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How many pairs of positive integers (x,y) can satisfy |(x + 3)(y - 3)|

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How many pairs of positive integers (x,y) can satisfy |(x + 3)(y - 3)|  [#permalink]

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New post Updated on: 06 Aug 2019, 20:24
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00:00
A
B
C
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E

Difficulty:

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Question Stats:

36% (01:34) correct 64% (02:05) wrong based on 83 sessions

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How many pairs of positive integers (x,y) can satisfy |(x + 3)(y - 3)| = 4 ?

A. 1
B. 2
C. 3
D. 4
E. None

Originally posted by chondro48 on 06 Aug 2019, 09:35.
Last edited by chondro48 on 06 Aug 2019, 20:24, edited 7 times in total.
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Re: How many pairs of positive integers (x,y) can satisfy |(x + 3)(y - 3)|  [#permalink]

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New post 06 Aug 2019, 10:00
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Since x and y are integers, (x+3) and (y-3) are also integers

Additionally since x is a positive integer, (x+3)≥4 so the minimum value that (x+3) can take is 4 and if (x+3) is greater than 4, we have no integer solution to get |(x+3)*(y-3)|=4

Therefore 4 is the only value that (x+3) can take which means x=1

Now we have 2 ways to get |(x+3)*(y-3)|=4 which are |4*1| and |4*-1|

(y-3) can be 1 or -1 for positive integer values of y (y=2 or y=4)

Therefore our possible solutions are (1,2) and (1,4)

We have 2 positive integer pairs

Answer is (B)

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Re: How many pairs of positive integers (x,y) can satisfy |(x + 3)(y - 3)|  [#permalink]

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New post 28 Mar 2020, 05:54
1
chondro48 wrote:
How many pairs of positive integers (x,y) can satisfy |(x + 3)(y - 3)| = 4 ?

A. 1
B. 2
C. 3
D. 4
E. None


Asked: How many pairs of positive integers (x,y) can satisfy |(x + 3)(y - 3)| = 4 ?

4 = 2*2 = 1*4

|x+3| = 1; |y-3| = 4; Since x= -3+-1 ; 0 solutions
|x+3| = 4; |y-3| = 1; (x,y) = {(1,2),(1,4)} ; 2 solutions
|x+3| = 2; |y-3| = 2; Since x=-3+-2 ; 0 solutions

IMO B
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Re: How many pairs of positive integers (x,y) can satisfy |(x + 3)(y - 3)|   [#permalink] 28 Mar 2020, 05:54

How many pairs of positive integers (x,y) can satisfy |(x + 3)(y - 3)|

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