🔹 Section A – Advanced MCQs (1 mark each)
- The number of factors of 36 is:
a) 6 b) 7 c) 8 d) 9 - Which number has exactly 3 factors?
a) 4 b) 6 c) 8 d) 10 - HCF of two consecutive numbers is always:
a) 0 b) 1 c) 2 d) depends - LCM of two co-prime numbers is:
a) sum b) difference c) product d) 1 - Which number is divisible by 2, 3, and 5?
a) 30 b) 45 c) 60 d) Both a & c - The smallest number divisible by 8, 12, and 15 is:
a) 60 b) 120 c) 240 d) 360 - Which is NOT co-prime?
a) (8,15) b) (9,10) c) (14,21) d) (17,18) - Number of prime numbers between 20 and 40:
a) 4 b) 5 c) 6 d) 7 - HCF × LCM of two numbers =
a) sum b) difference c) product d) square - Which number leaves remainder 1 when divided by 2, 3, and 4?
a) 11 b) 13 c) 25 d) 37
🔹 Section B – Integer & Logic Fill (2 marks each)
- The greatest 2-digit number divisible by 9 is ______
- The smallest 3-digit number divisible by 7 is ______
- If HCF = 5 and product = 500, LCM = ______
- A number divisible by 6 must be divisible by ______ and ______
- Number of factors of a prime number is ______
🔹 Section C – Short Answer (3 marks each)
- Find the number of factors of 72.
- Find the HCF of 36, 48, and 60.
- Find the LCM of 9, 12, and 15.
- Find prime factorization of 180.
- Find smallest number divisible by 4, 5, and 6.
🔹 Section D – Olympiad Case-Based (4 marks each)
📊 Case 1: School Parade Formation
- 84 boys and 126 girls are arranged in equal rows.
a) Maximum number of rows
b) Students per row
c) Boys and girls per row
📊 Case 2: Digital Timer Problem
- Three alarms ring after every 6, 8, and 12 minutes.
a) When will all ring together?
b) How many times in 1 hour?
📊 Case 3: Packaging Factory
- Items packed in boxes of 18 and 24.
a) Smallest equal number
b) If 5 such batches made, total items?
📊 Case 4: Sports League
- Teams formed from 45 players so each team has equal players.
Find all possible team sizes.
🔹 Section E – Long Answer (5 marks each)
- Find HCF and LCM of 48 and 180 using prime factorization.
- Verify: HCF × LCM = Product of numbers (use any two numbers)
- Find smallest number leaving remainder 2 when divided by 3, 4, and 5.
- Find the greatest number that divides 252 and 378 leaving remainder 0.
🔹 Section F – HIGH LEVEL HOTS (6 marks each)
- Find smallest number divisible by 2, 3, 4, 5, and 6 but not by 7.
- Find a number between 100 and 200 divisible by 9 and 12.
- Two numbers have HCF = 12 and LCM = 720
Find the product and one possible pair. - Find the least number which when divided by 8, 10, and 12 leaves remainder 3 in each case.
🔹 Section G – Assertion & Reason (3 marks each)
- Assertion: Every multiple of 6 is multiple of 3
Reason: 6 = 2 × 3 - Assertion: Prime numbers have exactly 2 factors
Reason: One factor is always itself - Assertion: 1 is neither prime nor composite
Reason: It has only one factor
🔹 Section H – MEGA CASE STUDY (10 marks)
📊 Case Study: Mega School Event
A school has:
- 96 boys
- 144 girls
- 192 badges
They want to form equal groups such that:
- Each group has same number of boys and girls
- Each group gets equal badges
- Maximum number of groups
- Boys per group
- Girls per group
- Badges per group
- Identify concept used
✅ ANSWER KEY (Concise)
Section A:
1-d, 2-a, 3-b, 4-c, 5-d, 6-c, 7-c, 8-a, 9-c, 10-b
Section B:
11. 99
12. 105
13. 100
14. 2 and 3
15. 2
Section C:
16. 12 factors
17. 12
18. 180
19. 2×2×3×3×5
20. 60
Section D:
21. 42 rows; 2 boys, 3 girls
22. 24 min; 2 times
23. 72; 360
24. 1,3,5,9,15,45
Section E:
25. HCF=12, LCM=720
26. Verified
27. 62
28. 126
Section F:
29. 60
30. 108 or 180
31. Product=8640; pair (24,360)
32. 123
Section G:
33. True
34. True
35. True
Section H:
36. 48 groups
37. 2
38. 3
39. 4
40. HCF