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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, 03:43
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Question Stats:

31% (02:16) correct 69% (02:15) wrong based on 108 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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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, 04:01
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

Answer: Option D

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, 00:35
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

Answer: Option D

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
_________________

Thanks,
Ankit
Target Score:730+

If the post was useful,please send the kudos
MBA VS MIM :https://www.mba.com/mbas-and-business-masters/articles/management-programs-and-careers/the-differences-between-masters-in-management-and-mbas

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

### Show Tags

08 Oct 2018, 01:15
AnkitOrYadav wrote:
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

Answer: Option D

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!
_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2711
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, 05:38
AnkitOrYadav wrote:
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

Answer: Option D

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

AnkitOrYadav

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, 05:38
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# If x and y are non-zero integers, what is the value of (x^2y − 1) ?

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