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If x and y both are integers, what is the value of x+y?

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If x and y both are integers, what is the value of x+y?  [#permalink]

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New post 03 Nov 2018, 10:03
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If x and y both are integers, what is the value of x+y?

1) \(x(x^2y)\) =1
2)\(y(y^2x)\)=1

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Re: If x and y both are integers, what is the value of x+y?  [#permalink]

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New post 03 Nov 2018, 10:18
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Abhi077 wrote:
If x and y both are integers, what is the value of x+y?

1) \(x(x^2y)\) =1
2)\(y(y^2x)\)=1


Consider -

x = 1,y = 1,
x = -1,y = -1

Hence, E.
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Re: If x and y both are integers, what is the value of x+y?  [#permalink]

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New post 26 Nov 2018, 12:19
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Abhi077 wrote:
If x and y both are integers, what is the value of x+y?

1) \(x(x^2y)\) =1
2)\(y(y^2x)\)=1


Dear Moderator,
Found this DS question, in the PS section of number properties , hope you will do the needful. Thank you.
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Re: If x and y both are integers, what is the value of x+y?  [#permalink]

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New post 26 Nov 2018, 12:23
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Re: If x and y both are integers, what is the value of x+y?  [#permalink]

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New post 26 Nov 2018, 17:10
Abhi077 wrote:
If x and y both are integers, what is the value of x+y?

1) \(x(x^2y)\) =1
2)\(y(y^2x)\)=1



From 1 : value of x & y can be +/-1
From 2: Same as 1 , two values of x & y +/- 1

IMO E
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Re: If x and y both are integers, what is the value of x+y?  [#permalink]

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New post 26 Nov 2018, 20:51
As the product of two integers is 1, we only two choices. Either -1 or 1.

Now consider x and y as -1.
Statement 1) True
Statement 2) True

x+y = -2

Now consider x and y as 1.
Statement 1) True
Statement 2) True

x+y = 2

Even after combining the statements we can't get a unique answer for x+y. So answer is E
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Re: If x and y both are integers, what is the value of x+y?  [#permalink]

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New post 27 Nov 2018, 04:06
Abhi077 wrote:
If x and y both are integers, what is the value of x+y?

1) \(x(x^2y)\) =1
2)\(y(y^2x)\)=1


From eqn1, we know x= y^-3
and from eqn2, y= x^-3

Combining, we get x=(( x^-3)^-3) or 1= x^5. This implies that x is positive. Hence, x+y should take the positive values of x and y respectively. (C)
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Re: If x and y both are integers, what is the value of x+y?  [#permalink]

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New post 27 Nov 2018, 04:53
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nishidesai wrote:
Abhi077 wrote:
If x and y both are integers, what is the value of x+y?

1) \(x(x^2y)\) =1
2)\(y(y^2x)\)=1


From eqn1, we know x= y^-3
and from eqn2, y= x^-3

Combining, we get x=(( x^-3)^-3) or 1= x^5. This implies that x is positive. Hence, x+y should take the positive values of x and y respectively. (C)



You are wrong in the highlighted portion...\((x^{-3})^{-3} = x^{-3*-3}=x^9.........x^8=1\), so x can be 1 or -1
just substitute x and y as -1, this will also satisfy the equation.
\(x^{-3}x^{-3}=x^{-6}\)
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Re: If x and y both are integers, what is the value of x+y?   [#permalink] 27 Nov 2018, 04:53
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