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# What is the value of x^2 - y^2?

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Intern
Joined: 15 Dec 2015
Posts: 5
What is the value of x^2 - y^2?  [#permalink]

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19 Jun 2016, 11:48
1
00:00

Difficulty:

15% (low)

Question Stats:

75% (00:39) correct 25% (00:36) wrong based on 82 sessions

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What is the value of x^2 - y^2?

(1) x + y = 16

(2) x - y = 0

Source is Magoosh.
My question is why the answer is not C and why can't we use difference of squares here.
Manager
Joined: 19 Dec 2015
Posts: 111
Location: United States
GMAT 1: 720 Q50 V38
GPA: 3.8
WE: Information Technology (Computer Software)
Re: What is the value of x^2 - y^2?  [#permalink]

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19 Jun 2016, 12:25
$$x^2 - y^2$$ can be factorized as (x+y)*(x-y). Now statement 2 gives us the value of x-y. So that means, irrespective of the values of (x+y), $$x^2 -y^2$$ will always be zero,
Thus B is sufficient, and you don't need A. Hope this helps.
Intern
Joined: 15 Dec 2015
Posts: 5
Re: What is the value of x^2 - y^2?  [#permalink]

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19 Jun 2016, 12:29
FacelessMan wrote:
$$x^2 - y^2$$ can be factorized as (x+y)*(x-y). Now statement 2 gives us the value of x-y. So that means, irrespective of the values of (x+y), $$x^2 -y^2$$ will always be zero,
Thus B is sufficient, and you don't need A. Hope this helps.

Thanks for the reply, but if we multiply by X+Y=16 by X-Y=0, then still we get the answer as "0". Which will then come to C?
Whats the logic behind it?
Intern
Joined: 15 Dec 2015
Posts: 5
Re: What is the value of x^2 - y^2?  [#permalink]

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19 Jun 2016, 12:32
Mangeshkhuspe wrote:
FacelessMan wrote:
$$x^2 - y^2$$ can be factorized as (x+y)*(x-y). Now statement 2 gives us the value of x-y. So that means, irrespective of the values of (x+y), $$x^2 -y^2$$ will always be zero,
Thus B is sufficient, and you don't need A. Hope this helps.

Thanks for the reply, but if we multiply by X+Y=16 by X-Y=0, then still we get the answer as "0". Which will then come to C?
Whats the logic behind it?

Got the logic, the highlighted sentence gives the answer.
Its really difficult being so aware about it on the GMAT.
But then it is what the GMAT tests.
Manager
Joined: 19 Dec 2015
Posts: 111
Location: United States
GMAT 1: 720 Q50 V38
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What is the value of x^2 - y^2?  [#permalink]

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Updated on: 19 Jun 2016, 12:45
2
Actually, this is a classic case of what is referred as the C Trap. Google "C-Trap GMAT". You need to understand the difference between B and C.
For B, only statement 2 is sufficient to answer this question. Statement 1 is not needed to answer.
For C, both statements are necessary for you to derive the answer.

here, statement 2 is enough to answer and thus it will be B.

Originally posted by FacelessMan on 19 Jun 2016, 12:39.
Last edited by FacelessMan on 19 Jun 2016, 12:45, edited 1 time in total.
Intern
Joined: 15 Dec 2015
Posts: 5
Re: What is the value of x^2 - y^2?  [#permalink]

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19 Jun 2016, 12:45
FacelessMan wrote:
Actually, this is a classic case of what is referred as the C Trap. Google "C-Trap GMAT". You need to answer the difference between B and C.
For B, only statement 2 is sufficient to answer this question. Statement 1 is not needed to answer.
For C, both statements are necessary for you to derive the answer.

here, statement 2 is enough to answer and thus it will be B.

Sure Will do. When the answer seems to easy and pointing towards "C". Just Double check.
Math Expert
Joined: 02 Sep 2009
Posts: 51281
Re: What is the value of x^2 - y^2?  [#permalink]

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19 Jun 2016, 12:47
Mangeshkhuspe wrote:
FacelessMan wrote:
Actually, this is a classic case of what is referred as the C Trap. Google "C-Trap GMAT". You need to answer the difference between B and C.
For B, only statement 2 is sufficient to answer this question. Statement 1 is not needed to answer.
For C, both statements are necessary for you to derive the answer.

here, statement 2 is enough to answer and thus it will be B.

Sure Will do. When the answer seems to easy and pointing towards "C". Just Double check.

Check C-Trap Question Collection from our Special Questions's Directory.
_________________
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Joined: 26 Mar 2013
Posts: 1919
Re: What is the value of x^2 - y^2?  [#permalink]

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19 Jun 2016, 17:56
Mangeshkhuspe wrote:
What is the value of x^2 - y^2?

(1) x + y = 16

(2) x - y = 0

Source is Magoosh.
My question is why the answer is not C and why can't we use difference of squares here.

Sometimes, people rush combining two statement to create 2 equations in 2 variables.

Without even factoring the question to (X-Y)(X+Y), Statement 2 tells:

X-Y=0 , simply this means X=Y, Substitute in equation above x^2 - X^2= 0.

value was achieved by Statement 2

Intern
Joined: 14 Jul 2016
Posts: 18
DS question: What is the value of x^2 - y^2?  [#permalink]

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14 Jul 2016, 12:45
1
Hello,

I ran into this DS question

What is the value of $$x^2 - y^2$$?
$$(1) x + y = 16$$
$$(2) x - y = 0$$

I immediately went x=16-y, and plugged it into the statement equation:
$$(16^2-32y+y^2)-y^2$$
and solved, resulting in $$y=8$$ and $$x=8$$
And thus concluded that statement 1 is sufficient.

I reviewed the solution and saw that statement 1 is NS as shown by counter examples:
$$x=7, y=9; x=8,y=8$$ (as well as others)

My question is: in a general sense, how can I know not just to dive and algebraically solve for x as I did? In my mind, I was sure that I was doing it right, because algebraically it was valid.

Thanks
Current Student
Joined: 27 Jan 2013
Posts: 97
Location: India
GMAT 1: 700 Q49 V35
GPA: 3.7
Re: DS question: What is the value of x^2 - y^2?  [#permalink]

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14 Jul 2016, 13:18
2
bzo34 wrote:
Hello,

I ran into this DS question

What is the value of $$x^2 - y^2$$?
$$(1) x + y = 16$$
$$(2) x - y = 0$$

I immediately went x=16-y, and plugged it into the statement equation:
$$(16^2-32y+y^2)-y^2$$
and solved, resulting in $$y=8$$ and $$x=8$$
And thus concluded that statement 1 is sufficient.

I reviewed the solution and saw that statement 1 is NS as shown by counter examples:
$$x=7, y=9; x=8,y=8$$ (as well as others)

My question is: in a general sense, how can I know not just to dive and algebraically solve for x as I did? In my mind, I was sure that I was doing it right, because algebraically it was valid.

Thanks

There are a couple of issues here.

Firstly, think logically. Statement 1: If x+y = 16, then x and y can take many different values. Firstly, its not given that x and y are integers, secondly there are different values like x =2 y=14, x=10, y=6 which will give different answers for x^2 - y^2. Thirdly, when you say you solved (16^2-32y+y^2)-y^2, it means you equated it to zero. Is it mentioned anywhere that x^2 - y^2 = 0 ?

Now coming to statement 2: x - y = 0. This means that x =y and x^2 - y^2 will be zero for all values of x and y, since they are equal. Hence, statement 2 is sufficient.

You'll learn these basics with more practice. Stay positive.

Please give kudos if this helps!
Intern
Joined: 14 Jul 2016
Posts: 18
Re: DS question: What is the value of x^2 - y^2?  [#permalink]

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14 Jul 2016, 13:24
Thanks for the helpful response Raghav. After your explanation, I see that I made a critical error in equating $$x^2 - y^2$$ to zero. Thanks for the encouragement as well
Senior Manager
Joined: 22 Feb 2018
Posts: 413
Re: What is the value of x^2 - y^2?  [#permalink]

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31 Jul 2018, 08:16
Mangeshkhuspe wrote:
What is the value of x^2 - y^2?

(1) x + y = 16

(2) x - y = 0

Source is Magoosh.
My question is why the answer is not C and why can't we use difference of squares here.

OA:B

Question stem : What is value of $$x^2 - y^2 or (x-y)(x+y)$$

Statement1: $$x+y=16$$
$$(x-y)(x+y)=(x-y)16$$
We still need value of $$x-y$$.
Statement 1 alone is not sufficient

Statement 2: $$x - y = 0$$
$$(x-y)(x+y)=0(x+y)=0$$
We are able to get unique value for $$x^2 - y^2 i.e 0$$

Another way $$x - y = 0,x=y$$
$$x^2 - y^2=x^2 - x^2=0$$
Statement 2 alone is sufficient
_________________

Good, good Let the kudos flow through you

Re: What is the value of x^2 - y^2? &nbs [#permalink] 31 Jul 2018, 08:16
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