Question

If $R$ is an integer between $1$ and $9$, $P - R = 2370$, what is the value of $R$?

\(\textbf{Statements:}\)
I. $P$ is divisible by $4$. 
II. $P$ is divisible by $9$. 

• A. The question can be answered with the help of statement I alone.
• B. The question can be answered with the help of statement II alone.
• C. Both statements I and II are needed to answer the question.
• D. The question cannot be answered even with the help of both the statements.

Hint:

For data sufficiency with divisibility, reduce the known part modulo $m$ and isolate the unknown's residue class. Check if the range constraints yield a unique value.

Answer 1

The Correct Option is B

1. Statement I alone: \(P=2370+R\) divisible by 4 happens for both \(R=2\) (\(P=2372\)) and \(R=6\) (\(P=2376\)) — two possible values, so \(R\) is not determined.
2. Statement II alone: \(P\) divisible by 9 requires \(3+R\) divisible by 9 (since \(2370\equiv3\pmod9\)); only \(R=6\) works among \(1\)-\(9\) — a unique value.
3. Conclusion: Statement II alone is enough to fix \(R=6\), so statement I is not needed.

\[ \boxed{R=6,\text{ from statement II alone}} \]