GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Apr 2019, 22:56

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# What is the value of x^2 – y^2?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 54544
What is the value of x^2 – y^2?  [#permalink]

### Show Tags

25 Jul 2016, 10:12
00:00

Difficulty:

45% (medium)

Question Stats:

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

### HideShow timer Statistics

What is the value of x^2 – y^2?

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

Official Solution is HERE.

_________________
Retired Moderator
Joined: 26 Nov 2012
Posts: 591
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

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.
Manager
Joined: 04 Mar 2016
Posts: 51
Location: United Kingdom
GMAT 1: 710 Q49 V38
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

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.
Director
Joined: 05 Mar 2015
Posts: 999
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

25 Jul 2016, 19:00
2
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
Senior Manager
Joined: 02 Mar 2012
Posts: 293
Schools: Schulich '16
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

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.

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

Manager
Joined: 07 Jul 2016
Posts: 78
GPA: 4
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

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

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

$$\sqrt{x^2} = \pm x = \vert x \vert$$

$$\vert x\vert = \vert y\vert \implies x^2 = y^2$$

$$x^2 - x^2 = 0$$

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

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 $$x^2 - y^2$$

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

_________________
Please press +1 Kudos if this post helps.
Math Expert
Joined: 02 Sep 2009
Posts: 54544
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

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.

_________________
Re: What is the value of x^2 – y^2?   [#permalink] 17 Jul 2017, 06:06
Display posts from previous: Sort by