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Solutions: Section 5.1

January 15, 2025
2 min read
solutions common-multiples

Page 108: Figure it Out

Q1. At what number is ‘idli-vada’ said for the 10th time?

Solution: ‘Idli-vada’ is said at common multiples of 3 and 5. LCM of 3 and 5 is 15. The sequence is: 15, 30, 45, 60… The 10th time will be 15×10=15015 \times 10 = \mathbf{150}.

Q2. Game played from 1 to 90.

a. How many times ‘idli’? Multiples of 3 in 90: 90÷3=3090 \div 3 = 30. Answer: 30 times.

b. How many times ‘vada’? Multiples of 5 in 90: 90÷5=1890 \div 5 = 18. Answer: 18 times.

c. How many times ‘idli-vada’? Multiples of 15 in 90: 90÷15=690 \div 15 = 6. (15, 30, 45, 60, 75, 90). Answer: 6 times.

Q3. Game played till 900?

  • ‘Idli’ (Multiples of 3): 900÷3=300900 \div 3 = 300 times.
  • ‘Vada’ (Multiples of 5): 900÷5=180900 \div 5 = 180 times.
  • ‘Idli-Vada’ (Multiples of 15): 900÷15=60900 \div 15 = 60 times.

Page 110: Figure it Out

Q1. Multiples of 40 between 310 and 410.

Multiples of 40: 40, 80… 280, 320, 360, 400, 440. Numbers between 310 and 410 are: Answer: 320, 360, 400.

Q2. Who am I?

a. Less than 40. Factor is 7. Sum of digits is 8. Multiples of 7 less than 40: 7, 14, 21, 28, 35. Sums of digits:

  • 7 (7)
  • 14 (1+4=5)
  • 21 (2+1=3)
  • 28 (2+8=10)
  • 35 (3+5=8) -> Match! Answer: 35.

b. Less than 100. Factors 3 and 5. Digits differ by 1. Multiples of 3 and 5 (i.e., 15): 15, 30, 45, 60, 75, 90. Digit Check:

  • 15: Diff = 4
  • 30: Diff = 3
  • 45: Diff = 1 (5−4=15-4=1) -> Match!
  • 60: Diff = 6
  • 75: Diff = 2
  • 90: Diff = 9 Answer: 45.

Q7. Treasure Hunt (Page 111)

Treasures on 28 and 70. Find jump sizes (Common Factors).

  • Factors of 28: 1, 2, 4, 7, 14, 28.
  • Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70.
  • Common Factors: 1, 2, 7, 14. Answer: Jump sizes 1, 2, 7, or 14.

Q9. Smallest multiple of 1 to 10 except 7.

We need the LCM of 1, 2, 3, 4, 5, 6, 8, 9, 10.

  • LCM(8, 9, 5) covers most. 8×9×5=3608 \times 9 \times 5 = 360.
  • Check divisibility:
    • 360 div by 1, 2, 3, 4, 5, 6, 8, 9, 10? Yes. Answer: 360.

Q10. Smallest multiple of 1 to 10.

We need LCM of 1 to 10 (including 7). From Q9, we have 360 (which contains factors for everything except 7). Since 7 is prime, multiply 360 by 7. 360×7=2520360 \times 7 = 2520. Answer: 2520.