Mental Ability & Aptitude — TNPSC Group 1 Prelims (Unit X Guide + Practice)

Unit X Overview — What TNPSC Tests

TNPSC Group 1 Prelims Unit X (Aptitude & Mental Ability) covers these topic clusters:

Total: ~15 questions, ~22 marks

Part 1 — Number Series

Types of Number Series

Type 1: Arithmetic Progression (constant difference)

Each term increases/decreases by a fixed number.

Example: 3, 7, 11, 15, ? Common difference = 4 → Answer: 19

Type 2: Geometric Progression (constant ratio)

Each term multiplied by a fixed number.

Example: 2, 6, 18, 54, ? Ratio = 3 → Answer: 162

Type 3: Squares / Cubes

Example: 1, 4, 9, 16, 25, ? 1², 2², 3², 4², 5² → Answer: 36 (6²)

Example: 1, 8, 27, 64, ? 1³, 2³, 3³, 4³ → Answer: 125 (5³)

Type 4: Mixed / Two-step series

Example: 2, 3, 5, 8, 13, ? Differences: 1, 2, 3, 5 (Fibonacci-like) → Answer: 21

Example: 1, 2, 6, 24, ? 1×1=1, 1×2=2, 2×3=6, 6×4=24 → Answer: 120 (24×5)

Type 5: Missing term in middle

Example: 4, 9, ?, 25, 36 Perfect squares: 4=2², 9=3², 16=4², 25=5² → Answer: 16

Number Series Practice (10 Questions)

1. 7, 14, 21, 28, ?

• a) 33
• b) 35 ✓
• c) 36
• d) 42

2. 3, 6, 12, 24, ?

• a) 36
• b) 42
• c) 48 ✓
• d) 54

3. 1, 1, 2, 3, 5, 8, ?

• a) 11
• b) 13 ✓
• c) 14
• d) 16

Fibonacci: each term = sum of previous two. 5+8 = 13.

4. 2, 5, 10, 17, 26, ?

• a) 35
• b) 36
• c) 37 ✓
• d) 38

Differences: 3, 5, 7, 9, 11 (odd numbers) → 26+11 = 37

5. 100, 50, 25, 12.5, ?

• a) 5
• b) 6.25 ✓
• c) 6
• d) 5.5

Divide by 2 each time → 12.5 ÷ 2 = 6.25

6. 1, 8, 27, 64, 125, ?

• a) 196
• b) 216 ✓
• c) 225
• d) 243

Cubes: 6³ = 216

7. 4, 7, 12, 19, 28, ?

• a) 37
• b) 39 ✓
• c) 40
• d) 41

Differences: 3, 5, 7, 9, 11 → 28+11 = 39

8. 2, 3, 5, 9, 17, ?

• a) 29
• b) 33 ✓
• c) 31
• d) 35

Each term = (previous term × 2) - 1. 17×2 - 1 = 33

9. 0, 1, 4, 9, 16, 25, ?

• a) 30
• b) 32
• c) 36 ✓
• d) 38

0², 1², 2², 3², 4², 5², 6² = 36

10. 6, 11, 21, 41, ?

• a) 70
• b) 75
• c) 81 ✓
• d) 85

Each term = (previous × 2) - 1. 41×2 - 1 = 81

Part 2 — Analogies (Number, Letter, Word)

Number Analogies

Find the relationship between first pair → apply to second.

Format: 4 : 16 :: 7 : ? → 4² = 16, so 7² = 49

Format: 3 : 12 :: 5 : ? → 3 × 4 = 12, so 5 × 4 = 20

Letter Analogies

Format: AC : EG :: BD : ? → AC skips one letter (A_C); EG skips one letter (E_G) → BD skips one letter (B_D) → FH skips one (F_H) → Answer: FH

Format: AB : YX :: CD : ? → AB reversed from end = YX (A=1st, Y=25th from end; B=2nd, X=24th) → CD → WV → Answer: WV

Word Analogies (Concept-based)

Format: Doctor : Hospital :: Teacher : ? → Doctor works in Hospital; Teacher works in School

Format: Pen : Write :: Scissors : ? → Pen is used to Write; Scissors are used to Cut

Analogy Practice (8 Questions)

11. 2 : 8 :: 3 : ?

• a) 18
• b) 12
• c) 27 ✓
• d) 24

2³ = 8; 3³ = 27

12. 9 : 3 :: 49 : ?

• a) 5
• b) 7 ✓
• c) 6
• d) 9

√9 = 3; √49 = 7

13. ACEG : BDFH :: IKMO : ?

• a) JLNP
• b) JLNP ✓
• c) KLNO
• d) JKMN

Each letter shifted +1: I→J, K→L, M→N, O→P

14. Doctor : Stethoscope :: Carpenter : ?

• a) Needle
• b) Saw ✓
• c) Spanner
• d) Plough

15. Pen : Ink :: Lamp : ?

• a) Wire
• b) Switch
• c) Oil/Electricity ✓
• d) Glass

16. 25 : 125 :: 36 : ?

• a) 196
• b) 216 ✓
• c) 206
• d) 256

5² : 5³ :: 6² : 6³ → 36 : 216

17. FILM : ADGH :: MILK : ?

• a) HADG
• b) HADE ✓
• c) HIAG
• d) GHAD

Each letter -5: F→A, I→D, L→G, M→H → M→H, I→D, L→G, K→F → HDGF

Wait — let me recheck: F(6)-5=A(1), I(9)-5=D(4), L(12)-5=G(7), M(13)-5=H(8) → ADGH ✓ M(13)-5=H(8), I(9)-5=D(4), L(12)-5=G(7), K(11)-5=F(6) → HDGF

• a) HDGF
• b) HDGF ✓
• c) GHDF
• d) FGDH

18. Aeroplane : Pilot :: Ship : ?

• a) Crew
• b) Engineer
• c) Captain ✓
• d) Sailor

Part 3 — Coding and Decoding

How Coding Works

A code assigns letters/numbers to words or letters using a consistent pattern.

Type 1: Letter substitution If APPLE = BQQMF, then each letter is shifted +1. So GRAPE = HSBQF

Type 2: Reverse alphabet A=Z, B=Y, C=X... (position from start + position from end = 27) MANGO → NZMTL

Type 3: Number codes If A=1, B=2, C=3... CAT = 3+1+20 = 24

Type 4: Position shift If COMPUTER is coded as DPNQVUFS (each +1), what is PRINTER? P→Q, R→S, I→J, N→O, T→U, E→F, R→S → QSJOUFS

Coding Practice (6 Questions)

19. If CHAIR = 25891 and TABLE = 23564, what is the code for TEACH?

• a) 35225
• b) 35928 ✓
• c) 23598
• d) 35298

T=2, E=5, A=3, C=9, H=8 → TEACH = 25398

Correction: T(Table)=2, A=3, B=4, L=6, E=5; C(Chair)=9, H=8, A=3, I=8...

Let me use a clean example instead:

19. If MANGO = NBOHP (each letter +1), what is PAPAYA coded as?

• a) QBQBZB
• b) QBQBZB ✓
• c) QBQAZA
• d) RAQBZB

P+1=Q, A+1=B, P+1=Q, A+1=B, Y+1=Z, A+1=B → QBQBZB

20. In a code language, ROAD is written as URDG. How is SWAN written?

• a) VXDQ
• b) VZDQ ✓
• c) VZCQ
• d) WZDQ

R+3=U, O+3=R, A+3=D, D+3=G. So S+3=V, W+3=Z, A+3=D, N+3=Q → VZDQ

21. If CAT = 24 (C=3, A=1, T=20; sum=24), what is DOG?

• a) 24
• b) 26
• c) 30 ✓
• d) 28

D=4, O=15, G=7 → 4+15+7 = 26

Wait: D=4, O=15, G=7 → 26. Let me fix: Answer is 26.

• a) 24
• b) 26 ✓
• c) 30
• d) 28

22. If DELHI is coded as EFMIJ (each letter +1), what is MUMBAI?

• a) NVNCBJ
• b) NVNCBJ ✓
• c) NUNCBJ
• d) NVMBAJ

M+1=N, U+1=V, M+1=N, B+1=C, A+1=B, I+1=J → NVNCBJ

23. In a certain code, 15789 = AEGKI and 2346 = BDFH. What is the code for 23549?

• a) BDFKI
• b) BDEAI
• c) BDFAI ✓
• d) BDEKG

2=B, 3=D, 5=F, 4=... wait 4=H... Let me fix: 1=A, 5=E, 7=G, 8=K, 9=I and 2=B, 3=D, 4=F, 6=H 23549 = B, D, E, F, I → BDEFI

• a) BDEFI
• b) BDEFI ✓
• c) BDFEI
• d) BDEIF

24. If in a code language, 'pen' is 'eraser', 'eraser' is 'book', 'book' is 'scale', what do you write with?

• a) Pen
• b) Book
• c) Eraser ✓
• d) Scale

In this code, 'pen' is called 'eraser' — so you write with what is called 'eraser'.

Part 4 — Arithmetic (Percentages, Ratio, SI/CI)

Key Formulas

Percentage:

• x% of y = (x × y) / 100
• % increase = (Increase / Original) × 100
• % decrease = (Decrease / Original) × 100

Ratio and Proportion:

• If a:b = c:d then a×d = b×c (cross multiply)
• Compound ratio of a:b and c:d = ac:bd

Simple Interest:

• SI = (P × R × T) / 100
• Amount = P + SI

Compound Interest:

• A = P(1 + R/100)^T
• CI = A - P

Common shortcut — CI for 2 years:

• CI = SI + (SI × R / 200)
• Or: CI = P[(1+r)² - 1]

Arithmetic Practice (10 Questions)

25. What is 15% of 240?

• a) 32
• b) 36 ✓
• c) 38
• d) 40

240 × 15/100 = 36

26. A price increased from ₹500 to ₹600. What is the percentage increase?

• a) 15%
• b) 20% ✓
• c) 25%
• d) 18%

(100/500) × 100 = 20%

27. If A:B = 3:4 and B:C = 2:3, what is A:B:C?

• a) 3:4:6
• b) 3:4:6 ✓
• c) 6:8:9
• d) 6:8:12

B is common. B = LCM(4,2) = 4. A:B = 3:4; B:C = 2:3 = 4:6. So A:B:C = 3:4:6

28. Find the Simple Interest on ₹8,000 at 5% per annum for 3 years.

• a) ₹1,000
• b) ₹1,100
• c) ₹1,200 ✓
• d) ₹1,500

SI = (8000 × 5 × 3)/100 = 1200

29. What is the Compound Interest on ₹10,000 at 10% per annum for 2 years?

• a) ₹2,000
• b) ₹2,050
• c) ₹2,100 ✓
• d) ₹2,200

A = 10000 × (1.1)² = 10000 × 1.21 = ₹12,100 → CI = ₹2,100

30. In a class of 50 students, 60% are girls. How many boys are there?

• a) 25
• b) 20 ✓
• c) 30
• d) 18

Girls = 60% of 50 = 30. Boys = 50 - 30 = 20

31. A bag contains ₹1, ₹2, and ₹5 coins in ratio 3:2:1. Total coins = 72. What is the total value?

• a) ₹96
• b) ₹120 ✓
• c) ₹108
• d) ₹144

Ratio 3:2:1 → 36 + 24 + 12 = 72 coins ✓ Value = (36×1) + (24×2) + (12×5) = 36 + 48 + 60 = ₹144

Correction: Answer is ₹144.

• a) ₹120
• b) ₹132
• c) ₹144 ✓
• d) ₹156

32. If 12 workers can complete a job in 15 days, how many days will 9 workers take?

• a) 18 days
• b) 20 days ✓
• c) 22 days
• d) 24 days

Workers × Days = constant. 12 × 15 = 9 × D → D = 180/9 = 20 days

33. A train travels 360 km in 4 hours. What is its speed in km/h?

• a) 80 km/h
• b) 90 km/h ✓
• c) 100 km/h
• d) 72 km/h

Speed = Distance/Time = 360/4 = 90 km/h

34. Find the average of 15, 25, 35, 45, 55.

• a) 30
• b) 35 ✓
• c) 40
• d) 45

Sum = 175; Count = 5; Average = 175/5 = 35

Part 5 — Data Interpretation

How to Approach DI Questions

1. Read the table/chart title first — understand what data is shown 2. Note the units — thousands, lakhs, percentages 3. Answer only what is asked — don't read extra data 4. Use approximation — exact calculation wastes time

Practice — Table DI

The following table shows the production (in thousand tonnes) of wheat and rice in 5 states:

35. Which state has the highest total grain production?

• a) Punjab
• b) Haryana
• c) UP ✓
• d) Tamil Nadu

UP = 200+160 = 360; Punjab = 300; TN = 260; Haryana = 220. UP is highest.

36. What is Tamil Nadu's rice production as a percentage of total rice production?

• a) 30%
• b) 36.4% ✓
• c) 40%
• d) 25%

Total rice = 120+80+160+60+240 = 660. TN share = 240/660 × 100 = 36.4%

37. The ratio of wheat to rice production in Punjab is:

• a) 2:1
• b) 3:2 ✓
• c) 4:3
• d) 5:3

Punjab wheat:rice = 180:120 = 3:2

38. How much more wheat does UP produce than Haryana?

• a) 50,000 tonnes
• b) 40,000 tonnes
• c) 60,000 tonnes ✓
• d) 70,000 tonnes

UP wheat = 200,000; Haryana = 140,000; Difference = 60,000 tonnes

Part 6 — Logical Reasoning & Syllogisms

Syllogism Rules (Using Venn Diagrams)

Always draw circles. The conclusion must be TRUE based ONLY on the given statements — not general knowledge.

Type 1: All A are B. All B are C. → Conclusion: All A are C. ✓ (A circle inside B inside C)

Type 2: All A are B. No B is C. → Conclusion: No A is C. ✓

Type 3: Some A are B. All B are C. → Conclusion: Some A are C. ✓ (the "some A" that are B must also be C)

Type 4: Some A are B. Some B are C. → Conclusion: Some A are C. ✗ (NOT necessarily true — the "some" may not overlap)

Syllogism Practice (6 Questions)

39. Statements: All cats are animals. All animals are living beings. Conclusion I: All cats are living beings. Conclusion II: Some living beings are cats.

• a) Only Conclusion I follows
• b) Only Conclusion II follows
• c) Both I and II follow ✓
• d) Neither follows

All cats → animals → living beings. So all cats are living beings (I). And since cats exist, some living beings are cats (II).

40. Statements: Some books are pens. All pens are erasers. Conclusion I: Some books are erasers. Conclusion II: All erasers are books.

• a) Only Conclusion I follows ✓
• b) Only Conclusion II follows
• c) Both follow
• d) Neither follows

"Some books are pens" and "all pens are erasers" → those books that are pens are also erasers → Some books are erasers (I ✓). But not all erasers need to be books (II ✗).

41. Statements: No table is a chair. All chairs are wooden. Conclusion I: No table is wooden. Conclusion II: Some wooden things are chairs.

• a) Only I follows
• b) Only II follows ✓
• c) Both follow
• d) Neither follows

No table is chair — but tables could still be wooden (they could be wooden through another path). So I doesn't necessarily follow. But since all chairs are wooden, some wooden things are chairs (II ✓).

42. Statements: All mangoes are fruits. Some fruits are sweet. Conclusion I: Some mangoes are sweet. Conclusion II: All sweet things are fruits.

• a) Only I
• b) Only II
• c) Both
• d) Neither ✓

"Some fruits are sweet" — those fruits may or may not include mangoes. Can't conclude I. And not all sweet things are necessarily fruits (II also fails).

43. Statements: All doctors are graduates. Ravi is a doctor. Conclusion: Ravi is a graduate.

• a) Does not follow
• b) Follows ✓
• c) Partially follows
• d) Cannot be determined

44. Statements: Some students passed. All who passed got medals. Conclusion I: Some students got medals. Conclusion II: All students got medals.

• a) Only II
• b) Only I ✓
• c) Both
• d) Neither

"Some students passed" and "all who passed got medals" → those some students got medals (I ✓). But not ALL students passed, so II doesn't follow.

Part 7 — Clocks and Calendars

Clock Problems

Key facts:

• Clock face = 360°
• Hour hand moves: 360° in 12 hours = 0.5° per minute
• Minute hand moves: 360° in 60 minutes = 6° per minute
• Relative speed = 6° - 0.5° = 5.5° per minute

Angle between hands formula:

• Angle = |30H - 5.5M| where H = hours, M = minutes

Example: Angle at 3:00

Example: Angle at 6:30

Calendar Problems

Key facts:

• Ordinary year = 365 days = 52 weeks + 1 odd day
• Leap year = 366 days = 52 weeks + 2 odd days
• Leap year: divisible by 4; century year divisible by 400
• Odd days in 100 years = 5; 200 years = 3; 300 years = 1; 400 years = 0

Day calculation: Add up odd days → divide by 7 → remainder gives the day (0=Sun, 1=Mon, 2=Tue, 3=Wed, 4=Thu, 5=Fri, 6=Sat)

Clocks & Calendars Practice (5 Questions)

45. What is the angle between the hands of a clock at 4:00?

• a) 100°
• b) 120° ✓
• c) 130°
• d) 90°

|30×4 - 5.5×0| = |120 - 0| = 120°

46. A clock shows 3:15. What is the angle between the hands?

• a) 0°
• b) 7.5° ✓
• c) 15°
• d) 22.5°

|30×3 - 5.5×15| = |90 - 82.5| = 7.5°

47. January 1, 2024 is a Monday. What day is January 1, 2025?

• a) Monday
• b) Wednesday ✓
• c) Tuesday
• d) Thursday

2024 is a leap year (366 days = 52 weeks + 2 odd days). Monday + 2 = Wednesday

48. How many leap years are there between 2001 and 2024?

• a) 5
• b) 6 ✓
• c) 7
• d) 4

2004, 2008, 2012, 2016, 2020, 2024 = 6 leap years

49. If today is Wednesday, what day will it be after 100 days?

• a) Monday
• b) Friday ✓
• c) Thursday
• d) Saturday

100 days = 14 weeks + 2 days. Wednesday + 2 = Friday

Part 8 — Area, Volume, Perimeter

Key Formulas

Use π = 22/7 or 3.14 in calculations.

Area & Volume Practice (5 Questions)

50. A rectangle has length 12 cm and breadth 8 cm. What is its area?

• a) 80 sq cm
• b) 96 sq cm ✓
• c) 100 sq cm
• d) 84 sq cm

51. What is the circumference of a circle with radius 7 cm? (π = 22/7)

• a) 42 cm
• b) 44 cm ✓
• c) 46 cm
• d) 40 cm

C = 2πr = 2 × (22/7) × 7 = 44 cm

52. A cube has side 5 cm. What is its volume?

• a) 100 cm³
• b) 125 cm³ ✓
• c) 150 cm³
• d) 75 cm³

V = 5³ = 125 cm³

53. The area of a triangle with base 10 cm and height 6 cm is:

• a) 60 sq cm
• b) 30 sq cm ✓
• c) 25 sq cm
• d) 45 sq cm

A = ½ × 10 × 6 = 30 sq cm

54. A cylinder has radius 7 cm and height 10 cm. What is its volume? (π = 22/7)

• a) 1,450 cm³
• b) 1,540 cm³ ✓
• c) 1,600 cm³
• d) 1,500 cm³

V = πr²h = (22/7) × 49 × 10 = 22 × 70 = 1,540 cm³

Exam Strategy — Unit X

Time allocation: 15 questions × 45 seconds = ~11 minutes. Attempt Unit X in one focused stretch.

Order of difficulty (easiest first): 1. Number series (pattern recognition — 20 seconds each) 2. Analogies (30 seconds each) 3. Basic arithmetic — average, ratio, percentage 4. Area/Volume (formula application) 5. Data Interpretation (read table once, answer 3–4 questions) 6. Syllogisms (draw Venn diagram — 60 seconds each) 7. Clocks (formula application)

Common mistakes to avoid:

• Series: Don't just look at +/- differences. Check ×, ², ³ too.
• Percentages: Remember "x% of y" ≠ "y% of x" in different contexts.
• Syllogisms: Never use outside knowledge — only what statements say.
• DI: Read the UNIT carefully (thousands vs lakhs changes everything).
• Clocks: Angle formula uses H × 30, not H × 60.

Board Exam Quick Facts

• Unit X in Group 1 Prelims = ~15 questions, 1.5 marks each = ~22 marks
• Number series: check differences, ratios, squares, cubes in order
• SI = PRT/100; CI for 2 years = P[(1+r/100)² - 1]
• Angle between clock hands = |30H − 5.5M|
• Leap year: divisible by 4 (not century) OR divisible by 400 (century)
• Syllogism: always draw Venn diagram — never assume from general knowledge
• Area of triangle = ½ × base × height; Circle area = πr²; Circle circumference = 2πr