x is an integer. Is x divisible by 18? (I) x is divisible by 6. (II) x is divisible by 27.

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)_