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.
Answer is B.
You'll learn these basics with more practice. Stay positive.
Please give kudos if this helps!