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# 2x + y = 12 |y| <= 12 For how many ordered pairs (x , y)

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Manager
Joined: 08 Aug 2008
Posts: 229
2x + y = 12 |y| <= 12 For how many ordered pairs (x , y) [#permalink]

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10 Nov 2008, 05:20
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

I'm getting 13 as ans however not sure what ordered pairs mean..
no OE guys, lets discuss...
Manager
Joined: 30 Sep 2008
Posts: 111

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10 Nov 2008, 05:34
|y| <= 12 <=> $$-12 <= y <= 12$$

2x + y = 12 => x = y/2 - 6, x is integer so y is even

=> y = -12, -10... , 8,10,12 => 13 possible y => 13 ordered pairs (x,y)
Manager
Joined: 14 Oct 2008
Posts: 160

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10 Nov 2008, 06:10
Yup i am getting 13 as well. whats the QA ?
SVP
Joined: 17 Jun 2008
Posts: 1507

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10 Nov 2008, 06:54
13 should be correct.
Re: Ordered Pairs   [#permalink] 10 Nov 2008, 06:54
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# 2x + y = 12 |y| <= 12 For how many ordered pairs (x , y)

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