Bunuel wrote:
If p, q, and r are non-negative integers such that the remainder when \(10^p – q\) is divided by 3 is equal to r, what is the value of R?
(1) p = 7
(2) q = 4
There are only three remainders possible when a number is divided by \(3\) and they are \(0\), \(1\) & \(2\). Also \(10^p\) will always leave a remainder of \(1\) when divided by \(3\), irrespective of the value of \(p\). Hence to know the value of \(r\), we only need to know the value of \(q\)
Statement 1: Nothing mentioned about \(q\).
InsufficientStatement 2: Directly provides the value of \(q\).
Sufficientfor the sake of calculation: \(\frac{10^p – q}{3}=\frac{10^p}{3} – \frac{q}{3}\)
\(\frac{10^p}{3}\) will leave a remainder of \(1\) and \(\frac{4}{3}\) will also leave a remainder of \(1\). Hence \(r=1-1=0\)
Option
B