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

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

Dear Moderator,
Found this DS question, in the PS section of number properties , hope you will do the needful. Thank you.

____________________________
Moved to DS. Thank you.
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Re: If x and y both are integers, what is the value of x+y? [#permalink]
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]
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]
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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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.
$$x^{-3}x^{-3}=x^{-6}$$
Re: If x and y both are integers, what is the value of x+y? [#permalink]
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