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xy and yx are reversed 2 digit integers. y is even. If xy+6x=yx+y^2

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xy and yx are reversed 2 digit integers. y is even. If xy+6x=yx+y^2  [#permalink]

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New post 13 Jul 2017, 21:46
2
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (02:31) correct 34% (03:28) wrong based on 56 sessions

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xy and yx are reversed 2 digit integers. y is even. If xy+6x=yx+y^2, what is the sum of x and y?

A. 10
B. 11
C. 12
D. 15
E. 17

(source:self)
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Re: xy and yx are reversed 2 digit integers. y is even. If xy+6x=yx+y^2  [#permalink]

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New post 13 Jul 2017, 22:22
3
1
Looking at the eq :-

xy+6x=yx+y^2

X(Y+6) =Y(X+Y)



When Y is even = 0,2,4,8,6 is possible

When Y=0 => X(0+6)=0(X+0) 0. Not Possible
When Y=2 => X(2+6) =2(X+2) = 8X-2X=4, Not an option. Non Integer Output
When Y=4=> X(4+6)=4(X+4) = 10X=4X+16 .. Not an option. Non Integer Output
When Y=6=> x(6+6)=6(X+6)= 12x=6x+36, x=6,y=6 x+y = 6+6 =12 = > Option C
When Y=8=> X14=8(X+8) Not an option. Non Integer Output

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xy and yx are reversed 2 digit integers. y is even. If xy+6x=yx+y^2  [#permalink]

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New post Updated on: 25 Aug 2018, 10:12
gracie wrote:
xy and yx are reversed 2 digit integers. y is even. If xy+6x=yx+y^2, what is the sum of x and y?

A. 10
B. 11
C. 12
D. 15
E. 17

(source:self)


xy+6x=yx+y^2➡
10x+y+6x=10y+x+y^2➡
(y^2)/3+3y=5x
if y is even integer, only possible value of y=6
if y=6, then x=6 also
12
C

Originally posted by gracie on 14 Jul 2017, 09:26.
Last edited by gracie on 25 Aug 2018, 10:12, edited 1 time in total.
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Re: xy and yx are reversed 2 digit integers. y is even. If xy+6x=yx+y^2  [#permalink]

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New post 14 Jul 2017, 09:51
Well the equation is xy + 6x = xy + y^2

6x = y^2

Now check for y=2 x is not a digit
For y=4 x is not a digit
For y=6 x is 6
For y=8 x is not a digit
Hence x+y will be 12
C


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Re: xy and yx are reversed 2 digit integers. y is even. If xy+6x=yx+y^2   [#permalink] 14 Jul 2017, 09:51
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xy and yx are reversed 2 digit integers. y is even. If xy+6x=yx+y^2

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