Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? Is a two-digit number divisible by 12? (I) If the number is divided by 5, the remainder is 2. (II) If the number is divided by 3, the remainder is 1.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I: Number gives remainder 2 when divided by 5, so it could be 12, 22, 32, 42, 52, 62, 72, 82, 92. Some of these are divisible by 12 (12, 24, 36, 48, 60, 72, 84, 96), some are not. Statement II: Number gives remainder 1 when divided by 3. Combining both statements: numbers with remainder 2 mod 5 are 12, 22, 32, 42, 52, 62, 72, 82, 92. Checking which give remainder 1 mod 3: only 22, 52, 82 satisfy both. None of these are divisible by 12. But we cannot conclude divisibility without checking each candidate - and there's no unique determination. Even together, insufficient.

Keep practicing — related questions