Is (x - y) divisible by 3?

Question

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

Source:4gmat

WiziusCareers1 · Answer

The question is asking if (x - y)/3 = int?

Considering statement (1) alone:
(x^2 - y^2)/3 = int
We can have x =2 and y = 1 but this gives (x - y)/3 is not an integer.
We can have x = 6 and y = 3, this gives (x - y)/3 is an integer.
Different answers. So, INSUFFICIENT.
AD goes out.

Considering statement (2) alone:
(x^3 + y^3)/3 = int
=> We can have x = 2 and y = 1, but it gives (x - y)/3 is not an integer.
We can also have x = 6, y = 3 and this gives (x - y)/3 as an integer.
DIFFERENT ANSWERS.
INSUFFICIENT
B goes out.

Combining together:

We can still have x = 2 and y = 1, it gives (x - y)/3 is not an integer.

And we can also have x = 6 and y = 3, it gives (x - y)/3 is an integer.

INSUFFICIENT.

The answer is (E)

Bunuel · Answer

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.

Cadaver · Answer

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

EMPOWERgmatRichC · Answer

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).

GMAT assassins aren't born, they're made,
Rich

bumpbot · Answer

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Is (x - y) divisible by 3?

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Is (x - y) divisible by 3?

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