This is the marking copy and it carries every answer. Her sheet is the other file — same numbering, same margin codes, so you can mark straight down the page.
Shirley packed 163 lollipops into plastic bags of 7 lollipops. She used the most number of plastic bags possible. She sold each plastic bag of lollipops at $6 and each remaining lollipop at $2. How much did she get after selling all the lollipops?
answer 142
method Divide to find the bags: 163 ÷ 7 = 23 bags with 2 lollipops left over. The bags bring in 23 × $6 = $138, and the 2 loose lollipops bring in 2 × $2 = $4. Total = $138 + $4 = $142.
watch Throwing away the remainder. The 2 left-over lollipops are still sold — at a different price, which is exactly why the remainder matters here.
Joshua had more than 10 and fewer than 40 candies. When she packed the candies in bags of 7, she was left with 2 candies. When she packed them in bags of 3, she had no candies left. How many candies did Joshua have?
answer 30
method "Bags of 7 with 2 left over" means the number is 2 more than a multiple of 7: 7+2=9, 14+2=16, 21+2=23, 28+2=30, 35+2=37. Keeping only those between 10 and 40: 16, 23, 30, 37. "Bags of 3 with none left" means a multiple of 3, and of those four only 30 is. So Joshua had 30 candies.
watch Listing the multiples of 7 themselves (14, 21, 28, 35) and forgetting to add the remainder of 2.
What is the smallest number greater than 1 that leaves a remainder of 1 when it is divided by 2, by 3 and by 4?
(A) 7 (B) 9 (C) 13 (D) 25 (E) 49
answer (C) — 13
method Take away the remainder: the number minus 1 must divide by 2, 3 and 4, so it is a multiple of 12. The smallest is 12, giving 13. (25 and 49 also work, but they are not the smallest.)