The missing number (?) in the following series: 60, 180, 90, 270, ?, 405 is

The correct answer is D, 135. The series alternates between two operations: multiply by 3, then divide by 2. Check it: 60 × 3 = 180, 180 ÷ 2 = 90, 90 × 3 = 270, 270 ÷ 2 = 135, 135 × 3 = 405. The last term, 405, confirms the rule, so the missing term is 135.

Why the others fail:

• A) 675: 270 × 2.5 would need a step of ×2.5, which appears nowhere else in the series.
• B) 540: 270 × 2 = 540 uses doubling, but the step after 270 is halving. Doubling also breaks the link to 405.
• C) 360: no consistent operation takes 270 to 360, and 360 does not lead cleanly to 405.

Core concept: alternating two-step number series, where odd and even positions follow different operations. Such questions build the pattern recognition used in Reasoning and Aptitude papers and in quick numerical reasoning under time pressure.

Trap: aspirants notice that 90 to 270 is ×3 and assume the same operation continues. Test the alternating rule at every step before filling the blank.