Bunuel wrote:

samuraijack256 wrote:

Bunuel wrote:

Official Solution:

Statement (1) by itself is insufficient. S1 gives us information about \((x - y)(x + y)\) but does not tell how \((x - y)\) and \((x + y)\) compare to each other.

Statement (2) by itself is insufficient. S2 gives no information about \((x + y)\).

Statements (1) and (2) combined are sufficient. From S1 and S2 it follows that \(2(x + y) = 9\) from where \((x + y) = 4.5\). Now we can state that \(|x - y| = 2 \lt |x + y| = 4.5\).

Answer: C

Hi bunuel,

Why can't (1) be sufficient. Here is my reasoning:

(x-y)(x+y)=9 can be rewritten as (5-4)(5+4) or even (4-5)(4+5).

Either ways, the answer to the main question will always yield a 'no'. Doesn't this mean statement 1 is sufficient?

Why do you assume that x and y are integers? x^2 - y^2 = 9 has infinitely many solutions for x and y.

Even if you consider only integers, which is not right, you'll have more solutions:

x = ±5 and y = -4;

x = ±3 and y = 0;

x = ±5 and y = 4.

Hi Bunuel,

Had a doubt here:

For this q - What if we have to simplify the question stem and open up the modulus sign?

1) Case 1: Both sides are positives - then we get

x-y> x+y... => y<0

2) Case 2: One is negative the other is positive:

X >0 in one case and X < 0 in the other

3) Case 3: Both sides are negative:

y>0

So now if we consider option c, X-y =2. X+y = 4.5... solving gives x = 3.25 and y = 1.25.

Now what case above to consider.

Is there a generic approach of solving these questions?