Year 7 extension

1. Aroha goes to the Ōtautahi library every 6 days and Wiremu goes every 8 days. They were both there on 2 March. On what date will they next both be at the library on the same day?
2. The number 12 has six factors: 1, 2, 3, 4, 6 and 12. No smaller number has six factors. Which number is the smallest odd number with exactly six factors?
3. On Tama's kitchen scales, a pear and two kiwifruit weigh 380 g. A pear and five kiwifruit weigh 650 g. All the kiwifruit weigh the same. How much does the pear weigh?
4. An isosceles triangle has one angle of 40°. What is the largest that any angle in this triangle could be?
5. A Dunedin bakery sells pies for $4.80 each. Deal A: in every group of 4 pies in one order, 1 pie is free. Deal B: 20% off every pie. Mere needs exactly 10 pies. Which deal is cheaper for her, and by how much?
6. Mere spent 1/3 of her money on a book. Then she spent 1/4 of what was left on lunch. She now has $24. How much money did she start with?
7. A fish tank is 60 cm long, 30 cm wide and 40 cm high. The water is 30 cm deep. Ana gently puts a rock in and it sinks completely. The water rises to 32 cm deep. What is the volume of the rock?
8. Hemi flips a fair coin four times. What is the probability that he never gets two heads in a row?
9. Sione writes the repeating pattern 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, ... What is the sum of the first 100 numbers in his pattern?
10. Five whole numbers have a mean of 8 and a median of 9. The mode is 10, and no other number appears as often as 10. What is the largest possible range of the five numbers?