January 21, 2019 January 21, 2019 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday. January 22, 2019 January 22, 2019 10:00 PM PST 11:00 PM PST In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.
Author 
Message 
TAGS:

Hide Tags

Director
Joined: 03 Sep 2006
Posts: 780

What is the value of integer x? (M2714)
[#permalink]
Show Tags
15 Jan 2013, 23:51
Question Stats:
26% (02:13) correct 74% (02:21) wrong based on 282 sessions
HideShow timer Statistics
What is the value of integer x? (1) 2x^2+9<9x (2) x+10=2x+8
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 52343

Re: What is the value of integer x?
[#permalink]
Show Tags
16 Jan 2013, 02:16




Director
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 934
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

Re: What is the value of integer x?
[#permalink]
Show Tags
17 Apr 2013, 13:46
I understand that statement 1 is sufficient....bt Statement 2, i tried solving and gt two different answers....
lx+10l = 2x+8 when x>0 x+10 =2x+8 x=2 Another case when x<0 (x+10) =2x+8 x=6
Am i wrong while solving the mod....
Help me with statement 2
Archit



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1060
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: What is the value of integer x?
[#permalink]
Show Tags
17 Apr 2013, 13:58
Hi Archit143, Lets see statement 2: (2) x+10=2x+8 We have to analyze the two cases so 1) Range: \(x+10>0, x>10\) \(x+10=2x+8\) \(x=2\) \(2\) is in the range we are analyzing (>10) so 2 is a solution 2) Range: \(x+10<0,x<10\) \(x10=2x+8\) \(x=6\) \(6\) is OUT of the range we are considering (<10) so is NOT a possible solution Let me know if 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]



Director
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 934
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

Re: What is the value of integer x?
[#permalink]
Show Tags
17 Apr 2013, 14:45
thnks that was subtle i frgot to check the range.....



Current Student
Joined: 19 Mar 2012
Posts: 4361
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: M2714 What is the value of integer x?
[#permalink]
Show Tags
26 Apr 2013, 13:52
HumptyDumpty wrote: My way: standard procedure: 1st: \(x+10=2x+8\) \(x=2\) OR 2nd:\((x+10)=2x+8\) \(x=6\) the condition \(x=i\) is met: Insufficient.
This approach is NOT correct. Always be sure to plug back the solutions for equations with modulus sign the values that you have found are x = 2 and x = 6 ONLY x=2 satisfies the given condition For X = 6 LHS = x+10 = 4 RHS = 2x + 8 = 4 SO x = 6 is NO GOOD This is happening because you have found the roots of \((x+10)^2\) = \((2x+8)^2\)
_________________
Have an MBA application Question? ASK ME ANYTHING!
My Stuff: Four Years to 760  MBA Trends for Indian Applicants
My GMAT Resources V30V40: How to do it!  GMATPrep SC  GMATPrep CR  GMATPrep RC  Critical Reasoning Megathread  CR: Numbers and Statistics  CR: Weaken  CR: Strengthen  CR: Assumption  SC: Modifier  SC: Meaning  SC: SV Agreement  RC: Primary Purpose  PS/DS: Numbers and Inequalities  PS/DS: Combinatorics and Coordinates
My MBA Resources Everything about the MBA Application  OverRepresented MBA woes  Fit Vs Rankings  Low GPA: What you can do  Letter of Recommendation: The Guide  Indian B Schools accepting GMAT score  Why MBA?
My Reviews How I got into five schools from zero  Applicant Lab Review Veritas Prep Live Online



Current Student
Joined: 19 Mar 2012
Posts: 4361
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: M2714 What is the value of integer x?
[#permalink]
Show Tags
26 Apr 2013, 13:57



Manager
Joined: 12 Dec 2012
Posts: 151
Location: Poland

Re: M2714 What is the value of integer x?
[#permalink]
Show Tags
26 Apr 2013, 14:00
Is this approach completely NOT correct, or is this approach just missing the checkstep? What's the earliest stage in solving in which the exclusion can be spotted (by a notsopro fellow)?
_________________
If I answered your question with this post, use the motivating power of kudos!



Current Student
Joined: 19 Mar 2012
Posts: 4361
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: M2714 What is the value of integer x?
[#permalink]
Show Tags
26 Apr 2013, 14:03
HumptyDumpty wrote: Is this approach completely NOT correct, or is this approach just missing the checkstep?
What's the earliest stage in solving in which the exclusion can be spotted (by a notsopro fellow)? Well you just need to know the definition of modulus sure x = 8 will give you 8 and 8 as solution but that will not hold true when the RHS also has a variable when both sides consist variable go by the definition. You have only taken a part of the definition. You need to look at the entire scene as explained in the second post.
_________________
Have an MBA application Question? ASK ME ANYTHING!
My Stuff: Four Years to 760  MBA Trends for Indian Applicants
My GMAT Resources V30V40: How to do it!  GMATPrep SC  GMATPrep CR  GMATPrep RC  Critical Reasoning Megathread  CR: Numbers and Statistics  CR: Weaken  CR: Strengthen  CR: Assumption  SC: Modifier  SC: Meaning  SC: SV Agreement  RC: Primary Purpose  PS/DS: Numbers and Inequalities  PS/DS: Combinatorics and Coordinates
My MBA Resources Everything about the MBA Application  OverRepresented MBA woes  Fit Vs Rankings  Low GPA: What you can do  Letter of Recommendation: The Guide  Indian B Schools accepting GMAT score  Why MBA?
My Reviews How I got into five schools from zero  Applicant Lab Review Veritas Prep Live Online



Math Expert
Joined: 02 Sep 2009
Posts: 52343

Re: M2714 What is the value of integer x?
[#permalink]
Show Tags
27 Apr 2013, 03:09
HumptyDumpty wrote: What is the value of integer x?
1) \(2x^2+9<9x\) 2) \(x+10=2x+8\)
1) is clear: compute the quadratic expression, consider the scope of values and the condition x=i:
\(2x^29x+9<0\) \(x^2\frac{9x}{2}+\frac{9}{2}<0\) \((x3)(x\frac{3}{2})<0\)
the sums in parentheses must have opposite signs, so:
\(\frac{3}{2}<x<3\)
consider the condition \(x=i\):
\(x=2\) Sufficient.
2) is not clear:
\(x+10=2x+8\)
My way: standard procedure: 1st: \(x+10=2x+8\) \(x=2\) OR 2nd:\((x+10)=2x+8\) \(x=6\) the condition \(x=i\) is met: Insufficient.
The original explanation: (2) \(x+10=2x+8\). The left hand side (LHS) is an absolute value, which is always nonnegative, hence RHS must also be nonnegative: \(2x+8\geq0\) giving us \(x\geq4\). Now, for this range \(x+10\) is positive, hence\(x+10=x+10\). So, \(x+10=2x+8\) can be written as \(x+10=2x+8\), solving for \(x\) gives \(x=2\). Sufficient.
Noting that \(2x+8\geq0\) excludes the negative value and leaves off only one value. But what the heck is the mechanics behind this problem that makes the the good old way of solving inequalities insufficiently precise here? Merging similar topics. The way you call "standard procedure" is not complete. When expanding \(x+10=2x+8\) you should consider x<10 range and x>=10 range: \(x<10\) > \((x+10)=2x+8\) > \(x=6\). Discard this solution since it's not in the range \(x<10\). \(x\geq{10}\) > \(x+10=2x+8\) > \(x=2\). 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



Senior Manager
Joined: 06 Aug 2011
Posts: 336

Re: What is the value of integer x?
[#permalink]
Show Tags
10 Mar 2014, 04:47
Bunuel wrote: LM wrote: What is the value of integer x?
(1) 2x^2+9<9x (2) x+10=2x+8 What is the value of integer x?(1) 2x^2+9<9x > factor qudratics: \((x\frac{3}{2})(x3)<0\) > roots are \(\frac{3}{2}\) and 3 > "<" sign indicates that the solution lies between the roots: \(1.5<x<3\) > since there only integer in this range is 2 then \(x=2\). Sufficient. (2) x+10=2x+8 > LHS is an absolute value, which is always non negative, hence RHS must also be nonnegative: \(2x+8\geq{0}\) > \(x\geq{4}\), for this range \(x+10\) is positive hence \(x+10=x+10\) > \(x+10=2x+8\) > \(x=2\). Sufficient. Answer: D. Check this for more on solving inequalities like the one in the first statement: x24x94661.html#p731476 inequalitiestrick91482.htmleverythingislessthanzero108884.html?hilit=extreme#p868863xyplane71492.html?hilit=solving%20quadratic#p841486Hope it helps. this wud be realy easy question.. how did u change this in fraction..?2x2+9<9x.. (x3/2) (x3) ... ?? I can change integers..bt this fraction
_________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !



Math Expert
Joined: 02 Sep 2009
Posts: 52343

Re: What is the value of integer x?
[#permalink]
Show Tags
10 Mar 2014, 05:15
sanjoo wrote: Bunuel wrote: LM wrote: What is the value of integer x?
(1) 2x^2+9<9x (2) x+10=2x+8 What is the value of integer x?(1) 2x^2+9<9x > factor qudratics: \((x\frac{3}{2})(x3)<0\) > roots are \(\frac{3}{2}\) and 3 > "<" sign indicates that the solution lies between the roots: \(1.5<x<3\) > since there only integer in this range is 2 then \(x=2\). Sufficient. (2) x+10=2x+8 > LHS is an absolute value, which is always non negative, hence RHS must also be nonnegative: \(2x+8\geq{0}\) > \(x\geq{4}\), for this range \(x+10\) is positive hence \(x+10=x+10\) > \(x+10=2x+8\) > \(x=2\). Sufficient. Answer: D. Check this for more on solving inequalities like the one in the first statement: x24x94661.html#p731476 inequalitiestrick91482.htmleverythingislessthanzero108884.html?hilit=extreme#p868863xyplane71492.html?hilit=solving%20quadratic#p841486Hope it helps. this wud be realy easy question.. how did u change this in fraction..?2x2+9<9x.. (x3/2) (x3) ... ?? I can change integers..bt this fraction If you cannot factor directly, then solve 2x^29x+9=0 to find the roots and factor that way. Factoring Quadratics: http://www.purplemath.com/modules/factquad.htmSolving Quadratic Equations: http://www.purplemath.com/modules/solvquad.htmHope this 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



Manager
Joined: 26 May 2013
Posts: 95

Re: What is the value of integer x? (M2714)
[#permalink]
Show Tags
11 Mar 2014, 09:01
Is this a type of question one can expect on the GMAT ?
The factoring of the quadratic isn't "clean", as opposed to one that can be solved using integers.



Senior Manager
Joined: 17 Sep 2013
Posts: 338
Concentration: Strategy, General Management
WE: Analyst (Consulting)

What is the value of integer x ? I 2x^2 + 9 < 9x II x+10
[#permalink]
Show Tags
12 Jun 2014, 10:38
What is the value of integer x ? I 2x^2 + 9 < 9x II x+10 = 2x+8 Bunuel or Karishma..Please explain how to approach statement II I got the answer with my standard approach i.e opening the absolute bracket in two different cases  x less than and greater than 0
_________________
Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..



Math Expert
Joined: 02 Sep 2009
Posts: 52343

Re: What is the value of integer x ? I 2x^2 + 9 < 9x II x+10
[#permalink]
Show Tags
12 Jun 2014, 10:45



Director
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 772
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)

Re: What is the value of integer x ? I 2x^2 + 9 < 9x II x+10
[#permalink]
Show Tags
12 Jun 2014, 10:59
What is the value of integer x ? I 2x^2 + 9 < 9x II x+10 = 2x+8 I took some time but solved it my way. IMO D. Stmt I. we can make equation \(2x^2 9x + 9 < 0\) solve for X = 1.5, 3  2 is the only integer in between satisfies the relation. Sufficient. II. Square both side. \((x+10) ^2=(2x+8)^2\) \(x^2 + 4x  12 = 0\) solve for X = 2, 6  substitute values back to original equation, only 2 satisfies the relation. Sufficient.
_________________
Piyush K
 Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison Don't forget to press> Kudos My Articles: 1. WOULD: when to use?  2. All GMATPrep RCs (New) Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".



Senior Manager
Joined: 17 Sep 2013
Posts: 338
Concentration: Strategy, General Management
WE: Analyst (Consulting)

Re: What is the value of integer x? (M2714)
[#permalink]
Show Tags
12 Jun 2014, 12:13
Sad..I carelessly took X>0 instead of X>10.. and hence both the answers for statement II fitted in Nice question
_________________
Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..



Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 89
Location: Canada
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)

What is the value of integer x? (M2714)
[#permalink]
Show Tags
03 Mar 2015, 15:54
Dear Bunuel, I always have problem with factoring Quadratics so, I tried to use the way that I found in the link 1 that you add.Factoring Quadratics: http://www.purplemath.com/modules/factquad.htmHowever, I did not get the right answer. that is how I answered the question: The coefficients are a = 2, b = –9, and c = 9, so ac = 18. Since 18 is positive, I need two factors that are either both positive or else both negative . Since –9 is negative, I need the factors both to be negative. The pairs of factors for 18 are 3 and 6. Since 6+(3) = –9, I will use –6 and –3 so the roots are (2x3) and (x6) which mean x=3/2 , x=6 so based on statement 1 x=6 based on statemebt 2 x=2 what I missed here ? What is the wrong in my way?
_________________
Click +1 Kudos if my post helped



NonHuman User
Joined: 09 Sep 2013
Posts: 9462

Re: What is the value of integer x? (M2714)
[#permalink]
Show Tags
01 Apr 2018, 12:14
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: What is the value of integer x? (M2714) &nbs
[#permalink]
01 Apr 2018, 12:14






