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

 It is currently 29 Sep 2016, 11:04

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 20 Mar 2005
Posts: 170
Followers: 2

Kudos [?]: 67 [1] , given: 0

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

### Show Tags

24 May 2007, 06:07
1
KUDOS
11
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

62% (02:10) correct 38% (01:38) wrong based on 350 sessions

### HideShow timer Statistics

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?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-how-many-ordered-pairs-x-y-that-are-solutions-of-the-110687.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Mar 2014, 23:57, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Intern
Joined: 20 Apr 2007
Posts: 12
Followers: 0

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

### Show Tags

24 May 2007, 09:28
Can you explain why the Y values go from -12 to 12? I a little new at this forum. I originally got 12 total possibilities.
Senior Manager
Joined: 11 Jun 2006
Posts: 254
Followers: 3

Kudos [?]: 8 [1] , given: 0

### Show Tags

24 May 2007, 10:17
1
KUDOS
2x + y = 12

|y| <= 12 means that y can be anything between 12 and -12 inclusive. Absolute values always indicates a range of numbers... this is the easy way to think about abs. values.

Ok, now you've narrowed down the answer choices to 25 possible numbers... which doesn't help you with the answers given. Next you need to find a way of eliminating more answer choices...

Simplify 2x + y = 12 to

x + y/2 = 3

Now looking at that, you know y has to be an even number to yield an integer... so the initial pool of 25 numbers is now narrowed down to 13, hence the answer.
Manager
Joined: 18 Sep 2006
Posts: 58
Followers: 1

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

### Show Tags

24 May 2007, 19:57
This is a good question, coz I did not pay attention to the "(x,y) that will yield x and y to be integers" part of the question, so I was stuck with the answer being 25 and was stumped by the choices.
Good job you guys....i guess I should read the question clearly
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 158

Kudos [?]: 1595 [8] , given: 376

Re: PS-ordered pairs (x , y) [#permalink]

### Show Tags

07 Sep 2011, 00:04
8
KUDOS
2
This post was
BOOKMARKED
Balvinder wrote:
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?
A. 7
B. 10
C. 12
D. 13
E. 14

|y| <= 12
-12<=y<=12

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

To find number of integer pairs, we just need to find even number of y's, because even y will make "(12-y)" even as well and only even numbers divide by 2 evenly to give an integer.

e.g.
x=(12-y)/2; for y=1; x=(12-1)/2=11/2=5.5(Not an integer because y is odd)
x=(12-y)/2; for y=0; x=(12-0)/2=12/2=6(An integer because y is even)

Thus, if we find the number of even y's, we should be good.

-12<=y<=12
What is the first even number greater than or equal to -12?
-12
What is the last even number smaller than or equal to +12?
+12

$$Count=\frac{Last Even-First Even}{2}+1$$

$$Count=\frac{12-(-12)}{2}+1=12+1=13$$

Ans: "D"
_________________
Manager
Joined: 06 Jun 2011
Posts: 157
Followers: 1

Kudos [?]: 56 [1] , given: 15

Re: PS-ordered pairs (x , y) [#permalink]

### Show Tags

07 Sep 2011, 02:02
1
KUDOS
Fluke ,
The approach was awesome
+1
abhijit
VP
Joined: 24 Jul 2011
Posts: 1067
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 112

Kudos [?]: 495 [0], given: 18

Re: PS-ordered pairs (x , y) [#permalink]

### Show Tags

07 Sep 2011, 05:34
1
This post was
BOOKMARKED
Number of ordered pairs = number of integers between 12 and 0 (both inclusive)
= 13
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11743
Followers: 529

Kudos [?]: 149 [0], given: 0

Re: 2x + y = 12 |y| <= 12 For how many ordered pairs (x [#permalink]

### Show Tags

09 Mar 2014, 17:11
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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 34899
Followers: 6501

Kudos [?]: 83049 [1] , given: 10134

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

### Show Tags

09 Mar 2014, 23:58
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
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?

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 $$x$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-how-many-ordered-pairs-x-y-that-are-solutions-of-the-110687.html
_________________
Re: For how many ordered pairs (x , y) that are solutions of the   [#permalink] 09 Mar 2014, 23:58
Similar topics Replies Last post
Similar
Topics:
2 How many solutions are possible for the inequality | x - 1 | + | x - 6 3 12 Sep 2016, 11:02
6 For how many integers pair (x,y) satisfies the result 5 18 Jan 2015, 15:01
34 For how many ordered pairs (x , y) that are solutions of the 4 11 Mar 2014, 23:54
2 For how many ordered pairs (x , y) that are solutions of the 7 17 Jul 2011, 00:05
60 For how many ordered pairs (x, y) that are solutions of the 17 14 Jan 2011, 16:40
Display posts from previous: Sort by