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Bunuel
alphonsa
Is (x - y) divisible by 3?

(1) (x^2 – y^2) is divisible by 3.
(2) (x^3 + y^3) is divisible by 3.


Source:4gmat

Not a GMAT-like question. Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers (ALL GMAT divisibility questions are limited to positive integers only).

Is (x - y) divisible by 3?

(1) (x^2 – y^2) is divisible by 3 --> (x - y)(x + y) is divisible by 3. If x = y = 0, then the answer is YES but if x = 2 and y = 1, then the answer is NO. Not sufficient.
(2) (x^3 + y^3) is divisible by 3 --> (x + y)(x^2 - xy + y^2) is divisible by 3. If x = y = 0, then the answer is YES but if x = 2 and y = 1, then the answer is NO. Not sufficient.

(1)+(2) We can use the same examples: if x = y = 0, then the answer is YES but if x = 2 and y = 1, then the answer is NO. Not sufficient.

Answer: E.


Hi Bunnuel...It took me 5-6 mins just to plug in the values and find out E....Any shortcut method?
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Hi Satyarath,

When you TESTed VALUES, did you use the number 0? In Bunuel's explanation, he sets BOTH variables equal to 0. In that same way, you could set JUST 1 of the variables equal to 0 and the other variable to the square-root of 3 or the cube-root of 3 (depending on which Fact you're dealing with. In this way, you could almost completely eliminate any calculations and go at that this question with a more 'conceptual' approach (while still TESTing VALUES).

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