The question below is followed by two statements numbered I and II. Choose the option that describes whether the statements are sufficient to answer the question.
\(n\) is a positive integer. Is \(n\) divisible by 36?
I. \(n\) is divisible by 9.
II. \(n\) is divisible by 6.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → The question cannot be answered even by using both statements together.
A statement is sufficient if it gives a definite yes or a definite no. One example of each kind is enough to show that the answer is not fixed.
Statement I alone:
9 is divisible by 9 but not by 36; 36 is divisible by both: not sufficient
Statement II alone:
6 is divisible by 6 but not by 36; 36 is divisible by both: not sufficient
Both together:
\(n\) is divisible by 9 and 6, so by their LCM, 18
\(n=18\) is not divisible by 36, but \(n=36\) is
The answer can be yes or no: not sufficient even together