Question:
Is 'x' divisible by 27?
I) 'x' is divisible by 3
II) 'x' is divisible by 6
Is 'x' divisible by 27?
I) 'x' is divisible by 3
II) 'x' is divisible by 6
I) 'x' is divisible by 3
II) 'x' is divisible by 6
Show Hint
Divisibility by factors (3 or 6) does not imply divisibility by a higher power (27).
Updated On: Jun 26, 2026
- Statement I alone is sufficient
- Statement II alone is sufficient
- Statements I and II together are sufficient
- Statements I and II together are not sufficient
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Divisibility by 27 requires $x$ to be a multiple of 27 ($x = 27k$).
Step 2: Analysis of Statement I
$x$ is divisible by 3. Examples: 3, 6, 9, 27. Some are divisible by 27, some are not. Not sufficient.
Step 3: Analysis of Statement II
$x$ is divisible by 6. Examples: 6, 12, 18, 54. Some are divisible by 27 (54), some are not. Not sufficient.
Step 4: Combined Analysis
If $x$ is divisible by both 3 and 6, it is divisible by their LCM (6). Still, being divisible by 6 does not guarantee divisibility by 27 (e.g., $x=12$).
Step 5: Conclusion
Correct choice is (4). Final Answer: (4)
Divisibility by 27 requires $x$ to be a multiple of 27 ($x = 27k$).
Step 2: Analysis of Statement I
$x$ is divisible by 3. Examples: 3, 6, 9, 27. Some are divisible by 27, some are not. Not sufficient.
Step 3: Analysis of Statement II
$x$ is divisible by 6. Examples: 6, 12, 18, 54. Some are divisible by 27 (54), some are not. Not sufficient.
Step 4: Combined Analysis
If $x$ is divisible by both 3 and 6, it is divisible by their LCM (6). Still, being divisible by 6 does not guarantee divisibility by 27 (e.g., $x=12$).
Step 5: Conclusion
Correct choice is (4). Final Answer: (4)
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