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x is an integer. Is x divisible by 18? (I) x is divisible by 6. (II) x is divisible by 27.
Answer & Solution
Correct answer: C.
1. From (I): x is a multiple of 6 — could be 6, 12, 18, 24, ... so divisibility by 18 unknown.
2. From (II): x is a multiple of 27 — could be 27, 54, 81, ... so divisibility by 18 unknown.
3. Together: x must be a multiple of LCM(6,27) = 54. Every multiple of 54 is a multiple of 18.
4. So both together are sufficient and neither alone is.
_Source: TSICET 2024 PYQ Q.1 (Shift 1, Data Sufficiency)_
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