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If P, Q, and R are positive integers, what is the reminder

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If P, Q, and R are positive integers, what is the reminder

by AAPL » Wed Jun 13, 2018 4:43 am

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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

The OA is C.

1) No information about Q. Insufficient.
2) No information about R. Insufficient.

1 & 2 together, R - P = P^3 - (P - 2)^3

So, P^3 gets canceled out and we only have multiples of 3 and a constant remaining. Sufficient. Option C
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Source: — Data Sufficiency |
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by deloitte247 » Fri Jul 27, 2018 1:34 pm

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$$Question\ =\ \frac{\left(Q-R\right)}{3}\ Whats\ the\ remainder?$$
$$Statement\ 1\ =\ R\ =P^3$$
There is not sufficient data for Q here.
Hence, statement 1 is not sufficient.
$$Statement\ 2=\ Q\ =\left(P-2\right)^3$$
There is no sufficient data for R
Hence, Statement 2 is not Sufficient.

Statement 1 and 2 together
$$\frac{\left(R\ -\ Q\right)}{3}$$
$$\frac{\left[P^3-\left(P-2\right)^3\right]}{3}\ =\frac{\left[P^3-\left(P^3-2^3\right)\right]}{3}=\frac{2^3}{3}$$
Both statement together are sufficient.
Hence, correct answer is Option C
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