> 16 ..............................(4) ................................8 Thus, two possible roots are 16 and +8 Sum of roots => 16+8=8
_________________
Thanks
Vishwa



Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
08 Sep 2012, 03:20
1
This post received KUDOS
tejal777 wrote: What is the sum of all roots of the equation \(x + 4^2  10x + 4 = 24?\)
Please help me find my mistake: Let \(x+4=y\) Now we get two cases, Case1: \(y^210y24=0\) Solving we get 2,12
Case2: \(y^2+10y24=0\) where we get 6,4 Case 1: You mean \(y\geq{0}\), right? Because \(x+4=y\) only if \(y\) is nonnegative. Only \(y=12\) is acceptable. From \(x+4=12\) we obtain \(x=8\) and \(x=16.\) Case 2: Now \(y<0,\) so \(x+4=y\). But \(x+4^2=(y)^2\) is still \(y^2\), doesn't matter that \(y\) is negative! Your equation should be \(y^2+10y24=0,\) solutions \(2, 12\). Now only \(12\) is acceptable (\(y\) must be negative), and we obtain the same solutions as in Case 1. It would have been better to denote \(x+4=y\geq{0}\) (see other posts above). Then \(x+4^2=y^2\), and for the quadratic equation \(y^2+10y24=0\) you choose only the nonnegative root, then find \(x\)...
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Intern
Joined: 25 Sep 2012
Posts: 1

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
25 Sep 2012, 10:42
tejal777 wrote: What is the sum of all roots of the equation \(x + 4^2  10x + 4 = 24?\)
24 ends with 4 and \(10x+4\) ends with 0. So \(x+4^2\) should end with 4. Options below 0 are out because of the absolute value. Let's take the squares ending with 4: \(2^2; 8^2; 12^2; 18^2\) etc... We find \(12^2  10*12 = 24\). From here \(x_1=8\) and \(x_2=16\), and the sum: 8.



Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GPA: 3.23

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
06 Dec 2012, 03:12
It also took me time to understand how to get solutions for absolute values. But thanks to GMATClub... Here is a detailed explanation on how you could solve for the roots http://burnoutorbreathe.blogspot.com/2012/12/howtogetsolutionforabsolutevalues.htmlMy answer: 8
_________________
Impossible is nothing to God.



Manager
Joined: 03 Oct 2009
Posts: 62

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
03 Feb 2013, 19:02
Have a question. There are two scenarios  1. x<=4
2. x>4
How do we determine whether to include equal sign (=) in first equation or second equation or does it not matter and can be included in any?



Math Expert
Joined: 02 Sep 2009
Posts: 39609

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
04 Feb 2013, 04:12



Manager
Joined: 04 Mar 2013
Posts: 88
Location: India
Concentration: General Management, Marketing
GPA: 3.49
WE: Web Development (Computer Software)

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
03 Jul 2013, 07:43
tejal777 wrote: What is the sum of all roots of the equation \(x + 4^2  10x + 4 = 24?\)
Please help me find my mistake: Let \(x+4=y\) Now we get two cases, Case1: \(y^210y24=0\) Solving we get 2,12
Case2: \(y^2+10y24=0\) where we get 6,4 dude here the key remember Bodmas childhood rule now keep lx+3 l as a k and re write equation we get k = 12 or k= 2 and then now substitute the mod value and remember mod can be negative or positive, as we dont know x and we are finding all possible values we get 8 and 16 once and also we get 2 and 6 i guess so now add them all wish u a very good luck and make a wish for me too logic and basic = magic in gmat



Senior Manager
Joined: 13 May 2013
Posts: 469

Re: What is the sum of all possible solutions of the equation x + 4^2  [#permalink]
Show Tags
03 Jul 2013, 14:51
What is the sum of all roots of the equation: x+4^2  10x+4 = 24
I. x+4 = y
y^2  10y = 24 y^2  10y = 24 y^2  10y 24 =0 (y12)(y+2) y=12, y=2 OR y^2  (10y) = 24 y^2 + 10y 24 =0 (y+12)(y2) y=12, y = 2
Y = 10 or Y=10 INSUFFICIENT
II. y^2 + 10y  24 = 0 This tells us nothing about X in the stem.
I+II) This validates one of the two solutions available for x+4^2  10x+4 = 24 (when we know what x+4 is from #1) SUFFICIENT
(C)
(I am a bit confused, is this a DS question?)




Re: What is the sum of all possible solutions of the equation x + 4^2 
[#permalink]
03 Jul 2013, 14:51



Go to page
1 2 3
Next
[ 43 posts ]




