Question

If R is an integer between 1 & 9, P - R = 2370, what is the value of R?
I. P is divisible by 4.
II. P is divisible by 9.

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

Hint:

For divisibility problems, check each statement’s filtering power individually, then combine to see if only one possibility remains.

Answer 1

The Correct Option is C

We know $P - R = 2370$ and $R$ is an integer between 1 and 9. This means $P = 2370 + R$.
From Statement I: $P$ is divisible by 4. Checking for $R = 1$ to $9$, we can see multiple values of $R$ make $P$ divisible by 4 (e.g., $R=2, 6$). Hence, Statement I alone is insufficient.
From Statement II: $P$ is divisible by 9. Again, checking for $R = 1$ to $9$, multiple values of $R$ satisfy this (e.g., $R=3, 9$). Hence, Statement II alone is also insufficient.
When we combine both statements: We need $P$ divisible by both 4 and 9, i.e., divisible by LCM(4,9) = 36. Checking $P = 2370 + R$ for $R = 1$ to $9$, only one value of $R$ will satisfy divisibility by 36. This uniquely determines $R$.
Therefore, both statements together are required.