📘CLASS 6 MATHS CHAPTER 3 – PLAYING WITH NUMBERS 📝 MODEL TEST PAPER

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Time: 2 Hours | Maximum Marks: 80

🔹 Section A – MCQs (1 mark each)

  1. Which of the following is a prime number?
    a) 27 b) 31 c) 39 d) 51
  2. The smallest composite number is:
    a) 1 b) 2 c) 3 d) 4
  3. HCF of 12 and 18 is:
    a) 2 b) 3 c) 6 d) 12
  4. LCM of 6 and 8 is:
    a) 12 b) 24 c) 48 d) 6
  5. Which pair is co-prime?
    a) (8, 16) b) (9, 27) c) (14, 15) d) (12, 18)
  6. Number of factors of 16:
    a) 3 b) 4 c) 5 d) 6
  7. Prime factorization of 20 is:
    a) 2×2×5 b) 2×10 c) 4×5 d) 1×20
  8. Which is NOT a prime number?
    a) 11 b) 13 c) 15 d) 17
  9. LCM of 5 and 9:
    a) 45 b) 14 c) 9 d) 5
  10. HCF of co-prime numbers is:
    a) 0 b) 1 c) same number d) product

🔹 Section B – Fill in the Blanks (1 mark each)

  1. The factors of 1 are ______
  2. The smallest prime number is ______
  3. Even numbers are divisible by ______
  4. A number divisible by 10 must end in ______
  5. HCF of two identical numbers is ______

🔹 Section C – Short Answer (2 marks each)

  1. Find all factors of 30.
  2. Find the prime factorization of 84.
  3. Find the HCF of 20 and 25.
  4. Find the LCM of 10 and 12.
  5. Check if 97 is prime.
  6. Write first five multiples of 9.
  7. Write two composite numbers between 10 and 20.
  8. Check if 121 is a perfect square.
  9. Write two co-prime numbers.
  10. Find common factors of 16 and 24.

🔹 Section D – Case-Based Questions (3 marks each)

📘 Case 1: Classroom Arrangement

  1. A teacher has 40 pencils and 60 pens. She wants to distribute them equally among students.
    a) Maximum number of students?
    b) Items each student gets?

📘 Case 2: Traffic Signals

  1. Two traffic lights blink every 12 seconds and 18 seconds.
    a) After how many seconds will they blink together?
    b) Which concept is used?

📘 Case 3: Sweet Boxes

  1. A shopkeeper has 54 chocolates and 72 candies.
    a) Maximum number of boxes?
    b) Items per box?

📘 Case 4: Sports Teams

  1. 36 boys and 48 girls form equal teams.
    a) Number of teams?
    b) Members per team?

📘 Case 5: School Bell

  1. Bells ring every 5 and 7 minutes.
    When will they ring together again?

🔹 Section E – Long Answer (4 marks each)

  1. Find HCF and LCM of 18 and 30. Verify relation.
  2. Find smallest number divisible by 3, 4, and 6.
  3. Find prime factorization of 96 using division method.
  4. Find HCF of 24, 36, and 60.
  5. Find LCM of 8, 12, and 15.

🔹 Section F – Higher Order Thinking (HOTS) (5 marks each)

  1. Find smallest number leaving remainder 1 when divided by 2, 3, 4.
  2. Find smallest number divisible by 4, 5, and 6.
  3. Two numbers have HCF = 6 and LCM = 180.
    Find their product.
  4. Find a number divisible by both 8 and 12 and lies between 50 and 100.
  5. A number is divisible by 3 and 5 but not by 2. Give one example.

🔹 Section G – Assertion & Reason (2 marks each)

  1. Assertion: 1 is a prime number
    Reason: It has only one factor
  2. Assertion: 2 is the only even prime number
    Reason: All other even numbers are divisible by 2
  3. Assertion: HCF of co-primes is 1
    Reason: They have no common factor except 1
  4. Assertion: LCM is always greater than HCF
    Reason: LCM includes all prime factors
  5. Assertion: 49 is prime
    Reason: It has only two factors

🔹 Section H – Case Study (Real-Life Application) (5 marks each)

📊 Case Study 6: School Picnic

  1. 84 students and 126 sandwiches are to be divided equally.
    a) Number of groups
    b) Students per group
    c) Sandwiches per group

📊 Case Study 7: Factory Packaging

  1. Boxes of 6 and 9 items are packed.
    a) Smallest equal number
    b) If tripled, new number

📊 Case Study 8: Festival Lights

  1. Lights blink every 8 and 10 seconds.
    Find when they blink together 3rd time.

📊 Case Study 9: Book Stacking

  1. 45 books and 75 notebooks arranged equally
    Find max groups and items

📊 Case Study 10: Sports Practice

  1. Players practice every 3, 4, and 6 days
    Find next common practice day

✅ FINAL ANSWER KEY (SHORT)

MCQs:
1-b, 2-d, 3-c, 4-b, 5-c, 6-c, 7-a, 8-c, 9-a, 10-b

Fill in blanks:
11. 1
12. 2
13. 2
14. 0
15. same number

Key Answers:
16. 1,2,3,5,6,10,15,30
17. 2×2×3×7
18. 5
19. 60
20. Prime
21. 9,18,27,36,45
22. 12,14
23. Yes
24. (8,15)
25. 1,2,4,8

Case-Based Highlights:
26. 20 students, (2 pencils + 3 pens)
27. 36 sec, LCM
28. 18 boxes, (3 + 4)
29. 12 teams
30. 35 minutes

Long Answers:
31. HCF=6, LCM=90
32. 12
33. 2×2×2×2×2×3
34. 12
35. 120

HOTS:
36. 13
37. 60
38. Product = 1080
39. 72 or 96
40. 15

Assertion:
41. False
42. True
43. True
44. True
45. False

Case Study:
46. 42 groups
47. 18 → 54
48. 40 × 3 = 120 sec
49. 15 groups
50. 12 days

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