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Integers x and y with x > y > 0 satisfy x + y + xy = 80. What is x?

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Integers x and y with x > y > 0 satisfy x + y + xy = 80. What is x?  [#permalink]

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New post Updated on: 19 Mar 2019, 06:21
00:00
A
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D
E

Difficulty:

  55% (hard)

Question Stats:

61% (02:01) correct 39% (02:00) wrong based on 38 sessions

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Integers x and y with \(x > y > 0\) satisfy \(x + y + xy\) = 80. What is x?

(A) 8

(B) 10

(C) 15

(D) 18

(E) 26

Originally posted by Noshad on 18 Mar 2019, 10:29.
Last edited by Noshad on 19 Mar 2019, 06:21, edited 1 time in total.
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Re: Integers x and y with x > y > 0 satisfy x + y + xy = 80. What is x?  [#permalink]

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New post 18 Mar 2019, 11:45
2
Noshad wrote:
Integers x and y with \(x > y > 0\)satisfy \(x + y + xy\) = 80. What is x?

(A) 8

(B) 10

(C) 15

(D) 18

(E) 26


x + y + xy = 80

Add 1 on both sides - x + y +xy + 1 = 81
=> (x+1)(y+1) = 81

So possibilities 81 = 9*9
= 27 * 3

If (x+1)(y+1)=9*9 then x=y=8 which is not possible since x>y>0

So (x+1)(y+1)=27*3 Equating x+1 = 27 and y+1=3
x= 26 and y=2 Satisfies x>y>0

Hence E)
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Re: Integers x and y with x > y > 0 satisfy x + y + xy = 80. What is x?  [#permalink]

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New post 19 Mar 2019, 06:01
x+y+xy=80
y=(80-x)/(1+x)
we know x > y and y is an integer
Only E satisfies the equation

if x=26
y=2, hence satisfying the equation
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Re: Integers x and y with x > y > 0 satisfy x + y + xy = 80. What is x?  [#permalink]

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New post 16 Jun 2019, 22:51
Noshad wrote:
Integers x and y with \(x > y > 0\) satisfy \(x + y + xy\) = 80. What is x?

(A) 8

(B) 10

(C) 15

(D) 18

(E) 26



Given,

x>y>0.

x + y + xy = 80

x + y( 1 + x) = 80.

Now back solve the question.

Only E works.

26 + y(26 + 1 ) = 80

y( 27) = 54

y = 2.

So, x = 26 and y = 2.
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Re: Integers x and y with x > y > 0 satisfy x + y + xy = 80. What is x?   [#permalink] 16 Jun 2019, 22:51
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Integers x and y with x > y > 0 satisfy x + y + xy = 80. What is x?

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