GMATGuruNY wrote:

Mo2men wrote:Are x and y integers?

(1) The product xy is an integer.
(2) x + y is an integer.

Both statements are satisfied by the following cases:
Case 1: x=0 and y=0, with the result that xy=0 and x+y=0
In this case, x and y are both integers, so the answer to the question stem is YES.
Case 2: x=√2 and y=-√2, with the result that xy=-2 and x+y=0
In this case, x and y and NOT integers, so the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.

Dear Mithc,
I have tried another approach to prove insufficiency.
Please not that 'i' represents word integer and each color of 'I' means different value.

From Statement 1:
Multiply both sides by...............Nothing will change..The result will be still integer
2xy = Integer = I

From Statement 2:

x +y = Integer = I.....................Square both sides
(x+y)^2 = I^2
x^2 + y^2 + 2xy = I^2
x^2 + y^2 = I^2 - 2xy = Integer = I

From here :
x^2 + y^2 = I
This could be valid if x and y are Integers, for example x =y =2 ...........x^2 + y^2 = 8...........Answer is Yes.
This could be valid if, for example x=y = √2................x^2 + y^2 =4...................................................Answer is No

So Insufficient

Is my approach above is correct? if yes, my example "x=y = √2" works for statement 1 but not 2. However, it works for the DERIVED equation. Can this still be ok, although the example does work for original statement 2?

Thanks

Mo2men wrote:√2" works for statement 1 but not 2. However, it works for the DERIVED equation. Can this still be ok, although the example does work for original statement 2?

In DS, each statement is a PREMISE: a fact that cannot be disputed.
The premise in Statement 2 is that x+y = integer.
Your conclusion -- that x²+y² = integer -- is based upon this premise..
√2 violates this premise and thus is not a valid case when the statements are combined.

GMATGuruNY wrote:

Mo2men wrote:√2" works for statement 1 but not 2. However, it works for the DERIVED equation. Can this still be ok, although the example does work for original statement 2?

In DS, each statement is a PREMISE: a fact that cannot be disputed.
The premise in Statement 2 is that x+y = integer.
Your conclusion -- that x²+y² = integer -- is based upon this premise..
√2 violates this premise and thus is not a valid case when the statements are combined.

Thanks Mitch for your response.

1- Does this mean that the DERIVED conclusion equation is wrong?

2- What is your advice when combined statements and choose plug-in values?

Thanks