REASONING – MASTER REVISION SHEET
(Complete 1-Hour Quick Guide for all RRB NTPC/Group-D/ALP/Technician)

SECTION-1 : CORE CONCEPTS (TOP-30)

1. Series – Number: find constant difference/ratio
2. Series – Letter: remember EJOTY & CFILORUX positions
3. Series – Mixed: alternate / double-step / −1,+2 pattern
4. Analogy – Word: A : B :: C : D ⇒ A→B relation replicated
5. Analogy – Number: same ratio, square, cube, digit-sum
6. Analogy – Letter: positional mirror, forward/backward shift
7. Classification – pick the odd one out (property, dimension, use)
8. Coding-Decoding – direct: A→1, reverse: A→26, reverse-sum=27
9. Coding – word: write backwards, +1/-1, middle-letter static
10. Coding – sentence: 1st/last letter code, word-position code
11. Blood Relation – draw generation tree; “only son of my father” = me
12. Direction Sense – N=↑, E=→, left turn = anti-clockwise
13. Distance – Pythagoras: √(E²+N²); 30°-60°-90°: sides 1:√3:2
14. Ranking – left+right-1 = total; interchange ⇒ ±2 positions
15. Calendar – 1600 & 400 yr →0 odd day; 100 yr→5; leap ⇒ +2
16. Clock – 360°/60 = 6° per minute; hour-hand 0.5°/min
17. Clock – opposite angle = 180°; right angle = 90° (22 times/day)
18. Syllogism – Venn quick: All A⊂B, No A∩B, Some A∩B
19. Venn Diagram – 3-circle formula: n(A∪B∪C)=A+B+C−(A∩B+B∩C+C∩A)+A∩B∩C
20. Inequality – priority: > ≥ < ≤ = ; chain rule signs same direction
21. Input-Output – single-side: shift/word-length; double-side: ascending/descending
22. Puzzle – floor: 2-variables ⇒ grid; 3-var ⇒ 2 tables
23. Seating – circular: “left” = anti-clock; facing centre = inward
24. Seating – linear/row: North-facing right→left 1,2,3…
25. Seating – square/rectangular: corners 4, mid-sides 4
26. Data Sufficiency – answer choices fixed: (a)1 alone (b)2 alone (c) both (d) none
27. Statement–Assumption – implicit, not explicitly given
28. Statement–Conclusion – must definitely follow
29. Cause–Effect – cause always earlier; same topic
30. Figure – Counting: triangle= n(n+2)(2n+1)/8 (n=rows), square=Σr²

SECTION-2 : FORMULAS & SHORTCUTS

Odd Days → Century: 100y≡5, 200y≡3, 300y≡1, 400y≡0
Leap Year → divisible by 4 & (not 100 ∨ divisible by 400)
Mirror Time → 11:60 – given time (≈ 23:60 – T)
Angle between hands → |30H – 5.5M|; if >180° → 360 – angle
Relative Speed → same direction: S1–S2; opposite: S1+S2
Average Speed → 2ab/(a+b) (up/down same distance)
% Change → (new–old)/old ×100
Venn 2-set → only A = A – A∩B; exactly one = A+B–2A∩B
Coding trick → write A-Z above Z-A; immediate mirror pair
Prime check → test upto √n; after 5 check 6k±1
Square (51-59) → 25±unit; append unit² (e.g. 53²=2809)
Cube <20 → 1-10 already memorised; 11³=1331…19³=6859
Alphabet pos → EJOTY = 5,10,15,20,25; CFILORUX = 3,6,9,12,15,18,21,24
Letter pair distance → (27 – sum) for reverse; half distance → opposite
Triangle count in star → n(n-1)(n-2)/6 (n=vertex)
Square in n×n grid → Σr² (r=1…n)
Rectangle in grid → C(m+1,2)×C(n+1,2)

SECTION-3 : 50 MUST-KNOW FACTS

1. 1 Jan 2000 → Sat (reference)
2. 1 Jan 1900 → Mon
3. 26 Jan 1950 → Thu
4. 15 Aug 1947 → Fri
5. Century leap years: 1600,2000,2400…
6. Months with 5 Sun/Mon in 31-day month: 3 (Jan-May-Jul/Oct-Dec)
7. Angle 90° between hands ≈ 22 times/day
8. Opposite letters: A-Z, B-Y… M-N (13 pairs)
9. Sum of 1st n odd = n²
10. Sum 1st n even = n(n+1)
11. 2²⁰ = 1048576
12. 3¹⁰ = 59049
13. 7³ = 343 (railway favourite)
14. 12²=144, 13²=169, 14²=196, 15²=225
15. 16²=256, 18²=324, 19²=361
16. π≈22/7≈3.14
17. √2≈1.41, √3≈1.73, √5≈2.24
18. Prime <100 → 25 total
19. Only even prime = 2
20. 1-9 digit sum = 45
21. 10-19 digit sum = 145
22. Alphabet has 5 vowels, 21 consonants
23. Positional value of K = 11, V = 22
24. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 → first 12 primes
25. 6! = 720
26. 5²+12²=13² (Pythagorean triplet)
27. 7,24,25 → another triplet
28. 8,15,17 → triple
29. Total 26 letters; middle = M (13), N (14)
30. 1²+2²+…10² = 385
31. 1³+…5³ = 225 = (1+…5)²
32. 100 yrs = 36524 days +1 century leap
33. 1 gross = 144
34. 1 ream = 500 sheets
35. 1 mile ≈1.6 km
36. 1 nautical mile = 1.852 km
37. 1000 yrs called millennium
38. 25 yrs = silver jubilee
39. 50 yrs = golden
40. 60 yrs = diamond (railway retirement!)
41. 7 odd days ≡0 same calendar
42. 6 days after Mon → Sun
43. 71/2 minutes past 3 → hands at 90°
44. If today Mon, 63rd day → Thu (63 mod7=0)
45. 100° Celsius = 212° F (water boils)
46. 0° C = 32° F
47. −40° C = −40° F
48. Normal body 37°C = 98.4°F
49. Speed of sound ≈343 m/s
50. Light speed ≈3×10⁸ m/s

SECTION-4 : PREVIOUS-YEAR TRENDS (RRB 2016-23)

(Approx weightage NTPC CBT-1, Group-D CBT)

Series (Num+Let+Mix) – 4-5 Q
Analogy (all types) – 3-4
Classification – 2-3
Coding-Decoding – 2-3
Blood Relation – 1-2
Direction & Distance – 2-3
Ranking & Ordering – 1
Calendar/Clock – 1 each
Syllogism – 1
Venn (2-set) – 1
Inequality – 1
Puzzle (floor/month/linear) – 4-5
Seating (Circ/Line/Sq) – 3-4
Input-Output – 0-1
Data Sufficiency – 0-1
Statement–Conclusion – 1
Figure Counting – 1
Mirror/Water Image – 1
Embedded / Completion – 1
Paper fold-cut – 1

Total 25 Q in 20 min → <48 s/Q

SECTION-5 : 100 ONE-LINER CAPSULE

1-10

1. 2,3,5,7,11,13,17,19,23,29 → first ten primes
2. A-Z sum pos = 351
3. Reverse sum pair = 27 (A-Z, B-Y…)
4. 1³+2³+3³+4³ = 100
5. 3²+4² = 5²
6. 6,8,10 → smallest Pythagorean triplet even
7. 100÷7 remainder 2 → century starts Mon+2
8. 1 Jan 2024 → Mon (leap)
9. 29 Feb 2020 → Sat
10. Mirror of 08:20 → 03:40

11-20
11. Water image keeps upper half same
12. Left turn from North → West
13. Sum of angles in polygon = (n-2)×180°
14. Heptagon = 7 sides
15. Nonagon = 9
16. 12! ends with 2 zeros
17. 15! ends with 3 zeros
18. 1-100 primes = 25
19. Twin primes (3,5),(5,7),(11,13)…
20. Only prime ending with 5 = 5

21-30
21. 1-9 letter count (A to I) = 3,3,5,4,4,3,5,5,4
22. 1-100 perfect squares = 10
23. 1-1000 perfect cubes = 10
24. 2¹⁰ = 1024 (1 KB)
25. 2²⁰ = 1 MB
26. 2³⁰ ≈ 1 GB
27. 45° right triangle: sides 1:1:√2
28. 30°-60°-90°: 1:√3:2
29. Speed = 60 kmph = 16.67 m/s
30. 1 km = 1000 m = 0.62 mile

31-40
31. 1 yard = 3 ft = 0.914 m
32. 1 pound ≈ 0.45 kg
33. 1 gallon (US) ≈ 3.78 L
34. 1 hp ≈ 746 W
35. E = mc² (Einstein)
36. 1 AU ≈ 149.6 million km
37. Sound faster in solids > liquids > gases
38. Light year = distance, not time
39. 1 micron = 10⁻⁶ m
40. 1 nanometre = 10⁻⁹ m

41-50
41. Full circle = 360° = 2π rad
42. Straight angle = 180°
43. Reflex angle >180° <360°
44. Acute <90°, obtuse >90° <180°
45. Sum external angle any polygon = 360°
46. Lines of symmetry in square = 4
47. Equilateral triangle = 3 lines + 60° each
48. Regular hexagon = 6 lines, 120° internal
49. Sphere: volume 4/3πr³, surface 4πr²
50. Cube: vol a³, surface 6a²

51-60
51. Cylinder: vol πr²h, curved 2πrh
52. Cone: vol 1/3πr²h
53. Profit % = (SP-CP)/CP ×100
54. Loss % = (CP-SP)/CP ×100
55. Discount % = (MP-SP)/MP ×100
56. SI = PRT/100
57. CI = P(1+R/100)ᵗ – P
58. Sum of AP = n/2[2a+(n-1)d]
59. nth term AP = a+(n-1)d
60. Sum GP = a(rⁿ–1)/(r–1)

61-70
61. HCF × LCM = product (for 2 nums)
62. Dividend = divisor×quotient + remainder
63. 0! = 1
64. nC₀ = 1 = nCn
65. nCᵣ = nCₙ₋ᵣ
66. Total surds: √2,√3,√5,√6,√7,√10…
67. Rationalising factor of 1/(√a+√b) = (√a–√b)
68. log 1 = 0 (any base)
69. logₐa = 1
70. Change base: logₐb = log b / log a

71-80
71. sin²θ+cos²θ = 1
72. 1+tan²θ = sec²θ
73. 1+cot²θ = cosec²θ
74. sin 30° = 1/2
75. cos 60° = 1/2
76. tan 45° = 1
77. Distance = √[(x₂–x₁)²+(y₂–y₁)²]
78. Mid-point = [(x₁+x₂)/2, (y₁+y₂)/2]
79. Slope m = (y₂–y₁)/(x₂–x₁)
80. Quadratic roots: –b±√(b²–4ac) / 2a

81-90
81. Discriminant D>0 → real & distinct
82. D=0 → real & equal
83. D<0 → imaginary
84. Sum roots = –b/a, product = c/a
85. (a+b)² = a²+2ab+b²
86. (a–b)² = a²–2ab+b²
87. a²–b² = (a–b)(a+b)
88. (a+b+c)² = a²+b²+c²+2(ab+bc+ca)
89. a³+b³ = (a+b)(a²–ab+b²)
90. a³–b³ = (a–b)(a²+ab+b²)

91-100
91. If CP=SP → no profit no loss
92. Marked price always ≥ SP
93. Brokerage decreases SP for buyer
94. Percentage increase/decrease same base
95. Work: M₁D₁H₁ = M₂D₂H₂ (W constant)
96. Speed × Time = Distance (km & hr compatible)
97. Upstream speed = b–s; downstream = b+s
98. Average = sum/n
99. Mode = most frequent
100. Median middle after arrange ascending

SECTION-6 : COMMON CONFUSIONS CLEARED

Often Confused | Correct Fact
“Every century year is leap” | Only if divisible by 400
“Mirror of 03:40 is 08:20” | Actually 08:20 (yes both same)
“Water image = mirror image” | No – mirror vertical, water horizontal
“Left of North is East” | Left of North = West
“Opposite of 3 o’clock is 9” | Yes, 90° both sides
“All rectangles are squares” | False; reverse true
“Some is opposite of All” | False – Some can include All
“Grandfather’s only son” may be father/uncle | Actually = father (only son)
“5% of 50 same as 50% of 5” | True – both 2.5
“Speed in m/s × 5 → kmph” | ×18/5, not 5

SECTION-7 : MEMORY TRICKS

1. EJOTY → 5-10-15-20-25 (every 5)
   CFILORUX → 3-6-9-12-15-18-21-24 (every 3)
2. Calendar odd days:
   “She Feels Bad, She Gets Mad” → 0,3,2,0,3,2,0 (Century codes)
3. Leap year check: “4 & (100 → 400)” – sing “four-and-four-hundred”
4. Mirror time = 11:60 – T (imagine 12-hr cycle)
5. Prime <100: 4×6+1 → 4 lines of 6, add 2,3,5,7 (total 25)
6. Pythagorean triplets: “3-4-5, 5-12-13, 7-24-25, 8-15-17” – odd hyp pattern
7. Blood tree symbols: □ male, ○ female, = couple, vertical child
8. Direction turns: “Left” = anti-clock; write N-E-S-W clock to see
9. Venn 3-circle: “Total = All sum – Pair-wise sum + Triple + None”
10. Figure triangles: count rows n → formula n(n+2)(2n+1)/8

SECTION-8 : LAST-HOUR REVISION (TOP-20)

1. EJOTY & CFILORUX positions
2. Reverse letter pair sum = 27
3. Odd-day codes: 0-3-2-0-3-2-0 (centuries)
4. Leap-year rule: ÷4 & (÷100→÷400)
5. Mirror time shortcut: 11:60 – T
6. Angle formula: |30H – 5.5M|
7. 25 primes <100; 2 only even
8. Pythagorean triplets: 3-4-5, 5-12-13, 7-24-25, 8-15-17
9. Direction: Left of North = West; Right = East
10. Blood: “only son of my father” = myself
11. Ranking: Total = left+right−1
12. Venn 2-set: Only A = A – A∩B
13. Calendar: 1 Jan 2000 → Sat (reference)
14. 1 Jan 2024 → Mon (leap)
15. Series gap check: constant diff → +/−; ratio → ×/÷
16. Coding: write A-Z & Z-A parallel → instant mirror
17. Syllogism Venn: All ⊆, Some ∩, No disjoint
18. Inequality: chain same direction, else can’t relate
19. Puzzle grid: start with definite; fill 2-variable first
20. Speed kmph→m/s: ×5/18; m/s→kmph: ×18/5

✔ Read sheet front-to-back once (≈45 min)
✔ Re-read Section-8 just outside hall (10 min)
✔ Attempt series/analogy first (easy & high-scoring)
✔ Keep calm, use rough sheet for tree/diagram

ALL THE BEST – Crack RRB!