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 \(q\). Insufficient

Statement 2: Directly provides the value of \(q\). Sufficient

for 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

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