Study note + questions

Logical reasoning

By TNPSC Guide editorial team · Last updated: 02.11.2026

Key numbers

Key answers

3 × 3 × 4 seats, 5 empty	36, 31 students (class 6, page 110)
2 shorts, 3 shirts	6 ways (class 6, page 110-111)
Four-digit numbers from 3, 6, 9, 5	24 (class 6, page 112)
7 snacks or 9 lunches	16 (class 8, page 243)
3 shirts, 2 trousers, 3 pairs of shoes	18 (class 8, page 244)
Leader and assistant from 4	12 (class 8, page 244-245)
Six-character password	67,60,000 (class 8, page 245)
A-E and three digits, without A000 and the like	4995 (class 8, page 288)
75 days before a Monday	Wednesday (class 10, page 51-52)
32 hours from Wednesday 22.30	Friday 6.30 (class 10, page 51)
Sunday 23:30 Chennai, 11 hours, London time	6 a.m. Monday (class 10, page 349)
Coimbatore-Karur: 131 / 66 + 101	through Vellakoil (class 7, page 126-127)

Easy to confuse

Addition principle / multiplication principle	"or", not at the same time: m + n / "and", both together: m × n; 7 or 9 = 16, not 63
"சார்ந்திராத" / "சார்ந்து அமையும்"	the book's words; "சார்ந்து" means happening together; do not decide by the word alone
Leader and assistant: 12 / 16	subtract the 4 ways with one person in both posts
4995 / 5000	only the 5 numbers A000, B000, C000, D000, E000 are left out
Backwards / forwards in modulo 7	75 days before: −4 + 7 = 3, Wednesday; adding the remainder 5 forwards gives Saturday (wrong)
Chennai time − 4.30 / + 4.30	the question gives Chennai as ahead, so subtract for London; adding gives 15:00 (wrong)
Systematic list / random list	fix one and vary the rest; a random list misses arrangements
Relation to whom / relation of whom	find the relation to the person asked about; reading it the other way gives a wrong option such as "daughter"
a ≠ b, b ≠ c / a ≠ c	a ≠ c is not certain; a = c may hold

The full note

Systematic listing

Counting in order, missing nothing and counting nothing twice, is systematic listing. With shorts A, B and shirts p, q, r there are 6 ways: Ap, Aq, Ar, Bp, Bq, Br. To paint three floors red, blue and green, fix one colour and swap the other two: 2 ways for each choice, 6 in all. Using 3, 6, 9, 5 once each, 6 numbers begin with each digit, so there are 24 four-digit numbers. Listing at random misses some arrangements. Example: picking one of two pairs of shorts and one of three shirts before school is exactly this.

Counting in a fixed order

Counting is easy when things sit in fixed places in order. 3 students on a long bench, 3 benches in a row and 4 rows make 3 × 3 × 4 = 36 students. If each of the three benches of the last row has only 2 and the bench in front of them only one, there are 3 + 2 = 5 empty places and 31 students. The book's answers: with black and blue shorts and white, blue and red shirts, avoiding a same-colour pair gives 5 ways; stacking two red and two blue blocks gives 6 kinds of four-floor building.

The addition and multiplication principles

The addition principle of counting: if two acts that do not depend on each other can happen in m ways and n ways, and cannot both happen at once, one or the other can happen in (m + n) ways. One of 7 snacks or one of 9 lunches: 7 + 9 = 16 ways. The multiplication principle: when both acts happen together, the first in m ways and, for each of those, the second in n ways, both can happen in (m × n) ways. 3 routes from A to B and 2 from B to C: 3 × 2 = 6 ways. 3 shirts, 2 pairs of trousers and 3 pairs of shoes: 3 × 2 × 3 = 18 ways.

The word "சார்ந்து"

The book calls the addition principle "ஒன்றையொன்று சார்ந்திராத" and the multiplication principle "ஒன்றையொன்று சார்ந்து அமையும்". Here "சார்ந்து" means that the two acts happen together. So do not decide by the word alone. "Or" (cannot happen at the same time) means addition; "and" (both together) means multiplication. 7 snacks or 9 lunches = 16, not 63; 3 routes then 2 routes = 6, not 5. Example: choosing only breakfast or lunch at a hotel is addition; choosing a bus and then an auto to reach a town is multiplication.

Example: A leader and an assistant

In how many ways can a leader and an assistant leader be chosen from the 4 members M, A, T, H? One person cannot hold both posts.

The leader has 4 choices; counting 4 for the assistant too gives 4 × 4 = 16.
Of these, the 4 ways with one person in both posts are impossible.
16 − 4 = 12.

Answer: 12 ways. Counting 16 is wrong.

Example: A six-character password

If the first two characters are any of the 26 English letters, the third is one of 10 special characters and the last three are digits from 0 to 9, how many passwords are there?

Every place must be filled together: the multiplication principle.
26 × 26 × 10 × 10 × 10 × 10.

Answer: 67,60,000 ways.

The book's other answers

One of 3 ice creams or one of 2 cakes: 5. One of 5 churidars or one of 4 gowns: 9. One each of 2 bags and 3 water bottles: 6. One of 26 boys or 15 girls: 41. A four-digit lock number with 0-9 in each place: 10000. Tossing three coins at once: 8 outcomes. Serial numbers with a letter A-E first and then three digits, leaving out the five A000, B000, C000, D000, E000: 5 × 10 × 10 × 10 − 5 = 4995, not 5000. Two-digit numbers with 7 as a digit: 18.

Days and hours: modular arithmetic

Number the weekdays 0 (Sunday), 1 (Monday), 2, 3, 4, 5, 6 (Saturday). Since a week has 7 days, work modulo 7 to find a day before or after; for hours, work modulo 24. Counting backwards gives a negative number; add 7 to make it a positive remainder. The book's answers: 100 hours after 7 a.m. is 11 a.m.; 15 hours before 11 p.m. is 8 a.m.; 45 days after a Tuesday is a Friday. Example: a market held every 7 days always falls on the same weekday.

Example: Which day was 75 days ago

Today is Monday. If the birthday was 75 days ago, which day was it?

Monday = 1. 1 − 75 = −74.
−74 ≡ −4 (mod 7); adding 7 gives 7 − 4 = 3.
3 stands for Wednesday.

Answer: Wednesday. Adding the remainder of 75 ÷ 7, which is 5, forwards (Monday + 5 = Saturday) is wrong. 2022 question 125 uses this same data.

Example: A 32-hour journey

A 32-hour journey starts at 22.30 on a Wednesday. When does it end?

22.30 + 32 = 54.30.
54.30 ≡ 6.30 (mod 24); 32 = 1 × 24 + 8: 24 hours bring Thursday 22.30, and 8 more hours cross another midnight.
From Wednesday night, past Thursday, to Friday morning.

Answer: 6.30 on Friday morning.

Time differences

If two places have a time difference, add the travel time first, then apply the difference in the right direction. An 11-hour flight that leaves Chennai at 23:30 on a Sunday ends on Monday morning, Chennai time. The question gives Chennai time as 4.30 hours ahead of London, so London time = Chennai time − 4.30. So the plane lands in London at 6 a.m. on Monday. Adding 4.30 gives the wrong answer 15:00.

Route maps

A route map helps plan a journey and shows the places to see and the ways between them. On the compass of the Arignar Anna Zoological Park map, north is up, south down, east right and west left. With the scale 1 unit = 100 m, 10 units between home and the library are 1000 m; from school to home through the library is 1100 + 1000 = 2100 m. From the children's park the school is 1100 m away and home 1200 m, so the school is nearer. Add up the total distance of each route separately and compare.

Example: The shortest route

From Coimbatore to Karur through Vellakoil is 131 km; through Erode it is two parts of 66 km and 101 km. Which is shorter?

Through Vellakoil: 131 km.
Through Erode: 66 + 101 = 167 km.
131 < 167.

Answer: through Vellakoil. In the same way, from A to D directly is 7 m, through B 4 + 5 = 9 m and through C 2 + 6 = 8 m, so the direct link uses the least cable. Of the four routes from B to F, 600, 520, 450 and 740 m, B → D → G → F (100 + 200 + 150 = 450 m) is the shortest.

Relation questions

In a relation question, start from the speaker and write each relation as one step. Two simple facts help: a person's sister is also a daughter of that person's father; a person's son's daughter is that person's granddaughter. Words such as "only son" make sure that the person in two relations is the same person. Before choosing the answer, read again whose relation is asked for; reading it the other way gives a wrong option.

Example: Finding a relation step by step

Muthu says, "Meena is the daughter of my only son Selvam." Kavitha is Meena's sister. How is Kavitha related to Selvam and to Muthu?

Selvam is Muthu's only son; Meena is Selvam's daughter.
Kavitha is Meena's sister, so Kavitha is also Selvam's daughter.
Muthu's son's daughter is Muthu's granddaughter.

Answer: Kavitha is Selvam's daughter and Muthu's granddaughter. Changing "to whom" changes the answer.

What is certain

From the two statements a ≠ b and b ≠ c nothing certain follows about a and c: a ≠ c may hold, or a = c may hold (for example a = c = 1, b = 2). In such a question the answer is the statement that is always true; "a, b, c are all different" is not certain. Example: if Arun and Balu are from different towns, and Balu and Chandran are from different towns, Arun and Chandran may be from the same town or from different towns.

Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (6ஆம் வகுப்புக் கணக்கு, பருவம் 1, இயல் 6 (தகவல் செயலாக்கம்), பக்கம் 109-117, விடைகள் பக்கம் 129; 7ஆம் வகுப்புக் கணக்கு, பருவம் 1, இயல் 6 (6.3 பாதை வரைபடம்), பக்கம் 124-127, விடைகள் பக்கம் 138; 8ஆம் வகுப்புக் கணக்கு, இயல் 7 (7.2 எண்ணுதலின் அடிப்படைக் கொள்கைகள்), பக்கம் 242-245, 254-255, விடைகள் பக்கம் 288; 10ஆம் வகுப்புக் கணிதம், இயல் 2 (2.5 மட்டு எண்கணிதம்), பக்கம் 51-52, விடைகள் பக்கம் 349; TNPSC வினாத்தாள்கள் CCSE4GT/2024 பக்கம் 88, CCSEIVGT/2025 பக்கம் 122 (வினாத்தாள் விதிகள் மட்டும்))

PYQ (2012-2025 papers)

2025 · G4 · Question 198 · Final answer key
2024 · G4 · Question 193 · Final answer key
2022 · G4 · Question 125 · Final answer key
2022 · G4 · Question 180 · Final answer key
2012 · G4 · Question 50 · Provisional answer key
2012 · G4 · Question 94 · Provisional answer key

Provisional key: until TNPSC publishes the final key; the answer may change.

Free questions

Question 1
A hall has 5 rows, each row has 4 long benches, and each bench seats 3 students. On each of the four benches of the last row 2 students sit, on one bench of the row before it one student sits, and every other bench has 3. How many students are in the hall?
1. A. 56
2. B. 60
3. C. 54
4. D. 48
Answer and explanation
Correct answer: C. 54
Seats in all: 3 × 4 × 5 = 60; each bench of the last row has 1 empty seat, 4 in all; one bench of the row before has 2 empty seats; empty seats 4 + 2 = 6; students 60 − 6 = 54.
Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம், p. 110 (PDF p. 114))
Question 2
Two shorts A, B and four shirts p, q, r, s are listed systematically as Ap, Aq, Ar, As, Bp, ... Which pair comes 7th?
1. A. Bq
2. B. Bs
3. C. Br
4. D. Ar
Answer and explanation
Correct answer: C. Br
Four with A: Ap, Aq, Ar, As (1-4); then with B: Bp (5), Bq (6), Br (7), Bs (8); so the 7th is Br; there are 8 pairs, none missed and none repeated.
Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம், pp. 110-111 (PDF pp. 114-115))
Question 3
Three floors are to be painted red, blue and green, each colour once. If the colour of one floor is fixed, in how many ways can the other two floors be painted?
1. A. 2
2. B. 1
3. C. 3
4. D. 6
Answer and explanation
Correct answer: A. 2
With green fixed for one floor, the other two take red-blue or blue-red: 2 ways; fixing each of the three colours in turn gives 3 × 2 = 6 ways in all.
Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம், pp. 111-112 (PDF pp. 115-116))
Question 4
Four-digit numbers are written using each of the digits 2, 4, 7, 8 once only. How many of them are greater than 7000?
1. A. 12
2. B. 6
3. C. 18
4. D. 24
Answer and explanation
Correct answer: A. 12
Using each of four digits once, 6 numbers begin with each digit; those greater than 7000 begin with 7 or 8: 6 + 6 = 12 (out of 24).
Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 6 தகவல் செயலாக்கம், p. 112 (PDF p. 116))

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