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

It is currently 28 Jul 2016, 08:08
GMAT Club Tests

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

For how many ordered pairs (x, y) that are solutions of the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

3 KUDOS received
Manager
Manager
User avatar
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 127
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
Followers: 12

Kudos [?]: 257 [3] , given: 210

For how many ordered pairs (x, y) that are solutions of the [#permalink]

Show Tags

New post 14 Jan 2011, 16:40
3
This post received
KUDOS
23
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (02:23) correct 40% (01:30) wrong based on 1039 sessions

HideShow timer Statistics

\(2x + y = 12\)
\(|y| \leq 12\)

For how many ordered pairs (x, y) that are solutions of the system above are x and y both integers?

A. 7
B. 10
C. 12
D. 13
E. 14
[Reveal] Spoiler: OA
Expert Post
13 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 6761
Location: Pune, India
Followers: 1877

Kudos [?]: 11563 [13] , given: 219

Re: Quant Rev. #152 [#permalink]

Show Tags

New post 14 Jan 2011, 17:28
13
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
tonebeeze wrote:
152.

\(2x + y = 12\)
\(|y| \leq 12\)

For how many ordered pairs (x, y) that are solutions of the system above are x and y both integers?

a. 7
b. 10
c. 12
d. 13
e. 14


The solution of \(|y| \leq 12\) is straight forward.
\(-12 \leq y \leq 12\)
(If you are not comfortable with this, check out my blog post:
http://www.veritasprep.com/blog/2011/01/quarter-wit-quarter-wisdom-do-what-dumbledore-did/

If both x and y have to be integers, y should be an integer and hence can take any value from the set {-12, -11, -10 ... 10, 11, 12} i.e. any one of 25 values (these are 25 values -12 to -1 (12 values), 0, 1 to 12 (another 12 values)) 13 of them are even and 12 of them are odd.

\(2x + y = 12\)
Every time y is even, x will be integer. e.g. y = 12, x = 0 (because x = (12 - even)/2 will be an integer)
Every time y is odd, x will be non-integer e.g. y = 1, x = 5.5 (because x = (12 - odd)/2 will not be an integer)

Therefore, for 13 values, x and y both will be integers.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

3 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2021
Followers: 156

Kudos [?]: 1527 [3] , given: 376

Re: 152. Algebra Absolute value [#permalink]

Show Tags

New post 10 Mar 2011, 11:15
3
This post received
KUDOS
Sol:
|y| <= 12
Means;
-12<=y<=12

2x + y = 12
x = (12-y)/2

x will be integers for y=even; because even-even = even and even is always divisible by 2.

We need to find out how many even integers are there between -12 and 12

((12-(-12))/2)+1 = (24/2)+1 = 12+1 = 13

Ans: "D"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34106
Followers: 6098

Kudos [?]: 76734 [5] , given: 9981

Re: 152. Algebra Absolute value [#permalink]

Show Tags

New post 10 Mar 2011, 11:19
5
This post received
KUDOS
Expert's post
Baten80 wrote:
2x + y = 12
|y| <= 12

152. For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?
A. 7
B. 10
C. 12
D. 13
E. 14


Given: \(-12\leq{y}\leq{12}\) and \(2x+y=12\) --> \(y=12-2x=2(6-x)=even\), (as \(x\) must be an integer). Now, there are 13 even numbers in the range from -12 to 12, inclusive each of which will give an integer value of \(x\).

Answer: D.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1353
Followers: 16

Kudos [?]: 209 [1] , given: 10

Re: 152. Algebra Absolute value [#permalink]

Show Tags

New post 16 Jun 2011, 00:00
1
This post received
KUDOS
-12<= y <=12
gives 0<=x <=12

thus 13 values in total.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Manager
Manager
avatar
Joined: 26 Jul 2011
Posts: 125
Location: India
WE: Marketing (Manufacturing)
Followers: 1

Kudos [?]: 88 [0], given: 15

Re: Quant Rev. #152 [#permalink]

Show Tags

New post 07 Sep 2012, 00:22
Hi Karishma

Using the number properties this indeed is very convenient to solve. I was wondering can we substitute y = 12 - 2x in the inequality and solve for the possible values of x.
Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 6761
Location: Pune, India
Followers: 1877

Kudos [?]: 11563 [2] , given: 219

Re: Quant Rev. #152 [#permalink]

Show Tags

New post 09 Sep 2012, 21:21
2
This post received
KUDOS
Expert's post
ratinarace wrote:
Hi Karishma

Using the number properties this indeed is very convenient to solve. I was wondering can we substitute y = 12 - 2x in the inequality and solve for the possible values of x.


Certainly and it is quick too.

y = 12 - 2x
Whenever x is an integer, y will be an integer. So if we can solve for integral values of x, the number of values we get will be the number of solutions.

\(|y| \leq 12\)

\(|12 - 2x| \leq 12\)

\(|x - 6| \leq 6\)

From 6, x should be at a distance less than or equal to 6. So x will lie from 0 to 12 i.e. 13 values. (Check http://www.veritasprep.com/blog/2011/01 ... edore-did/ if this is not clear)

There are 13 solutions.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Manager
Manager
avatar
Joined: 26 Jul 2011
Posts: 125
Location: India
WE: Marketing (Manufacturing)
Followers: 1

Kudos [?]: 88 [0], given: 15

Re: For how many ordered pairs (x, y) that are solutions of the [#permalink]

Show Tags

New post 10 Sep 2012, 10:36
Thanks Karishma..Wonderful explaination
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 6761
Location: Pune, India
Followers: 1877

Kudos [?]: 11563 [0], given: 219

Re: For how many ordered pairs (x, y) that are solutions of the [#permalink]

Show Tags

New post 25 Sep 2012, 02:50
Expert's post
Responding to a pm:
Changing the sign within the mod has no impact on anything outside the mod.

\(|6 - x| \leq 12\) is same as
\(|x - 6| \leq 12\)

Think about it: Whether you write |x| or |-x|, it is the same.
|6| = |-6|

So for every value of x,
|x - 6| = |6 - x|
So you don't need to flip the inequality sign.

|x - 6| and - |x - 6| are of course different. If you change |x - 6| to - |x - 6|, you will need to flip the inequality sign.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34106
Followers: 6098

Kudos [?]: 76734 [0], given: 9981

Re: For how many ordered pairs (x, y) that are solutions of the [#permalink]

Show Tags

New post 04 Jul 2013, 01:44
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Abolute Values: math-absolute-value-modulus-86462.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

3 KUDOS received
Intern
Intern
avatar
Joined: 05 May 2013
Posts: 27
GMAT 1: 730 Q50 V39
GRE 1: 1480 Q800 V680
Followers: 0

Kudos [?]: 22 [3] , given: 5

Re: For how many ordered pairs (x, y) that are solutions of the [#permalink]

Show Tags

New post 05 Jul 2013, 03:54
3
This post received
KUDOS
\(y=12-2x=2*(6-x).\)
Since \(|y| \leq 12 , -12 \leq y \leq 12\) . Substituting for y from above, \(-6 \leq (6-x) \leq 6.\). This reduces to \(x \geq 0\) and \(x \leq 12.\) Including 0 and 12 there are thus 13 integer solutions.
Answer is (d)
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 472
Followers: 3

Kudos [?]: 136 [1] , given: 134

Re: For how many ordered pairs (x, y) that are solutions of the [#permalink]

Show Tags

New post 09 Jul 2013, 16:34
1
This post received
KUDOS
2x+y=12
|y|<=12

For how many ordered pairs (x, y) that are solutions of the system above are x and y both integers?

y=12-2x
|y|<=12
|12-2x| <= 12
12 - 2x <= 12
-2x <= 0
x>=0

-(12-2x) <= 12
-12+2x <= 12
2x <= 24
x<=12

13 solutions between 0 and 12 inclusive.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 10632
Followers: 496

Kudos [?]: 130 [0], given: 0

Premium Member
Re: For how many ordered pairs (x, y) that are solutions of the [#permalink]

Show Tags

New post 08 Aug 2014, 07:41
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

Intern
Intern
User avatar
Joined: 17 May 2012
Posts: 49
Followers: 0

Kudos [?]: 8 [0], given: 126

Re: For how many ordered pairs (x, y) that are solutions of the [#permalink]

Show Tags

New post 24 Nov 2014, 22:20
Hi Moderators,

Does this qualify as a 700 level question, I think it should be in the lower range?

Thanks
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34106
Followers: 6098

Kudos [?]: 76734 [0], given: 9981

Re: For how many ordered pairs (x, y) that are solutions of the [#permalink]

Show Tags

New post 25 Nov 2014, 04:47
Expert's post
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 10632
Followers: 496

Kudos [?]: 130 [0], given: 0

Premium Member
Re: For how many ordered pairs (x, y) that are solutions of the [#permalink]

Show Tags

New post 22 Dec 2015, 15:29
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

Intern
Intern
avatar
Joined: 17 Nov 2013
Posts: 26
Followers: 0

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

GMAT ToolKit User
Re: For how many ordered pairs (x, y) that are solutions of the [#permalink]

Show Tags

New post 09 Apr 2016, 14:15
abs 12 = -12 all the way to 12, which is 25 integers including "0".

y= 2(6-x) = even.

So y = even. and y is equal the 25 number range. How many possible even numbers are in that range?

Answer is 13 possible even y numbers including zero "0".
Senior Manager
Senior Manager
avatar
Joined: 22 Jun 2014
Posts: 390
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
Followers: 10

Kudos [?]: 118 [0], given: 90

Premium Member CAT Tests
Re: For how many ordered pairs (x, y) that are solutions of the [#permalink]

Show Tags

New post 12 Apr 2016, 00:23
tonebeeze wrote:
\(2x + y = 12\)
\(|y| \leq 12\)

For how many ordered pairs (x, y) that are solutions of the system above are x and y both integers?

A. 7
B. 10
C. 12
D. 13
E. 14


|y| <= 12 means range of y is -12 <= Y <= +12. which means Y can take any of the value in the set (-12, -11, -10......-1,0,1.....10,11,12).

now that we are given 2x + y = 12, y = 12 - 2x

we can include all the integer values for X as a solution for y = 12 - 2x as long as y falls in the above range mentioned. Such values of X are (0,1,2....12). 13 is the count for this set. Answer is D.
_________________

---------------------------------------------------------------
Target - 720-740
helpful post means press '+1' for Kudos!
http://gmatclub.com/forum/information-on-new-gmat-esr-report-beta-221111.html
http://gmatclub.com/forum/list-of-one-year-full-time-mba-programs-222103.html

Re: For how many ordered pairs (x, y) that are solutions of the   [#permalink] 12 Apr 2016, 00:23
    Similar topics Author Replies Last post
Similar
Topics:
6 Experts publish their posts in the topic If g(x) = 2^x + x, how many solutions satisfy the equation g(x) = 2? TeamGMATIFY 4 07 Feb 2016, 19:10
6 For how many integers pair (x,y) satisfies the result Celestial09 5 18 Jan 2015, 15:01
31 Experts publish their posts in the topic For how many ordered pairs (x , y) that are solutions of the Bunuel 4 11 Mar 2014, 23:54
2 Experts publish their posts in the topic For how many ordered pairs (x , y) that are solutions of the jamifahad 7 17 Jul 2011, 00:05
27 Experts publish their posts in the topic For how many ordered pairs (x , y) that are solutions of the Balvinder 8 24 May 2007, 06:07
Display posts from previous: Sort by

For how many ordered pairs (x, y) that are solutions of the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| 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®.