What is X in the sequence 24, X, 12, 18, 36, 90 ?
- (a) 18
- (b) 12 ✓ UPSC's answer
- (c) 9
- (d) 6
Why the answer is (b)
• Look at the multiplier between successive terms: 24 → X → 12 → 18 → 36 → 90.
• From 12 onward the multipliers are 12 × 1.5 = 18, 18 × 2 = 36 and 36 × 2.5 = 90, so the multiplier rises by 0.5 at every step.
• Working backwards, the two earlier multipliers must be 0.5 and 1.
• So X = 24 × 0.5 = 12, and then 12 × 1 = 12, which is the next term.
• The full chain is ×0.5, ×1, ×1.5, ×2, ×2.5, so X = 12, option (b).
Why the other options are wrong
- (a) 18
- If X were 18, the multiplier from 24 to 18 would be 0.75, which does not fit the arithmetic progression of multipliers (0.5, 1.0, 1.5...) established by the rest of the sequence.
- (c) 9
- If X were 9, the multiplier from 24 to 9 would be 0.375, which breaks the consistent 0.5 increment pattern in the multipliers.
- (d) 6
- If X were 6, the multiplier from 24 to 6 would be 0.25, which is inconsistent with the subsequent multipliers of 1.0, 1.5, 2.0, and 2.5.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.