1. Find the next number in the series: 325, 200, 136, 109, 101, ?
Options: A. 101 B. 900 C. 102 D. 100
Soln:
- 325 - 53 = 325 - 125 = 200
- 200 - 43 = 200 - 64 = 136
- 136 - 33 = 136 - 27 = 109
- 109 - 23 = 109 - 8 = 101
- 101 - 13 = 101 – 1 = 100
Ans: D. 100
Short Trick: Subtract consecutive cubes in descending order: −5³, −4³, −3³, −2³, −1³
⇒ 325, 200, 136, 109, 101, 100.
Q. Find the next number in the series: 65, 40, 24, 15, 11, ?
Options: A. 12 B. 09 C. 10 D. 6
Soln:
Observe the pattern:
- 65 – 25 = 40 (25 = 52)
- 40 – 16 = 24 (16 = 42)
- 24 – 9 = 15 (9 = 32
- 15 – 4 = 11 (4 = 22)
Next, 11 – 1 = 10 (1 = 12)
Pattern: Subtract consecutive squares: −52, −42, −32, −22, −12
Therefore, 11- 1 = 10
Ans: C. 10
Short Trick
Series: 19, 20, 28, 55, 119, ?
Look at the differences:
- 20 − 19 = 1 = 1³
- 28 − 20 = 8 = 2³
- 55 − 28 = 27 = 3³
- 119 − 55 = 64 = 4³
So next difference: 5³ = 125
Therefore, 119 + 125 = 244
Ans: C. 244
One-line Trick: Add consecutive cubes: +1³, +2³, +3³, +4³, +5³.