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Pansi
Joined: 04 Jul 2011
Last visit: 01 Dec 2019
Posts: 42
Given Kudos: 87
Status:Fighting hard
Schools: Kellogg '15 ISB '14 (S)
GMAT Date: 10-01-2012
C
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If P, Q, and R are positive integers, what is the remainder when R – Q is divided by 3?
(1) R = P^3
(2) Q = (P – 2)^3
(1) R = P^3
(2) Q = (P – 2)^3
27 Oct 2012, 23:14
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Pansi
1)No information about Q. Insufficient
2) No information about R. Insufficient
1 & 2 together. \(R-Q = P^3 - (P-2)^3\)
So \(P^3\)gets cancelled out and we only have multiples of 3 and a constant remaining.
Sufficient
Answer is C.
Kudos Please... If my post helped.
29 Oct 2012, 05:37
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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.
Answer: C.
Similar questions to practice:
if-a-b-and-c-are-positive-integers-what-is-the-remainder-140495.html
if-a-b-and-c-are-positive-integers-what-is-the-remainder-127028.html
Hope it helps.
(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.
Answer: C.
Similar questions to practice:
if-a-b-and-c-are-positive-integers-what-is-the-remainder-140495.html
if-a-b-and-c-are-positive-integers-what-is-the-remainder-127028.html
Hope it helps.
