Giới thiệu cùng các em một vài bàitoán trích từ các đề thi Olympiad bậc tiểu học kèm theo bàigiải bằng tiếng Anh để các em tham khảo. TÔN NỮ BÍCH VÂN Suppose today is Tuesday. What day of the week will it be 100 days from now? I have four 30¢ stamps and three 50¢ stamps. Using one or more of these stamps, how many different amounts of postage can I make? Find the sum of the counting numbers from 1 to 25 inclusive. In other words, if S = 1 + 2 + 3 + . + 24 + 25, find the value of S. In a stationery store, pencils have one price and pens have another price. 2 pencils and 3 pens cost 90¢. But 3 pencils and 2 pens cost 85¢. How much does 1 pencil cost? A work crew of 3 people requires 3 weeks and 2 days to do a certain job. How long would it take a work crew of 4 people to do the same job if each person of both crews works at the same rate as each of the others? Note: Each week contains 6 work days SOLUTIONS Every 7 days from "today" will be Tuesday. Since 98 is a multiple of 7, the 98th day from today will be Tuesday. Then the 100th day from today will be Thursday. Method 1 List the amounts in an organised manner. Amounts Number Amounts from 30¢ stamps: 30, 60, 90, 120 4 Amounts from 50¢ stamps: 50, 100, 150 3 Amounts from combining 30¢ stamps and 50¢ stamps: 30+50, 30+100, 30+150 3 60+50, 60+100, 60+150 3 90+50, 90+100, 90+150 3 120+50, 120+100, 120+150 3 Total 19 Method 2 The number of choices we have in using the 30¢ stamps is 5; we can use either 0, 1, 2, 3 or 4 of the 30¢ stamps. Similarly, we have 4 choices with respect to the 50¢ stamps; we can use either 0, 1, 2 or 3 of the 50¢ stamps. Each of the 5 choices for stamps. This gives a total of 20¢ combinations. However, this total includes the combination of zero 30¢ stamps and zero 50¢ stamps. Since one or more of the stamps must be used, we exclude the combination of none of each. Therefore, 19 different amounts of postage can be made. Method 1: Arrange the numbers like this: 1 + 25 = 25 2 + 23 = 25 3 + 22 = 25 • • • 12 + 13 = 25 25 = 25 Method 2: Given (1) S = 1 + 2 + 3 + . + 23 + 24 + 25 Reverse order of right side of (1) (2) S = 25 + 24 + 23 + . + 3 + 2 + 1 Add (1) and (2) (3) 2S = 26 + 26 + 26 + . + 26 + 26 + 26 Simplify the right side of (3) (4) 2S = 26 x 25 Divide both sides of (4) by 2 (5) S = 13 x 25 or 325 The required sum is 325 Method 1: By combining both purchases, we find that 5 pencils and 5 pens cost 175¢. Then 1 pencil and 1 pen cost 35¢, or 2 pencils and 2 pens cost 70¢. Since 3 pencils and 2 pens cost 85¢, 1 pencil costs 15¢. Method 2: Algebra: Let x represent the cost of one pencil and y the cost of one pen. Give (1) 2x + 3y = 90 Give (2) 3x + 2y = 85 Multiply both sides of (2) by 3 (3) 9x + 6y = 255 Multiply both sides of (1) by 2 (4) 4x + 6y = 180 Subtract (4) from (3) (5) 5x = 75 Divide both sides of (5) by 5 (6) x = 15 Answer: A pencil costs 15¢ Each person of the work crew of 3 people worked 20 days. Thus the number of individual work days needed to do the job was 60. Then each member of the work crew of 4 people must work 15 days in order to provide a total of 60 individual work days. 13 x 25 = 325 . Giới thiệu cùng các em một vài bài toán trích từ các đề thi Olympiad bậc tiểu học kèm theo bài giải bằng tiếng Anh để các em tham khảo.