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Re: Dividing cubicle [#permalink]
29 Oct 2012, 04:37
If P, Q, and R are positive integers, what is the remainder when R – Q is divided by 3?
(1) R = P^3. No info about Q. Not sufficient. (2) Q = (P – 2)^3. No info about R. Not sufficient.
(1)+(2) Important tip: x^3-y^3 can be factored as follows: \(x^3-y^3=(x-y)(x^2+xy+y^2)\). Apply this factoring to \(R-Q\) --> \(R-Q=P^3-(P-2)^3=(P-P+2)(P^2+P^2-2P+P^2-4P+4)=2(3P^2-6P+4)=6c^2-12c+8=6(c^2-2c+1)+2\) --> remainder upon division this expression by 3 is 2. Sufficient.