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# If x and y are non-zero integers, what is the value of (x^2y 1) ?

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Re: If x and y are non-zero integers, what is the value of (x^2y 1) ? [#permalink]
GMATinsight wrote:
Bunuel wrote:
If x and y are non-zero integers, what is the value of $$(x^{2y} − 1)$$?

(1) $$|x| + |y| = 5$$, where $$1 < |x| < y$$

(2) $$| x^2 − 4| + | y − 3| = 0$$

Question: what is the value of $$(x^{2y} − 1)$$?

To answer the question we need to know the value of $$x^y$$ irrespective of the sign of this expression because we finally have to square it to calculate $$(x^{2y} − 1)$$

Statement 1: $$|x| + |y| = 5$$, where $$1 < |x| < y$$

This statement is Possible only when $$x = +2$$ or $$-2$$ and $$y = +3$$
i.e. $$x^y = 2^3 or -2^3 = +8 or -8$$
i.e. $$x^{2y} = 8^2 = 64$$
SUFFICIENT

Statement 2: $$| x^2 − 4| + | y − 3| = 0$$
Since modulus of any expression can't be Negative hence minimum it may be zero
therefore in this case $$| x^2 − 4|$$ and $$| y − 3|$$ both MUST be zero

i.e. $$x = +2$$ or $$-2$$ and $$y = 3$$
i.e. $$x^y = 2^3 or -2^3 = +8 or -8$$
i.e. $$x^{2y} = 8^2 = 64$$
SUFFICIENT

P.S.This is GMATINSIGHT Method taught at GMATINSIGHT class which is so logical and so quick that any mathematical solutionmay be left behind. To know more, you may get in touch.

i understand the secondstatement explanation,but unable to understand 1 statement:
This statement is Possible only when $$x = +2$$ or $$-2$$ and $$y = +3$$

Why cannot we consider x=-3 and y=-2
or x=3 and y=-3

Because the statement tells us that y is larger than 1 - it can't be a negative number!
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Re: If x and y are non-zero integers, what is the value of (x^2y 1) ? [#permalink]
GMATinsight wrote:
Bunuel wrote:
If x and y are non-zero integers, what is the value of $$(x^{2y} − 1)$$?

(1) $$|x| + |y| = 5$$, where $$1 < |x| < y$$

(2) $$| x^2 − 4| + | y − 3| = 0$$

Question: what is the value of $$(x^{2y} − 1)$$?

To answer the question we need to know the value of $$x^y$$ irrespective of the sign of this expression because we finally have to square it to calculate $$(x^{2y} − 1)$$

Statement 1: $$|x| + |y| = 5$$, where $$1 < |x| < y$$

This statement is Possible only when $$x = +2$$ or $$-2$$ and $$y = +3$$
i.e. $$x^y = 2^3 or -2^3 = +8 or -8$$
i.e. $$x^{2y} = 8^2 = 64$$
SUFFICIENT

Statement 2: $$| x^2 − 4| + | y − 3| = 0$$
Since modulus of any expression can't be Negative hence minimum it may be zero
therefore in this case $$| x^2 − 4|$$ and $$| y − 3|$$ both MUST be zero

i.e. $$x = +2$$ or $$-2$$ and $$y = 3$$
i.e. $$x^y = 2^3 or -2^3 = +8 or -8$$
i.e. $$x^{2y} = 8^2 = 64$$
SUFFICIENT

P.S.This is GMATINSIGHT Method taught at GMATINSIGHT class which is so logical and so quick that any mathematical solutionmay be left behind. To know more, you may get in touch.

i understand the secondstatement explanation,but unable to understand 1 statement:
This statement is Possible only when $$x = +2$$ or $$-2$$ and $$y = +3$$

Why cannot we consider x=-3 and y=-2
or x=3 and y=-3

Because it's given that $$1 < |x| < y$$ i.e.y can NOT be taken less than or equal to 2

I hope this helps!!!
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Re: If x and y are non-zero integers, what is the value of (x^2y 1) ? [#permalink]
am i missing something here? where are the arrows in the original question?
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Re: If x and y are non-zero integers, what is the value of (x^2y 1) ? [#permalink]
dbcoupie123 wrote:
am i missing something here? where are the arrows in the original question?

There are no arrows in the original question. It's a copy-paste error.
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GMAT 1: 670 Q49 V32
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Re: If x and y are non-zero integers, what is the value of (x^2y 1) ? [#permalink]
Bunuel wrote:
dbcoupie123 wrote:
am i missing something here? where are the arrows in the original question?

There are no arrows in the original question. It's a copy-paste error.

Thanks! then the first question stem should read |y|, not |4|
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Re: If x and y are non-zero integers, what is the value of (x^2y 1) ? [#permalink]
dbcoupie123 wrote:
Bunuel wrote:
dbcoupie123 wrote:
am i missing something here? where are the arrows in the original question?

There are no arrows in the original question. It's a copy-paste error.

Thanks! then the first question stem should read |y|, not |4|

________________________________________________________
Fixed. Thank you.
Re: If x and y are non-zero integers, what is the value of (x^2y 1) ? [#permalink]
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