Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1267
Concentration: Strategy, General Management

What is the value of x? [#permalink]
Show Tags
30 May 2010, 02:52
1
This post received KUDOS
4
This post was BOOKMARKED
Question Stats:
61% (01:09) correct 39% (01:17) wrong based on 315 sessions
HideShow timer Statistics



Current Student
Affiliations: ?
Joined: 20 Jul 2009
Posts: 189
Location: Africa/Europe
Schools: Kellogg; Ross ($$); Tuck

Re: Absolute Value [#permalink]
Show Tags
30 May 2010, 03:24
(1) 63x = x2 <=> 63x = x2 or 63x = (x2)
solving these equations you will have x=2 or x = 2 then (1) is sufficient. X = 2
(2) 5x+3 = 2x+9 or 5x+3 = (2x+9)
3x = 6 or 7x = 12 we will have two values for x. (2) is not sufficient
Would pick (A)



Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1267
Concentration: Strategy, General Management

Re: Absolute Value [#permalink]
Show Tags
30 May 2010, 03:39
OA is "A". My query:: 6  3x = x  2 As a module is always positive, hence we can say that x2>0 If x2>0 then it implies x>2. But our answer is showing that x=2 What am I missing here??
_________________
[ From 470 to 680My Story ] [ My Last Month Before Test ] [ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]
I Can, I Will
GMAT Club Premium Membership  big benefits and savings



CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2700
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35

Re: Absolute Value [#permalink]
Show Tags
30 May 2010, 03:45
1
This post received KUDOS
madeinafrica wrote: (1) 63x = x2 <=> 63x = x2 or 63x = (x2)
solving these equations you will have x=2 or x = 2 then (1) is sufficient. X = 2
(2) 5x+3 = 2x+9 or 5x+3 = (2x+9)
3x = 6 or 7x = 12 we will have two values for x. (2) is not sufficient
Would pick (A) I agree A is right. But do not neglect 2nd statement just because it gave 2 answers. 5x+3 = (2x+ 9) only when 5x+3 <0 so the answer obtained 7x=12 must satisfy this domain. In this case it is satisfying thus making it insufficient. Imagine a case when the 2nd solution does not satisfy the domain, in that case it will be sufficient. So do not neglect the statement just because it gave two answers.
_________________
Fight for your dreams :For all those who fear from Verbal lets give it a fight
Money Saved is the Money Earned
Jo Bole So Nihaal , Sat Shri Akaal
Support GMAT Club by putting a GMAT Club badge on your blog/Facebook
GMAT Club Premium Membership  big benefits and savings
Gmat test review : http://gmatclub.com/forum/670to710alongjourneywithoutdestinationstillhappy141642.html



Math Expert
Joined: 02 Sep 2009
Posts: 44282

Re: Absolute Value [#permalink]
Show Tags
30 May 2010, 04:13
3
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Hussain15 wrote: OA is "A".
My query::
6  3x = x  2
As a module is always positive, hence we can say that x2>0 If x2>0 then it implies x>2. But our answer is showing that x=2
What am I missing here?? Red part is not correct: absolute value is never negative (absolute value \(\geq{0}\)). Stepbystep solution: (1) \(6  3x = x  2\) > as LHS (left hand side) is absolute value, which is never negative (absolute value \(\geq{0}\)), RHS also must be \(\geq{0}\) > \(x2\geq{0}\) > \(x\geq{2}\). For \(x\geq{2}\), \(6  3x=6+3x\), so \(6  3x = x  2\) becomes \(6+3x=x2\) > \(x=2\). Sufficient. (2) \(5x + 3 = 2x + 9\). (note that by the same logic as above \(x\geq\frac{9}{2}=4.5\)) One check point \(x=\frac{3}{5}\) (check point(s) the value of x when absolute value equals to zero). \(x\leq{\frac{3}{5}}\) > \(5x3=2x+9\) > \(x=\frac{12}{7}\)  valid solution as \(\frac{9}{2}<\frac{12}{7}<\frac{3}{5}\); \(x>{\frac{3}{5}}\) > \(5x+3=2x+9\) > \(x=2\)  valid solution as \(\frac{9}{2}<\frac{3}{5}<2\); Two valid solutions. Not sufficient. Answer: A. Hope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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
Status: The last round
Joined: 18 Jun 2009
Posts: 1267
Concentration: Strategy, General Management

Re: Absolute Value [#permalink]
Show Tags
30 May 2010, 04:28



Manager
Joined: 20 Apr 2010
Posts: 141
Location: I N D I A

Re: Absolute Value [#permalink]
Show Tags
31 May 2010, 07:26
very nicely explained Bunuel... +1.. thanks



Intern
Joined: 20 Apr 2013
Posts: 16

Re: Absolute Value [#permalink]
Show Tags
27 May 2013, 05:20
Bunuel wrote: Hussain15 wrote: OA is "A".
My query::
6  3x = x  2
As a module is always positive, hence we can say that x2>0 If x2>0 then it implies x>2. But our answer is showing that x=2
What am I missing here?? Red part is not correct: absolute value is never negative (absolute value \(\geq{0}\)). Stepbystep solution: (1) \(6  3x = x  2\) > as LHS (left hand side) is absolute value, which is never negative (absolute value \(\geq{0}\)), RHS also must be \(\geq{0}\) > \(x2\geq{0}\) > \(x\geq{2}\). For \(x\geq{2}\), \(6  3x=6+3x\), so \(6  3x = x  2\) becomes \(6+3x=x2\) > \(x=2\). Sufficient. (2) \(5x + 3 = 2x + 9\). (note that by the same logic as above \(x\geq\frac{9}{2}=4.5\)) One check point \(x=\frac{3}{5}\) (check point(s) the value of x when absolute value equals to zero). \(x\leq{\frac{3}{5}}\) > \(5x3=2x+9\) > \(x=\frac{12}{7}\)  valid solution as \(\frac{9}{2}<\frac{12}{7}<\frac{3}{5}\); \(x>{\frac{3}{5}}\) > \(5x+3=2x+9\) > \(x=2\)  valid solution as \(\frac{9}{2}<\frac{3}{5}<2\); Two valid solutions. Not sufficient. Answer: A. Hope it helps. I am not satisfied with the solution. How do we solve modulus, we take two cases, 1)if (63x)>0 then given equation comes out to be 63x=x2 which gives x=2 ,but we are considering the case when 63x>0 or x<2, hence this soln x=2 is not possible. 2) When we consider (63x)<0 then equation comes out to be 6+3x= x2 which again gives x=2 , but this time we are considering 63x<0 or x>2, hence this soln x=2 is not feasible in this case also. So according to me answer is E.



Math Expert
Joined: 02 Sep 2009
Posts: 44282

Re: Absolute Value [#permalink]
Show Tags
27 May 2013, 05:26
gchawla123 wrote: Bunuel wrote: Hussain15 wrote: OA is "A".
My query::
6  3x = x  2
As a module is always positive, hence we can say that x2>0 If x2>0 then it implies x>2. But our answer is showing that x=2
What am I missing here?? Red part is not correct: absolute value is never negative (absolute value \(\geq{0}\)). Stepbystep solution: (1) \(6  3x = x  2\) > as LHS (left hand side) is absolute value, which is never negative (absolute value \(\geq{0}\)), RHS also must be \(\geq{0}\) > \(x2\geq{0}\) > \(x\geq{2}\). For \(x\geq{2}\), \(6  3x=6+3x\), so \(6  3x = x  2\) becomes \(6+3x=x2\) > \(x=2\). Sufficient. (2) \(5x + 3 = 2x + 9\). (note that by the same logic as above \(x\geq\frac{9}{2}=4.5\)) One check point \(x=\frac{3}{5}\) (check point(s) the value of x when absolute value equals to zero). \(x\leq{\frac{3}{5}}\) > \(5x3=2x+9\) > \(x=\frac{12}{7}\)  valid solution as \(\frac{9}{2}<\frac{12}{7}<\frac{3}{5}\); \(x>{\frac{3}{5}}\) > \(5x+3=2x+9\) > \(x=2\)  valid solution as \(\frac{9}{2}<\frac{3}{5}<2\); Two valid solutions. Not sufficient. Answer: A. Hope it helps. I am not satisfied with the solution. How do we solve modulus, we take two cases, 1)if (63x)>0 then given equation comes out to be 63x=x2 which gives x=2 ,but we are considering the case when 63x>0 or x<2, hence this soln x=2 is not possible. 2) When we consider (63x)<0 then equation comes out to be 6+3x= x2 which again gives x=2 , but this time we are considering 63x<0 or x>2, hence this soln x=2 is not feasible in this case also. So according to me answer is E. Note that OA for this questio is A, not E. Next, to check whether x=2 is a root of 6  3x = x  2 just substitute x=2 into it: 6  3*2 = 0 = 2  2. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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



Manager
Status: Working hard to score better on GMAT
Joined: 02 Oct 2012
Posts: 89
Location: Nepal
Concentration: Finance, Entrepreneurship
GPA: 3.83
WE: Accounting (Consulting)

Re: What is the value of x? [#permalink]
Show Tags
29 May 2013, 21:05
Hussain15 wrote: What is the value of x?
(1) 6  3x = x  2
(2) 5x + 3 = 2x + 9 Hi Bunuel, cann't it be solved by the following approach? Statement 1: 63x=x2 X=2 Again, (63x)=x2 ie 6+3x=x2 X= 2 Similar solution from in both scenario. Hence sufficient. Statement 2: Similar process and we will get x= 12/7 and 2. Two different solutions. hence Insufficient. Ans: A Atal Pandit
_________________
Do not forget to hit the Kudos button on your left if you find my post helpful.



Math Expert
Joined: 02 Sep 2009
Posts: 44282

Re: What is the value of x? [#permalink]
Show Tags
30 May 2013, 01:33



Senior Manager
Joined: 13 May 2013
Posts: 456

Re: What is the value of x? [#permalink]
Show Tags
04 Jun 2013, 17:15
It seems that I have solved some abs. value problems by finding what makes the equation in the abs. value sign = to zero, so for #2, why do we find what makes the equation outside the abs. value sign = to zero? In other words...
5x + 3 = 2x + 9. ==> When x=4.5 2x+9 = 2(4.5)+9 = 9+9 = 0.
Thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 44282

Re: What is the value of x? [#permalink]
Show Tags
04 Jun 2013, 17:33



Intern
Joined: 22 Feb 2013
Posts: 9

Re: What is the value of x? [#permalink]
Show Tags
04 Jun 2013, 21:29
How did you get "for X> or = 2, 6x3 = 6x+3" ?



Math Expert
Joined: 02 Sep 2009
Posts: 44282

Re: What is the value of x? [#permalink]
Show Tags
05 Jun 2013, 00:35



Director
Joined: 25 Apr 2012
Posts: 722
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: What is the value of x? [#permalink]
Show Tags
05 Jun 2013, 01:40
Bunuel wrote: atalpanditgmat wrote: Hussain15 wrote: What is the value of x?
(1) 6  3x = x  2
(2) 5x + 3 = 2x + 9 Hi Bunuel, can't it be solved by the following approach? Statement 1: 63x=x2 X=2 Again, (63x)=x2 ie 6+3x=x2 X= 2 Similar solution from in both scenario. Hence sufficient. Statement 2: Similar process and we will get x= 12/7 and 2. Two different solutions. hence Insufficient. Ans: A Atal Pandit Yes, we can do this way too. Typo: 5x + 3 = 2x + 9 > x=12/7 or x=2. Hello Bunuel, I followed the same approach but looking at solution given by you, It is actually not required . I have seen some question types where in we just check for one condition (X>/0 or X<0) and we can conclude the answer (Like you just did in this one) Are there particular question type where in your approach to this question will work. For ex  Some expression in x = x some no. Again since LHS >/0, we can say xsome no >/ > x>/ some no. This can be helpful in saving time by avoiding checking expression for 2 possible case of x (<0,>0) Thanks Mridul
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Math Expert
Joined: 02 Sep 2009
Posts: 44282

Re: What is the value of x? [#permalink]
Show Tags
05 Jun 2013, 01:43
mridulparashar1 wrote: Bunuel wrote: atalpanditgmat wrote: Yes, we can do this way too.
Typo: 5x + 3 = 2x + 9 > x=12/7 or x=2. Hello Bunuel, I followed the same approach but looking at solution given by you, It is actually not required . I have seen some question types where in we just check for one condition (X>/0 or X<0) and we can conclude the answer (Like you just did in this one) Are there particular question type where in your approach to this question will work. For ex  Some expression in x = x some no. Again since LHS >/0, we can say xsome no >/ > x>/ some no. This can be helpful in saving time by avoiding checking expression for 2 possible case of x (<0,>0) Thanks Mridul Yes, in such kind of questions this approach might be helpful.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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



Senior Manager
Joined: 13 May 2013
Posts: 456

Re: What is the value of x? [#permalink]
Show Tags
05 Jun 2013, 11:54
I just wanted to make sure the way I solved this problem is correct:
What is the value of x?
1. 63x=x2 2. 5x+3=2x+9
1. 63x is positive when x<2. For example, if x=1 then 63x = 63(1) = 3. 63x is negative when x>2. For example, if x=3 then 63(x) = 63(3) = 3.
For positive cases: 63x=x2 ==> x=2 For negative cases: 6+3x=x2 ==> x=2
My issue here is that for the positive case x must be less than 2 and for the negative case x must be greater than 2 but for both cases here, I got x =2. The answer is sufficient, but I thought that for the cases to be sufficient the results had to be in line with what x= (for example, for the positive case here, x=2 but before I found that X must be LESS than 2 for 63x to be positive)
Could someone explain? I see why #2 fails (because for the positive case, 2 is greater than 3/5 but for the negative case, 7/12 is NOT greater than 3/5 but I am a bit lost with #1)
Thanks!



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1118
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: What is the value of x? [#permalink]
Show Tags
05 Jun 2013, 12:02
1
This post received KUDOS
WholeLottaLove wrote: I just wanted to make sure the way I solved this problem is correct:
What is the value of x?
1. 63x=x2 2. 5x+3=2x+9
1. 63x is positive when x<2. For example, if x=1 then 63x = 63(1) = 3. 63x is negative when x>2. For example, if x=3 then 63(x) = 63(3) = 3.
For positive cases: 63x=x2 ==> x=2 For negative cases: 6+3x=x2 ==> x=2
My issue here is that for the positive case x must be less than 2 and for the negative case x must be greater than 2 but for both cases here, I got x =2. The answer is sufficient, but I thought that for the cases to be sufficient the results had to be in line with what x= (for example, for the positive case here, x=2 but before I found that X must be LESS than 2 for 63x to be positive)
Could someone explain? I see why #2 fails (because for the positive case, 2 is greater than 3/5 but for the negative case, 7/12 is NOT greater than 3/5 but I am a bit lost with #1)
Thanks! You have a point here. When you study a function, an abs value, you correctly define where is positive or negative \(x>a\) positve for example \(x<a\) negative for example As you see the value \(a\) is not contained in neither interval... How do we solve this? Just put an \(=\) sign under one of the above inequalities, so \(x\geq{}a\) and \(x<a\)  or \(x>a\) and \(x\leq{}a\). Where you put the sign, it doesn not matter, the result will not change. So just rewrite your equation into For positive cases (\(x\leq{2}\)): 63x=x2 ==> x=2 VALIDFor negative cases (\(x>2\)): 6+3x=x2 ==> x=2 and you have the result! Nothing changes, everything you did is absolutely correct, just put an \(=\) sign in one of the intervals Hope it's clear
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Senior Manager
Joined: 13 May 2013
Posts: 456

Re: What is the value of x? [#permalink]
Show Tags
05 Jun 2013, 12:18
Ok...I see that. But isn't the whole point to test cases where 63x is positive and negative? if X=2 then 63x is neither positive or negative, it's just zero.




Re: What is the value of x?
[#permalink]
05 Jun 2013, 12:18



Go to page
1 2 3
Next
[ 42 posts ]



