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.
\(m\) is a positive integer. Is \(m\) divisible by 24?
I. \(m\) is divisible by 6.
II. \(m\) is divisible by 4.
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:
6 is divisible by 6 but not by 24; 24 is divisible by both: not sufficient
Statement II alone:
4 is divisible by 4 but not by 24; 24 is divisible by both: not sufficient
Both together:
\(m\) is divisible by 6 and 4, so by their LCM, 12
\(m=12\) is not divisible by 24, but \(m=24\) is
The answer can be yes or no: not sufficient even together