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# If x^2 = y^2, is true that x>0?

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Manager
Joined: 31 Jul 2017
Posts: 142
Location: Malaysia
WE: Consulting (Energy and Utilities)
Re: If x^2 = y^2, is true that x>0? [#permalink]

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19 Nov 2017, 17:21
burnttwinky wrote:
If x^2 = y^2, is true that x>0?

(1) x=2y+1

(2) y<= -1

Hi Bunuel, VeritasPrepKarishma

Can you please let me know if my below approach is wrong.

Given, (x+y)(x-y) = 0

1. x - y = y + 1
(x+y)(y+1)=0
So, x = -y or y = -1

2. y <= -1

combining 1 + 2, we get

y = -1, x =-1
Math Expert
Joined: 02 Sep 2009
Posts: 43363
Re: If x^2 = y^2, is true that x>0? [#permalink]

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19 Nov 2017, 22:19
rahul16singh28 wrote:
burnttwinky wrote:
If x^2 = y^2, is true that x>0?

(1) x=2y+1

(2) y<= -1

Hi Bunuel, VeritasPrepKarishma

Can you please let me know if my below approach is wrong.

Given, (x+y)(x-y) = 0

1. x - y = y + 1
(x+y)(y+1)=0
So, x = -y or y = -1

2. y <= -1

combining 1 + 2, we get

y = -1, x =-1

The question asks whether x > 0. It's not clear how you got that (1) is not sufficient.
_________________
Manager
Joined: 31 Jul 2017
Posts: 142
Location: Malaysia
WE: Consulting (Energy and Utilities)
Re: If x^2 = y^2, is true that x>0? [#permalink]

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19 Nov 2017, 22:27
Bunuel wrote:
rahul16singh28 wrote:
burnttwinky wrote:
If x^2 = y^2, is true that x>0?

(1) x=2y+1

(2) y<= -1

Hi Bunuel, VeritasPrepKarishma

Can you please let me know if my below approach is wrong.

Given, (x+y)(x-y) = 0

1. x - y = y + 1
(x+y)(y+1)=0
So, x = -y or y = -1

2. y <= -1

combining 1 + 2, we get

y = -1, x =-1

The question asks whether x > 0. It's not clear how you got that (1) is not sufficient.

Hi Bunuel,

Given is (x+y)(x-y)=0 and From Statement 1, x-y = y +1
So substituting x - y = y+1 in above eqn. we get (x+y)(y+1)=0
So, X=-Y or Y = -1
May I please know if anything wrong with above approach??
Math Expert
Joined: 02 Sep 2009
Posts: 43363
If x^2 = y^2, is true that x>0? [#permalink]

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19 Nov 2017, 22:30
rahul16singh28 wrote:
Hi Bunuel,

Given is (x+y)(x-y)=0 and From Statement 1, x-y = y +1
So substituting x - y = y+1 in above eqn. we get (x+y)(y+1)=0
So, X=-Y or Y = -1
May I please know if anything wrong with above approach??

Again, how does x = -y or y = -1 give both an YES and a NO answer to the question whether x > 0?
_________________
Manager
Joined: 31 Jul 2017
Posts: 142
Location: Malaysia
WE: Consulting (Energy and Utilities)
If x^2 = y^2, is true that x>0? [#permalink]

### Show Tags

19 Nov 2017, 22:37
Bunuel wrote:
[quote="rahul16singh28"
Hi Bunuel,

Given is (x+y)(x-y)=0 and From Statement 1, x-y = y +1
So substituting x - y = y+1 in above eqn. we get (x+y)(y+1)=0
So, X=-Y or Y = -1
May I please know if anything wrong with above approach??

Thanks.. Got it
If x^2 = y^2, is true that x>0?   [#permalink] 19 Nov 2017, 22:37

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