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

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 152
Category: Algebra Absolute value
Page: 82
Difficulty: 600


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SOLUTION

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 \(x\).

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

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2x + y = 12 --> x= (12 - y)/2 = 6 - y/2. Thus every even value of y will yield integer value of x too.

|y| <= 12 --> There are 13 even values of y: 12 - (-12) = 24/2 + 1 = 13

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

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New post 18 Dec 2014, 13:58
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|y| <= 12 means the range of Y is -12<=Y<=12
Let'ssimplify the first equation X=(12-y)/2 -> So in order both x and y to be an integer 12-y must be even.
We have 13 even numbers in the range of -12<=Y<=12: These are -12,-10,-8,-6,-4,-2,0,2,4,6,8,10,12 (don't forget to count 0 and 12)

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

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New post 26 Sep 2017, 09:32
Given that |y| <= 12 -----> y<=12 and y>= -12
Given that 2x + y = 12 and x,y are integers
In order for x to be integer, y would always take even value
Hence, no of even integers between -12 and 12(both inclusive) are 13.
Option D.

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Re: For how many ordered pairs (x , y) that are solutions of the   [#permalink] 26 Sep 2017, 09:32
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