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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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I chose (A) for this one. If x - y > 0 then x > y. So x2-y2 will be a +ve number.

the OA is C though x2 - y2 = (x+y)(x-y)

Is x^2 – y^2 a positive number?

Is x^2 - y^2 > 0? is x^2 > y^2? --> is |x| > |y|? So, the question asks whether x is further from 0 than y.

(1) x – y is a positive number --> x > y. One number is greater than another. Also, insufficient to say which one is further from 0. For example, if x = 2 and y = 1, then x is further but if x = 2 and y = -3, then y is further. Not sufficient.

(2) x + y is a positive number. The sum of two numbers is greater than 0. Clearly insufficient to say which one is further from 0.

(1)+(2) Is x^2 - y^2 > 0? Can be rephrased as "is (x - y)(x + y) > 0?" (1) says that x - y > 0 and (2) says that x + y > 0, thus their product, the product of two positive values, must be greater than 0. Sufficient.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Almost all data sufficiency questions (and generally most problem solving questions) benefit from the "dumb" approach. I'll elaborate on that in a second but first, as a trigger, you should ALWAYS attempt to rearrange the question they give you especially when you see exponents. When you see x^2 – y^2 you should immediately realize that it equals (x + y)(x - y).

Now for the dumb approach: The question asks is (x + y)(x - y) > 0. The dumb approach says that you take this problem and translate it to the simplest terms possible. "Is a number times a number positive?" For this to be true, both numbers must either be positive or negative. That's why you need to both statements. And knowing number properties such as "a positive times a positive is a positive" or "an odd number to any power is odd" will save you the hassle of plugging and chugging.

We can take two values which say \(x – y\) is a positive number. a. x=10, y=5 by plugging these values we get \(10^2 – 5^2\)=100-25=75

i.e., \(x^2 – y^2\) a positive number

b. x=-5, y=-10 by plugging these values we get \((-5)^2 – (-10)^2\)=25-100=-75 a negative number

i.e., \(x^2 – y^2\) is a negative number.

Hence result is uncertain and statement 1 is not sufficient on its own.

(2) \(x + y\) is a positive number.

We can take two values which say \(x + y\) is a positive number. a. x=10, y=-5 by plugging these values we get \(10^2 – (-5)^2\)=100-25=75

i.e., \(x^2 – y^2\) a positive number

b. x=-5, y=10 by plugging these values we get \((-5)^2 – (10)^2\)=25-100=-75 a negative number

i.e., \(x^2 – y^2\) is a negative number.

Hence result is uncertain and statement 2 is not sufficient on its own.

Now combine both of them and multiplication of tw positive numbers is always a positive number.

And \(x-y>0\) indicates that x is greater than y(both positive and negative) Whereas \(x+y>0\) indicates that x,y are either both positive or only one is negative thus eliminating both of them to be negative. _________________

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