P5 Math EOY Practice A1 (Answer Key)
Section A: “as many bags as possible” means the highest common factor of the quantities — then read again to see whether the last line wants the number of bags or the number in each bag.
Section B: “an equal number of small and big” means the lowest common multiple of the two box sizes — then use the prices to build one set and see how many sets the money allows.
Step 1 - the number of bags is the HCF.
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Common factors: 1, 2, 4, 7, 14, 28 -> greatest common factor is 28, so there are 28 bags.
Step 2 - what the question actually asks for. With 28 bags: 2 apples, 3 oranges in each bag.
Answer: 3.
Step 1 - the number of bags is the HCF.
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Common factors: 1, 2, 3, 4, 6, 8, 12, 24 -> greatest common factor is 24, so there are 24 bags.
Step 2 - what the question actually asks for. With 24 bags: 4 muffins, 5 raisin cookies in each bag.
Answer: 5.
Step 1 - the number of bags is the HCF.
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Common factors: 1, 2, 3, 6, 7, 14, 21, 42 -> greatest common factor is 42, so there are 42 bags.
Step 2 - what the question actually asks for. With 42 bags: 2 red beads, 3 blue beads in each bag.
Answer: 42.
Step 1 - the number of bags is the HCF.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Common factors: 1, 2, 3, 4, 6, 12 -> greatest common factor is 12, so there are 12 bags.
Step 2 - what the question actually asks for. With 12 bags: 3 apples, 4 oranges, 5 pears in each bag.
Answer: 5.
(a) Equal numbers of both -> the LCM. The smallest number of cupcakes that can be bought as equal numbers of small and big is the lowest common multiple of 6 and 8 = 24. That is 4 boxes of 6 + 3 boxes of 8 = 4 × $9.60 + 3 × $15.20 = $84.00 for 24 small and 24 big.
With $250.00: 2 sets cost $168.00, and 3 sets would cost $252.00 - too much. So she buys 2 sets: 2 × 24 small + 2 × 24 big = 96 cupcakes (that is 48 of each size).
(b) Work through the possibilities. Small cupcakes come in boxes of 6, so the number of small must be a multiple of 6; big ones come in boxes of 8, so the number of big must be a multiple of 8. The number of small is 8 more than the number of big, and the total is more than 30 but fewer than 50.
Try the multiples of 8: only 16 big and 24 small fits - a total of 40 cupcakes.
Cost: 24 ÷ 6 = 4 boxes of small at $9.60, and 16 ÷ 8 = 2 boxes of big at $15.20.
4 × $9.60 + 2 × $15.20 = $68.80
(a) Equal numbers of both -> the LCM. The smallest number of tarts that can be bought as equal numbers of small and big is the lowest common multiple of 4 and 10 = 20. That is 5 boxes of 4 + 2 boxes of 10 = 5 × $11.60 + 2 × $27.00 = $112.00 for 20 small and 20 big.
With $300.00: 2 sets cost $224.00, and 3 sets would cost $336.00 - too much. So she buys 2 sets: 2 × 20 small + 2 × 20 big = 80 tarts (that is 40 of each size).
(b) Work through the possibilities. Small tarts come in boxes of 4, so the number of small must be a multiple of 4; big ones come in boxes of 10, so the number of big must be a multiple of 10. The number of small is 10 more than the number of big, and the total is more than 25 but fewer than 45.
Try the multiples of 10: only 10 big and 20 small fits - a total of 30 tarts.
Cost: 20 ÷ 4 = 5 boxes of small at $11.60, and 10 ÷ 10 = 1 boxes of big at $27.00.
5 × $11.60 + 1 × $27.00 = $85.00