Find all School-related info fast with the new School-Specific MBA Forum

It is currently 16 Apr 2014, 12:08

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the value of integer x? (M27-14)

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 895
Followers: 6

Kudos [?]: 63 [0], given: 33

What is the value of integer x? (M27-14) [#permalink] New post 15 Jan 2013, 23:51
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

34% (01:28) correct 65% (01:35) wrong based on 26 sessions
What is the value of integer x?

(1) 2x^2+9<9x
(2) |x+10|=2x+8
[Reveal] Spoiler: OA
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17283
Followers: 2868

Kudos [?]: 18333 [0], given: 2345

GMAT Tests User CAT Tests
Re: What is the value of integer x? [#permalink] New post 16 Jan 2013, 02:16
Expert's post
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})(x-3)<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 non-negative: 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:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863
xy-plane-71492.html?hilit=solving%20quadratic#p841486

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

VP
VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1080
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Followers: 26

Kudos [?]: 210 [0], given: 65

Re: What is the value of integer x? [#permalink] New post 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
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1125
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 92

Kudos [?]: 998 [0], given: 219

GMAT ToolKit User GMAT Tests User
Re: What is the value of integer x? [#permalink] New post 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
-x-10=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 I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

VP
VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1080
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Followers: 26

Kudos [?]: 210 [0], given: 65

Re: What is the value of integer x? [#permalink] New post 17 Apr 2013, 14:45
thnks that was subtle i frgot to check the range.....
MBA Section Director
User avatar
Joined: 19 Mar 2012
Posts: 1502
Location: India
GPA: 3.8
WE: Marketing (Energy and Utilities)
Followers: 503

Kudos [?]: 1597 [0], given: 624

GMAT ToolKit User Premium Member CAT Tests
Re: M27-14 What is the value of integer x? [#permalink] New post 26 Apr 2013, 13:52
Expert's post
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
_________________

My GMAT Resources
V30-V40: 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 | Over-Represented 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
Veritas Prep Live Online

MBA Section Director
User avatar
Joined: 19 Mar 2012
Posts: 1502
Location: India
GPA: 3.8
WE: Marketing (Energy and Utilities)
Followers: 503

Kudos [?]: 1597 [0], given: 624

GMAT ToolKit User Premium Member CAT Tests
Re: M27-14 What is the value of integer x? [#permalink] New post 26 Apr 2013, 13:57
Expert's post
This could ALSO be solved YOUR way but you have missed the definition of the modulus sign
|x|= x WHEN x >or = 0
|x| = -x WHEN x<0

Now lets come back to the problem,

|x+10| = 2x+8

SO x+10 = 2x+8 when x+10> 0
So it gives x=2
Now lets check: is 2+10 > 0 YES. So this is GOOD
Next
-(x+10) = 2x+8 when x+10<0
it gives x=-6
Lets check: is -6+10 < 0 NO. So this is what you call an extraneous root. Does no good.
_________________

My GMAT Resources
V30-V40: 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 | Over-Represented 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
Veritas Prep Live Online

Manager
Manager
User avatar
Joined: 12 Dec 2012
Posts: 163
Location: Poland
Followers: 3

Kudos [?]: 77 [0], given: 67

Re: M27-14 What is the value of integer x? [#permalink] New post 26 Apr 2013, 14:00
Is this approach completely NOT correct,
or
is this approach just missing the check-step?

What's the earliest stage in solving in which the exclusion can be spotted (by a not-so-pro fellow)?
_________________

If I answered your question with this post, use the motivating power of kudos!

1 KUDOS received
MBA Section Director
User avatar
Joined: 19 Mar 2012
Posts: 1502
Location: India
GPA: 3.8
WE: Marketing (Energy and Utilities)
Followers: 503

Kudos [?]: 1597 [1] , given: 624

GMAT ToolKit User Premium Member CAT Tests
Re: M27-14 What is the value of integer x? [#permalink] New post 26 Apr 2013, 14:03
1
This post received
KUDOS
Expert's post
HumptyDumpty wrote:
Is this approach completely NOT correct,
or
is this approach just missing the check-step?

What's the earliest stage in solving in which the exclusion can be spotted (by a not-so-pro 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.
_________________

My GMAT Resources
V30-V40: 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 | Over-Represented 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
Veritas Prep Live Online

Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17283
Followers: 2868

Kudos [?]: 18333 [0], given: 2345

GMAT Tests User CAT Tests
Re: M27-14 What is the value of integer x? [#permalink] New post 27 Apr 2013, 03:09
Expert's post
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^2-9x+9<0
x^2-\frac{9x}{2}+\frac{9}{2}<0
(x-3)(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 non-negative, hence RHS must also be non-negative: 2x+8\geq0 giving us x\geq-4. 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 MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Senior Manager
Senior Manager
Joined: 06 Aug 2011
Posts: 402
Followers: 2

Kudos [?]: 41 [0], given: 81

GMAT Tests User CAT Tests
Re: What is the value of integer x? [#permalink] New post 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})(x-3)<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 non-negative: 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:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863
xy-plane-71492.html?hilit=solving%20quadratic#p841486

Hope it helps.


this wud be realy easy question..

how did u change this in fraction..?2x2+9<9x.. (x-3/2) (x-3) ... ?? I can change integers..bt this fraction :(
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17283
Followers: 2868

Kudos [?]: 18333 [0], given: 2345

GMAT Tests User CAT Tests
Re: What is the value of integer x? [#permalink] New post 10 Mar 2014, 05:15
Expert's post
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})(x-3)<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 non-negative: 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:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863
xy-plane-71492.html?hilit=solving%20quadratic#p841486

Hope it helps.


this wud be realy easy question..

how did u change this in fraction..?2x2+9<9x.. (x-3/2) (x-3) ... ?? I can change integers..bt this fraction :(


If you cannot factor directly, then solve 2x^2-9x+9=0 to find the roots and factor that way.

Factoring Quadratics: http://www.purplemath.com/modules/factquad.htm

Solving Quadratic Equations: http://www.purplemath.com/modules/solvquad.htm

Hope this helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Intern
Intern
Joined: 26 May 2013
Posts: 15
Followers: 0

Kudos [?]: 2 [0], given: 10

Re: What is the value of integer x? (M27-14) [#permalink] New post 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.
Re: What is the value of integer x? (M27-14)   [#permalink] 11 Mar 2014, 09:01
    Similar topics Author Replies Last post
Similar
Topics:
New posts 8 Experts publish their posts in the topic What is the value of integer x ? MBAUncle 9 20 Apr 2010, 06:04
New posts 1 Experts publish their posts in the topic If x is an integer, what is the value of x? ajitsah 5 02 Jun 2010, 08:48
Popular new posts 7 Experts publish their posts in the topic If x is an integer, what is the value of x? rohitgoel15 15 01 Feb 2012, 21:58
New posts Experts publish their posts in the topic If x is an integer, what is the value of x? srujani 5 01 Jul 2013, 18:54
New posts 1 Experts publish their posts in the topic What is the value of integer x? 3111987 6 21 Jan 2014, 14:48
Display posts from previous: Sort by

What is the value of integer x? (M27-14)

  Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: Bunuel, WoundedTiger



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.