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

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Joined: 02 Sep 2009
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If x and y are non-zero integers, what is the value of (x^2y − 1) ?  [#permalink]

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01 Oct 2018, 04:43
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Difficulty:

95% (hard)

Question Stats:

31% (01:57) correct 69% (02:07) wrong based on 86 sessions

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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) $$| x^2 − 4| + | y − 3| = 0$$

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Joined: 08 Jul 2010
Posts: 2569
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: If x and y are non-zero integers, what is the value of (x^2y − 1) ?  [#permalink]

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01 Oct 2018, 05:01
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.
_________________

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

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08 Oct 2018, 01:35
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
_________________

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Ankit
Target Score:730+

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Joined: 07 Dec 2017
Posts: 724
Re: If x and y are non-zero integers, what is the value of (x^2y − 1) ?  [#permalink]

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08 Oct 2018, 02:15
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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CEO
Joined: 08 Jul 2010
Posts: 2569
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: If x and y are non-zero integers, what is the value of (x^2y − 1) ?  [#permalink]

### Show Tags

08 Oct 2018, 06:38
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!!!
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Re: If x and y are non-zero integers, what is the value of (x^2y − 1) ? &nbs [#permalink] 08 Oct 2018, 06:38
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