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

\(x^2 - y^2\) 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.

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.

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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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

Answer: B

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.
Answer is B.

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

Please give kudos if this helps!

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

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

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