Various math problems
1. When traveling by aircraft, passengers have a maximum allowable weight for their luggage. They are then charged 10 dollars for every kilogram overweight. If a passenger carrying 40 kg of luggage is charged 50 dollars, how much would a passenger carrying 80 kg be charged?
2. Two wooden cubes have digits painted on each face in such a way that it is possible to display any date of the month. Show clearly how you would label each face to achieve this.
3. Let a = 1, b = 2, c = 3, ... , z = 26. What is the exact value of (x - a)(x - b)(x - c)...(x - z)?
4. The number 13 is prime and so too is its reverse, 31. How many two digit primes can you find for which their reverse is also prime?
5. To discourage guessing on a math test, Malik's teacher announced that she would take off seven points for every wrong answer. However, each correct answer only added five to the score. Malik attempted all the problems and "broke even". In other words, he got exactly zero points. Of the 24 problems on the test, how many did Malik get correct?
6. Linda, Aziza, and Iroda decide to play cards. They keep score using almonds. They agree that when a player loses a hand, she will give each of the others an amount equal to the amount each player already has. Linda loses the first hand and pays Aziza and Iroda the amount of peanuts each has; Aziza loses the second hand and pays Linda and Iroda the amount of peanuts each has; Iroda loses the third hand and pays Linda and Aziza the amount of peanuts each has. At this point, each player has 8 almonds. How many almonds did each player start with?
7. There are 30 students in a class. Eleven have blue eyes. Fifteen have brown hair. Three students have both blue eyes and brown hair. How many students have neither blue eyes nor brown hair?
8. An insurance scheme pays benefits to its members who are sick for extended periods of time at the following rates
1st month: nil
2nd-4th months: 50% of normal salary
5th and succeeding months: 25% of normal salary
on the first 240,000 som per annum of salary for each month in which the member is sick and is not paid by the employer. How much does the scheme pay to:
Tursun, who is off work for two months, whose salary is 120,000 som per annum, and who gets no sick pay from his employer?
Murod, who is ill for six months, but who is paid normally for the first two months by his employer and whose salary is 180,000 som per annum.
Iroda, whose salary is 300,000 som per annum, who gets 3 months sick pay from her employer, and who has to take nine months off?
9. A total of 15 delegates from Kazakhstan, Uzbekistan, Tajikistan, and Kyrgyzstan are attending a meeting. Each country sent a different number of delegates, and each was represented by at least one delegate. Tajikistan and Uzbekistan sent a total of 6 delegates. One country sent exactly four delegates. Uzbekistan and Kyrgyzstan sent a total of 7 delegates. How many delegates were sent by each country?
10. You take out some cards from a standard pack of 52. Of those selected, there is at least one queen, two cards in the spades suit, three aces and four cards in the diamonds suit. What is the fewest number of cards you could have removed?
11. Each of a group of 19 students have 3, 4 or 5 books in his/her bag. The total number of books is 71. The number of students who had 4 books each is a multiple of 10. How many students have 3 books each, how many 4 and how many 5? Answer:
12. Village A has a population of 6,800, which is decreasing at a rate of 120 per year. Village B has a population of 4,200, which is increasing at a rate of 80 per year. In how many years will the population of the two villages be equal? Answer:
13. The average of 8 numbers is 6, the average of 6 other numbers is 8. what is the average of all 14 numbers?
14. If you count from 1 to 200, how many 7's will you pass on the way?
15. A right-angle parallelepiped with edges 10, 4 and 4 was painted and divided into cubes with an edge of 1. What percent of the cubes are painted at least from one side?
16. There is enough food at a picnic to feed 20 adults or 32 children. If there are 15 adults at the picnic, how many children can still be fed?
17. Sue and Nancy wish to buy a snack. They combine their money and find they have $4.00, consisting of quarters, dimes, and nickels. If they have 35 coins and the number of quarters is half the number of nickels, how many quarters do they have?
18. All of the 120 seniors in Coolidge High School are members of the chess club, the pep club or both. If 90 seniors are in the pep club and 70 seniors are in the chess club, how many seniors are in both clubs?
19. Find the number that, if you square it, add 27, multiply it by 3, take the square root and subtract 18 you end up with nothing.
20. I am a number between 100 and 200. I read the same forward and backward. The sum of my digits is 8. Who am I?
21. There are 600 students in a school, 30 students in every class. Every student has 5, and every teacher has 4 lessons every day. In every lesson there is a full class and one teacher together. How many teachers are there in the school?
22. My uncle said that he saves every candle-leftover, and he can make a new candle from the wax leftovers of seven candles. How many candles can he burn if he bought 92 candles?
23. A certain pipe can fill a swimming pool in 2 hours; another pipe can fill it in five hours; a third pipe can empty the pool in six hours. With all three pipes turned on at exactly the same time, and starting with an empty pool, how long will it take to fill the pool?
24. John says to Brenda, "If you give me eight dollars, we will have an equal amount of money." Brenda responds, "That may be true, but if you give me eight dollars, I will have twice as much money as you." How much money did John and Brenda each have?
25. (1 + 1/2)(1 + 1/3)(1 + 1/4) ... (1 + 1/2005) = ?
26. Which number is greater and why: 191919/999999, or 191919191919/999999999999?
27. In a warehouse there are two identical barrels: one of them is full of oil, the other one is exactly half way. Their masses are 86 kg and 53 kg. What is the mass of an empty barrel?
28. Find four sets of numbers from the grid below that each total 300.
27 41 67 12 Set A is , , and
89 24 168 76 Set B is , , and
6 31 123 186 Set C is , , and
154 91 75 30 Set D is , , and
29. Can you get 16 as the sum of a few consecutive integers?
30. The sum of two whole numbers is 968. One of them ends with a zero, but if you delete this zero, you get the other number. What are these numbers?
31. Any time, can be displayed as HH:MM:SS. So, three fifty four and twenty seconds is 03:54:20. Also, any day of the year can be displayed as DD/MM. So, the 5th of July is 05/07. What is the latest point in the year when you can use all digits from 0 to 9 to display the date in the format HH:MM:SS DD/MM?
32. There are five balls in a row: a yellow, a brown, a blue, a red and a green. Find their order if you know that the blue ball is not in the middle; the red is the same distance from the blue, as the blue is from the green; the left-side neighbor of the yellow is the red ball.
to be continued...
