Q11: Ravi buys pencils in packs of 7. He wants exactly 56 pencils. How many packs should he buy?
Sol:
Each pack has 7 pencils.
Total pencils needed = 56
Number of packs = 56 ÷ 7 = 8 packs
8 packs
Q12: A clothing store packs shirts into bundles of 5, 10, or 15. What is the smallest number of shirts the store should have to make up the bundles without any left?
Sol: Find the LCM of 5, 10, and 15.
Prime factors:
5 = 5
10 = 2 × 5
15 = 3 × 5
Highest powers: 2, 3, and 5 → LCM = 2 × 3 × 5 = 30
30 shirts
Q13: A rectangular garden has an area of 30 square meters. Its length and width must be whole numbers. List all possible pairs of length and width.
Sol:
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Pairs (L, W): (1, 30), (2, 15), (3, 10), (5, 6)
(1, 30), (2, 15), (3, 10), (5, 6)
Q14: A bus comes every 18 minutes and a train comes every 24 minutes. If both come together at 8:00 AM, when will they next come together?
Sol: Find LCM of 18 and 24.
18 = 2 × 3², 24 = 2³ × 3 → LCM = 2³ × 3² = 8 × 9 = 72 minutes
8:00 AM + 72 minutes = 9:12 AM
9:12 AM
Q15: During a clean-up event, trash bags were filled in groups of 4, 6, or 10 without leaving any trash out. What is the minimum number of trash bags needed?
Sol: Find LCM of 4, 6, and 10.
4 = 2², 6 = 2 × 3, 10 = 2 × 5
LCM = 2² × 3 × 5 = 60
60 trash bags
