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What is the value of x^2 – y^2?

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What is the value of x^2 – y^2?  [#permalink]

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New post 25 Jul 2016, 10:12
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

56% (01:00) correct 44% (01:09) wrong based on 173 sessions

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Re: What is the value of x^2 – y^2?  [#permalink]

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New post 25 Jul 2016, 11:56
Bunuel wrote:
What is the value of x^2 – y^2?

(1) |x| = |y|
(2) x^2 + y^2 = 0



Given to find the value of value of x^2 – y^2 ?

Stat 1: |x| = |y| => When there is mod on both LHS and RHS and being positive square both sides.

=> x^2 = y^2 => x^2 - y^2 = 0. Sufficient....

Stat 2 : x^2 + y^2 = 0 => x^2 = - ( y^2 ).

Sub this value in question stem we - ( y^2 ) - ( y^2 ) = - ( 2 * y^2 )...Insufficient..

IMO option A is correct answer...

OA please...will correct if I missed anything.
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Re: What is the value of x^2 – y^2?  [#permalink]

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New post 25 Jul 2016, 15:21
2
I think it is D. Both (1) and (2) are sufficient.
x^2 – y^2=(x+y)(x-y)

(1) abs(x)=abs(y) therefore either x=y or x=-y so either x+y or x-y are zero

(2) for those numbers to sum zero either the two of them are zero or one is the negative version of the other. Since x^2 cannot be a negative number, both x and y are zero.
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Re: What is the value of x^2 – y^2?  [#permalink]

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New post 25 Jul 2016, 19:00
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1
Bunuel wrote:
What is the value of x^2 – y^2?

(1) |x| = |y|
(2) x^2 + y^2 = 0

(1) sq. both side x^2=y^2
x^2 – y^2=0
suff....

(2) x^2 + y^2=0
two positive quantities add to 0 means both are 0

let write it as X^2=-y^2
since LHS is >=0 so as RHS
-y^2>=0---->y^2<=0
sq of a number is never negative so y must be 0
thus x=0
x^2-y^2=0
suff

Ans D
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Re: What is the value of x^2 – y^2?  [#permalink]

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New post 26 Jul 2016, 04:33
msk0657 wrote:
Bunuel wrote:
What is the value of x^2 – y^2?

(1) |x| = |y|
(2) x^2 + y^2 = 0



Given to find the value of value of x^2 – y^2 ?

Stat 1: |x| = |y| => When there is mod on both LHS and RHS and being positive square both sides.

=> x^2 = y^2 => x^2 - y^2 = 0. Sufficient....

Stat 2 : x^2 + y^2 = 0 => x^2 = - ( y^2 ).

Sub this value in question stem we - ( y^2 ) - ( y^2 ) = - ( 2 * y^2 )...Insufficient..

IMO option A is correct answer...

OA please...will correct if I missed anything.


answer will be D

1st statement u have explained above

for 2nd
x^2+y^2=0

we know square of a positive number is always +ve.
as per 2nd statement ,
x^2+y^2=0

+ve + +ve =0

wait this should be positive(which is not possible here) or else if x and y both 0

so x and y are equal and their value=0

Suff


answer D
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Re: What is the value of x^2 – y^2?  [#permalink]

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New post 26 Jul 2016, 05:16
\(\text{What is the value of } x^2 – y^2?\)


\(\textbf{(1) } \vert x\vert = \vert y\vert\)

\(\sqrt{x^2} = \pm x = \vert x \vert\)

\(\vert x\vert = \vert y\vert \implies x^2 = y^2\)

\(x^2 - x^2 = 0\)

Sufficient. Answer = 0


\(\textbf{(2) } x^2 + y^2 = 0\)

The minimum value of squaring a number is 0.

Therefore, to obtain the answer of 0, \(x^2\) and \(y^2\) must both produce 0.
0 is the single single input which produces 0 as output. Therefore \(x = y = 0\)

As we know \(x\) and \(y\), we can obtain \(x^2 - y^2\)

Sufficient. Answer = 0

Note that (1) provides the answer, whereas (2) provides both the answer and the value of x and y.

(D) each statement alone is sufficient

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Re: What is the value of x^2 – y^2?  [#permalink]

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New post 17 Jul 2017, 06:06
Bunuel wrote:
What is the value of x^2 – y^2?

(1) |x| = |y|
(2) x^2 + y^2 = 0


Official Solution:


What is the value of \(x^2 – y^2\)?

(1) \(|x| = |y|\)

Square: \(x^2 = y^2\)

Re-arrange: \(x^2 – y^2=0\). Sufficient.

(2) \(x^2 + y^2 = 0\)

We are given that the sum of two non-negative values is 0. This is only possible if both equal 0. Thus, \(x^2 = y^2=0\) and therefore \(x^2 – y^2=0\). Sufficient.


Answer: D
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Re: What is the value of x^2 – y^2?   [#permalink] 17 Jul 2017, 06:06
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