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# If x and y are positive integers and 2x + 3y + xy = 12, what is the

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Math Expert
Joined: 02 Sep 2009
Posts: 54544
If x and y are positive integers and 2x + 3y + xy = 12, what is the  [#permalink]

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03 Jul 2017, 04:01
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25% (medium)

Question Stats:

82% (02:12) correct 18% (02:00) wrong based on 88 sessions

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If x and y are positive integers and 2x + 3y + xy = 12, what is the value of (x + y)?

(A) 2
(B) 4
(C) 5
(D) 6
(E) 8

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Re: If x and y are positive integers and 2x + 3y + xy = 12, what is the  [#permalink]

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03 Jul 2017, 04:17
Bunuel wrote:
If x and y are positive integers and 2x + 3y + xy = 12, what is the value of (x + y)?

(A) 2
(B) 4
(C) 5
(D) 6
(E) 8

\(2x+3y+xy=12 \implies (2x+xy) + (3y+6) =18 \implies (x+3)(y+2)=18\)

Note that \(x+y = (x+3)+(y+2) - 5\)

Also, \(18= 3 * 6 \implies x+y = 3+6-5=4\)

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If x and y are positive integers and 2x + 3y + xy = 12, what is the  [#permalink]

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03 Jul 2017, 04:19
x+y= 4, B
Plugin rationale:
Integers are likely to be 1,2,3
x= 3 and y=1
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Joined: 14 Sep 2016
Posts: 10
Re: If x and y are positive integers and 2x + 3y + xy = 12, what is the  [#permalink]

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05 Jul 2017, 11:34
1
1
Bunuel wrote:
If x and y are positive integers and 2x + 3y + xy = 12, what is the value of (x + y)?

(A) 2
(B) 4
(C) 5
(D) 6
(E) 8

2x + 3y + xy = 12
3y + xy + 2x + 6 = 18
y(x + 3) + 2(x + 3) = 18
(x+3)(y+2)=18
Two numbers multiplied to make 18
1*18 >>> not possible as both x and y are positive integers
2*9 >>> not possible as both x and y are positive, here y will become 0
3* 6 >>> possible if x+3 = 6 and y+2 = 3, which means x = 3 and y = 1

so, x + y = 4 ANS (B)
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Re: If x and y are positive integers and 2x + 3y + xy = 12, what is the  [#permalink]

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05 Jul 2017, 11:37
I solved via plugging

x = 3 and y = 1 : worked
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Re: If x and y are positive integers and 2x + 3y + xy = 12, what is the   [#permalink] 05 Jul 2017, 11:37
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