Number Series Advanced
Key Concepts
| # | Concept | Explanation |
|---|---|---|
| 1 | Difference Pattern | Observe the constant or changing difference between consecutive terms. |
| 2 | Multiplication/Division | Identify if each term is multiplied or divided by a fixed or changing number. |
| 3 | Square/Cube Series | Terms are squares or cubes of natural numbers or their variations. |
| 4 | Prime Number Series | Terms are prime numbers or related to them. |
| 5 | Alternate Series | Two or more independent series are merged into one. |
| 6 | Fibonacci-type | Each term is the sum of the two preceding terms. |
| 7 | Digit-based Logic | Pattern lies in the digits, not the number (e.g., sum of digits, reverse). |
| 8 | Mixed Operations | Combination of two or more operations (e.g., ×2+1, ×3–2). |
15 Practice MCQs
1. 5, 7, 10, 15, 22, ?
**Options:** A) 29 B) 31 C) 33 D) 35Answer: C) 33
Solution: Differences: +2, +3, +5, +7 (consecutive primes). Next prime is 11 → 22+11=33
Shortcut: Spot prime gaps quickly.
Tag: Prime difference
2. 3, 8, 18, 38, 78, ?
**Options:** A) 148 B) 158 C) 168 D) 178Answer: B) 158
Solution: ×2+2 pattern: 3×2+2=8, 8×2+2=18 … 78×2+2=158
Shortcut: Check ×2±k first.
Tag: Mixed operation
3. 1, 4, 9, 16, 25, ?
**Options:** A) 30 B) 36 C) 42 D) 49Answer: B) 36
Solution: Perfect squares: 1², 2² … 6²=36
Shortcut: Visualise square grid.
Tag: Square series
4. 2, 3, 5, 9, 17, ?
**Options:** A) 31 B) 33 C) 35 D) 37Answer: B) 33
Solution: Differences double: +1, +2, +4, +8 → next +16 → 17+16=33
Shortcut: Powers of 2 in gaps.
Tag: Double difference
5. 1, 1, 2, 3, 5, 8, ?
**Options:** A) 11 B) 13 C) 15 D) 17Answer: B) 13
Solution: Classic Fibonacci: add previous two.
Shortcut: Remember 1-1-2-3-5-8-13-21…
Tag: Fibonacci
6. 6, 12, 24, 48, 96, ?
**Options:** A) 144 B) 192 C) 168 D) 180Answer: B) 192
Solution: Simple ×2 chain.
Shortcut: Count doubling steps.
Tag: Multiplication
7. 27, 64, 125, 216, ?
**Options:** A) 243 B) 343 C) 512 D) 289Answer: B) 343
Solution: 3³, 4³, 5³, 6³ → 7³=343
Shortcut: Cube table 1-10.
Tag: Cube series
8. 4, 7, 12, 19, 28, ?
**Options:** A) 37 B) 39 C) 41 D) 43Answer: B) 39
Solution: Differences: +3, +5, +7, +9 → next +11 → 28+11=39
Shortcut: Odd-gap series.
Tag: Odd difference
9. 1, 8, 9, 64, 25, ?
**Options:** A) 216 B) 121 C) 144 D) 169Answer: A) 216
Solution: Alternate squares & cubes: 1², 2³, 3², 4³, 5² → 6³=216
Shortcut: Odd pos square, even pos cube.
Tag: Alternate operation
10. 5, 10, 13, 26, 29, ?
**Options:** A) 58 B) 56 C) 54 D) 52Answer: A) 58
Solution: ×2, +3, ×2, +3 … 29×2=58
Shortcut: Spot ×2+3 cycle.
Tag: Cyclic operation
11. 9, 18, 15, 30, 27, ?
**Options:** A) 45 B) 54 C) 51 D) 48Answer: B) 54
Solution: ×2, –3, ×2, –3 … 27×2=54
Shortcut: Alternating ×2–3.
Tag: Alternating op
12. 2, 5, 11, 23, 47, ?
**Options:** A) 95 B) 97 C) 99 D) 101Answer: A) 95
Solution: ×2+1 each step: 47×2+1=95
Shortcut: Remember ×2+1 family.
Tag: Mixed operation
13. 1, 4, 10, 22, 46, ?
**Options:** A) 92 B) 94 C) 96 D) 98Answer: B) 94
Solution: ×2+2, ×2+2 … 46×2+2=94
Shortcut: Same as Q2.
Tag: ×2+2
14. 3, 7, 15, 31, 63, ?
**Options:** A) 125 B) 127 C) 129 D) 131Answer: B) 127
Solution: ×2+1 throughout: 63×2+1=127
Shortcut: Close to 2ⁿ–1.
Tag: ×2+1
15. 12, 15, 21, 33, 57, ?
**Options:** A) 105 B) 99 C) 111 D) 108Answer: A) 105
Solution: Differences: +3, +6, +12, +24 (×2) → next +48 → 57+48=105
Shortcut: Geometric difference.
Tag: Double gap
Speed Tricks
| Situation | Shortcut | Example |
|---|---|---|
| Constant ×2 | Just keep doubling | 3→6→12→24… |
| ×2±k seen twice | Apply same to next | 5→11→23→47… (×2+1) |
| Prime gaps | Recall primes ≤30 | 2,3,5,7,11,13,17,19,23,29 |
| Squares 1-20 | Memorise | 1,4,9,16…400 |
| Cubes 1-10 | Memorise | 1,8,27…1000 |
Quick Revision
| Point | Detail |
|---|---|
| 1 | Always compute first 2-3 differences immediately. |
| 2 | If differences rise sharply, suspect multiplication or square/cube. |
| 3 | Two interleaved series? Check odd & even positions separately. |
| 4 | Same number added→constant difference; doubling difference→×2 gap. |
| 5 | ×2±1, ×2±2 are RRB favourites—spot them fast. |
| 6 | Prime-gap series: differences list = primes. |
| 7 | Digit sum pattern: ignore place value, add digits. |
| 8 | Fibonacci seed 1-1-2-3-5-8-13-21-34. |
| 9 | Squares end 0,1,4,5,6,9; cubes can end any digit. |
| 10 | Time-saver: once pattern locks, extend one step only—answer is that next term. |
BETA
