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

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Manager
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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
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

56% (02:05) correct 44% (02:18) wrong based on 16 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

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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.
Manager
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Posts: 79
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Concentration: Finance, International Business
Schools: ISB '21, IIMA , IIMB
GPA: 4
WE: Analyst (Energy and Utilities)
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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
1
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
GMAT Club Bot
Re: Integers x and y with x > y > 0 satisfy x + y + xy = 80. What is x?   [#permalink] 19 Mar 2019, 06:01
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Integers x and y with x > y > 0 satisfy x + y + xy = 80. What is x?

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