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

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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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New post 01 Oct 2018, 04:43
1
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

28% (02:37) correct 72% (02:24) wrong based on 114 sessions

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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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New post 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

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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New post 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

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
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Tom
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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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New post 08 Oct 2018, 02:15
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!
_________________
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User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: If x and y are non-zero integers, what is the value of (x^2y − 1) ?  [#permalink]

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