Idea is to have a small competition among kids. We can break them in 3 teams and ask to solve the following problems.
Problem #1
There are 2 empty jars: 3 gallons and 5 gallons. How to get 4 gallons of water in 5 gallon jar? All you can use these two jars.
Problem #2
There is a soccer competition with 11 teams. Each team palys with any other team 4 games. How many games in total are played in this competition?
Problem #3: 36-5
In the following sequence of numbers, each number has one more 1 than the preceding number: 1, 11, 111, 1111, 11111, ... . What is the tens digit of the sum of the first 30 numbers of the sequence?
Problem #4
There are 9 coins. 8 of them have the same weight and one is lighter, which is fake. How to determine which coin is fake in two attempts?
Thursday, December 22, 2011
Thursday, December 8, 2011
Math problems for Dec. 9 2011
Problem #1: 43-2
The product of two numbers is 128 and their quotient is 8. What are the numbers?
Problem #2: 43-5
Barbara has 20 coins consisting of nickels and dimes. If the nickels were dimes and the dimes were nickels, she would have 30 cents more than she has now. How many dimes did she have to begin with?
Problem #3
In hoopball, a field goal is worth 2 points and a foul shot is worth 1 point. Suppose a team scored 72 points and made 6 more field goals than foul shots. How many foul shots did the team make?
Problem #4: 58-5
A bus was rented at a fixed cost by a group of 30 people. When 10 people were added to the group, the fixed cost of the bus did not change, but the charge for each person in the original group was $2 less than before. If each person paid the same charge as each of the others, find the fixed cost of renting the bus
Problem #5: 62-3
A fisherman sold some big fish at $4 each and twice as many small fish at $1 each. He received a total of $72 for the big and small fish. How many big fish did he sell?
Problem #6: 69-4
A crew of 8 people can build a wall in 6 days. Suppose 4 more people had joined the crew at the start. Assume that each person works at the same rate as each of the other people. How many days would it have taken the new crew to build the same wall?
Problem #7: 1-5
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.
Problem #8: 42-5
A work team of four people completes half of a job in 30 days. How many days will it take a team of ten people to complete the remaining half of the job? (Assume that each person of both teams works at the same rate as each of the other people).
The product of two numbers is 128 and their quotient is 8. What are the numbers?
Problem #2: 43-5
Barbara has 20 coins consisting of nickels and dimes. If the nickels were dimes and the dimes were nickels, she would have 30 cents more than she has now. How many dimes did she have to begin with?
Problem #3
In hoopball, a field goal is worth 2 points and a foul shot is worth 1 point. Suppose a team scored 72 points and made 6 more field goals than foul shots. How many foul shots did the team make?
Problem #4: 58-5
A bus was rented at a fixed cost by a group of 30 people. When 10 people were added to the group, the fixed cost of the bus did not change, but the charge for each person in the original group was $2 less than before. If each person paid the same charge as each of the others, find the fixed cost of renting the bus
Problem #5: 62-3
A fisherman sold some big fish at $4 each and twice as many small fish at $1 each. He received a total of $72 for the big and small fish. How many big fish did he sell?
Problem #6: 69-4
A crew of 8 people can build a wall in 6 days. Suppose 4 more people had joined the crew at the start. Assume that each person works at the same rate as each of the other people. How many days would it have taken the new crew to build the same wall?
Problem #7: 1-5
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.
Problem #8: 42-5
A work team of four people completes half of a job in 30 days. How many days will it take a team of ten people to complete the remaining half of the job? (Assume that each person of both teams works at the same rate as each of the other people).
Wednesday, November 30, 2011
Math problems for Dec. 2 2011
Problem #1
In a stationary store, pencils have one price and pens have another price. Two pencils and three pens cost 78 cents. But three pencils and two pens cost 72 cents. How much does one pencil cost?
Problem #2: 17-2
One loaf of bread and six rolls cost $1.80. At the same price, two loaves of bread and four rolls cost $2.40. How much does one loaf of bread cost?
Problem #3: 41-5
A restaurant has a total of 30 tables which are of two types. The first type seats two people at each table; the second type seats five people at each table. A total of 81 people are seated when all seats are occupied. How many tables for two are there?
Problem #4: 12-4
A dollar was changed into 16 coins consisting of just nickels and dimes. How many coins of each kind were in the change?
Problem #5
From a pile of 100 pennies(P), 100 nickels(N), and 100 dimes(D), select 21 coins which have a total value of exactly $1.00. In your selection you must also use at least one coin of each type. How many coins of each of the three types(P, N, D) should be selected?
Problem #6
A dealer packages marbles in two different box sizes. One size holds 5 marbles and the other size holds 12 marbles. If the dealer packaged 99 marbles and used more than 10 boxes, how many boxes of each size did he use?
Problem #7: 43-5
Barbara has 20 coins consisting of nickles and dimes. If the nickles were dimes and the dimes were nickels, she would have 30 cents more than she has now. How many dimes did she have to begin with?
Problem #8: 46-2
Tickets for a concert cost $2 each for children and $5 each for adults. A group of thirty people consisting of children and adults paid a total of $87 for the concert. How many adults were in the group?
In a stationary store, pencils have one price and pens have another price. Two pencils and three pens cost 78 cents. But three pencils and two pens cost 72 cents. How much does one pencil cost?
Problem #2: 17-2
One loaf of bread and six rolls cost $1.80. At the same price, two loaves of bread and four rolls cost $2.40. How much does one loaf of bread cost?
Problem #3: 41-5
A restaurant has a total of 30 tables which are of two types. The first type seats two people at each table; the second type seats five people at each table. A total of 81 people are seated when all seats are occupied. How many tables for two are there?
Problem #4: 12-4
A dollar was changed into 16 coins consisting of just nickels and dimes. How many coins of each kind were in the change?
Problem #5
From a pile of 100 pennies(P), 100 nickels(N), and 100 dimes(D), select 21 coins which have a total value of exactly $1.00. In your selection you must also use at least one coin of each type. How many coins of each of the three types(P, N, D) should be selected?
Problem #6
A dealer packages marbles in two different box sizes. One size holds 5 marbles and the other size holds 12 marbles. If the dealer packaged 99 marbles and used more than 10 boxes, how many boxes of each size did he use?
Problem #7: 43-5
Barbara has 20 coins consisting of nickles and dimes. If the nickles were dimes and the dimes were nickels, she would have 30 cents more than she has now. How many dimes did she have to begin with?
Problem #8: 46-2
Tickets for a concert cost $2 each for children and $5 each for adults. A group of thirty people consisting of children and adults paid a total of $87 for the concert. How many adults were in the group?
Wednesday, November 9, 2011
Math problems for Nov. 11 2011
Problem #1
In the USA, the symbol 5/2 means the 5th month, 2nd day, or May 2. But in England, 5/2 means the fifth day, 2nd month, or February 5. How many days of the year each have the same symbol in both the USA and England?
Problem #2
The product of two numbers is 504 and each of the numbers is divisible by 6. However, neither of the two numbers is 6. What is the larger of the two numbers?
Problem #3
A rectangular garden is 14 ft. by 21 ft. and is bordered by a concrete walk 3 ft. wide as shown below. How many square feet are in the surface area of just the concrete walk?
Problem #4
Four numbers are arranged in order of size and the difference between any two adjacent numbers is the same. Suppose 1/3 is the first and 1/2 is the fourth of these numbers. What are the two numbers between 1/3 and 1/2?
Problem #5
Each o the three diagrams at the right shows a balance of weights using different objects. How many cubes will balance a ball?
In the USA, the symbol 5/2 means the 5th month, 2nd day, or May 2. But in England, 5/2 means the fifth day, 2nd month, or February 5. How many days of the year each have the same symbol in both the USA and England?
Problem #2
The product of two numbers is 504 and each of the numbers is divisible by 6. However, neither of the two numbers is 6. What is the larger of the two numbers?
Problem #3
A rectangular garden is 14 ft. by 21 ft. and is bordered by a concrete walk 3 ft. wide as shown below. How many square feet are in the surface area of just the concrete walk?
Problem #4
Four numbers are arranged in order of size and the difference between any two adjacent numbers is the same. Suppose 1/3 is the first and 1/2 is the fourth of these numbers. What are the two numbers between 1/3 and 1/2?
Problem #5
Each o the three diagrams at the right shows a balance of weights using different objects. How many cubes will balance a ball?
Thursday, October 27, 2011
Math problems for Oct. 27
Problem #1
I am less than 6 feet tall but more than 2 feet tall. My height in inches is a multiple of 7 and is also 2 inches more than a multiple of 6. What is my height in inches?
Problem #2
In the multiplication example below, A nad B represent different digits, AB is a two-digit number and BBB is a three-digit number. (* means multiply). What two-digit number does AB represent?
Problem #3
Tom went to a store and spent one-third of his money. He went to a second store where he spent one-third of what remained, and then had $12 when he left. How much money did he have to begin with at the first store?
Problem #4
The tower below has no gaps. Suppose it is painted red on all exterior sides including the bottom, and then cut into cubes along the indicated lines. How many cubes will each have red paint on just three faces?
Problem #5
A9543B represents a six-digit number in which A and B are digits different from each other. The number is divisible by 11 and also by 8. What digit does A represent?
I am less than 6 feet tall but more than 2 feet tall. My height in inches is a multiple of 7 and is also 2 inches more than a multiple of 6. What is my height in inches?
Problem #2
In the multiplication example below, A nad B represent different digits, AB is a two-digit number and BBB is a three-digit number. (* means multiply). What two-digit number does AB represent?
Problem #3
Tom went to a store and spent one-third of his money. He went to a second store where he spent one-third of what remained, and then had $12 when he left. How much money did he have to begin with at the first store?
Problem #4
The tower below has no gaps. Suppose it is painted red on all exterior sides including the bottom, and then cut into cubes along the indicated lines. How many cubes will each have red paint on just three faces?
Problem #5
A9543B represents a six-digit number in which A and B are digits different from each other. The number is divisible by 11 and also by 8. What digit does A represent?
Wednesday, October 19, 2011
Math problems for Oct. 21 2011
Problem #1
Two cash registers of a store had a combined total of $300. When the manager transferred $15 from one register to the other register, each register then had the same amount. How much did the register with the larger amount have before the transfer was made?
Problem #2
The product of two numbers is 128 and their quotient is 8. What are the numbers?
Problem #3
In the figure below, each number represents the length of the segment which is nearest it. How many square units are in the area of the figure if there is a right angle at each corner of the figure?
Problem #4
In the addition problem below, different letters stand for different digits. AH represents a two-digit number and HEE represents a three-digit number. What number does HEE represent?
Problem #5
Barbara has 20 coins consisting of nickels and dimes. If the nickels were dimes and the dimes were nickels, she would have 30 cents more than she has now. How many dimes did she have to begin with?
Two cash registers of a store had a combined total of $300. When the manager transferred $15 from one register to the other register, each register then had the same amount. How much did the register with the larger amount have before the transfer was made?
Problem #2
The product of two numbers is 128 and their quotient is 8. What are the numbers?
Problem #3
In the figure below, each number represents the length of the segment which is nearest it. How many square units are in the area of the figure if there is a right angle at each corner of the figure?
Problem #4
In the addition problem below, different letters stand for different digits. AH represents a two-digit number and HEE represents a three-digit number. What number does HEE represent?
Problem #5
Barbara has 20 coins consisting of nickels and dimes. If the nickels were dimes and the dimes were nickels, she would have 30 cents more than she has now. How many dimes did she have to begin with?
Tuesday, October 11, 2011
Math problems for October 14 2011
Problem #1
The cost of a book is $1 and a whole number of cents. The total cost of six copies of the book is less than $8. However, the total cost of seven copies of the same book at the same price per book is more than $8. What is the least a single copy of the book could cost?
Problem #2
The sum of all digits in the numbers 34, 35, and 36 is 24 because (3+4)+(3+5)+(3+6)=24. Find the sum of all digits in the first twenty-five counting numbers: 1, 2,3, ..., 23, 24, 25
Problem #3
Alice earned a total of $65 for working five days after school. Each day after the first day, she earned $2 more than she earned the day before. How much did she earn on the first day?
Problem #4
Each of the small boxes in the figure is a square and the area of the figure is 52 square units. How many units are there in the outer perimeter of the figure?
Problem #5
A work team of four people completes half of a job in 15 days. How many days will it take a team of ten people to complete the remaining half of the job? (Assume that each person of both teams works at the same rate as each of the other people.)
The cost of a book is $1 and a whole number of cents. The total cost of six copies of the book is less than $8. However, the total cost of seven copies of the same book at the same price per book is more than $8. What is the least a single copy of the book could cost?
Problem #2
The sum of all digits in the numbers 34, 35, and 36 is 24 because (3+4)+(3+5)+(3+6)=24. Find the sum of all digits in the first twenty-five counting numbers: 1, 2,3, ..., 23, 24, 25
Problem #3
Alice earned a total of $65 for working five days after school. Each day after the first day, she earned $2 more than she earned the day before. How much did she earn on the first day?
Problem #4
Each of the small boxes in the figure is a square and the area of the figure is 52 square units. How many units are there in the outer perimeter of the figure?
Problem #5
A work team of four people completes half of a job in 15 days. How many days will it take a team of ten people to complete the remaining half of the job? (Assume that each person of both teams works at the same rate as each of the other people.)
Wednesday, October 5, 2011
Math problems for October 7 2011
Problem #1
Suppose the time is now 2 o'clock on a twelve-hour clock which runs continuously. What time will it show 1,000 hours from now?
Problem #2
The average of five numbers is 6. If one of the five numbers is removed, the average of the four remaining numbers is 7. What is the value of the number that was removed?
Problem #3
If you start with 3 and count by 7s, you get the terms of the sequence 3, 10, 17, ..., 528 where 3 is the 1st term, 10 is the 2nd term, 17 is the 3rd term, and so forth up to 528 which is Nth term. What is the value of N?
Problem #4
When a counting number is multiplied by itself, the result is a perfect square. For example 1, 4, 9 are perfect squares because 1 x 1 = 1, 2 x 2 = 4, and 3 x 3 = 9. How many perfect squares are less than 10,000?
Problem #5
A restaurant has a total of 30 tables which are of two types. The first type seats two people at each table; the second type seats five people at each table. A total 81 people are seated when all seats are occupied. How many tables for two are there?
Suppose the time is now 2 o'clock on a twelve-hour clock which runs continuously. What time will it show 1,000 hours from now?
Problem #2
The average of five numbers is 6. If one of the five numbers is removed, the average of the four remaining numbers is 7. What is the value of the number that was removed?
Problem #3
If you start with 3 and count by 7s, you get the terms of the sequence 3, 10, 17, ..., 528 where 3 is the 1st term, 10 is the 2nd term, 17 is the 3rd term, and so forth up to 528 which is Nth term. What is the value of N?
Problem #4
When a counting number is multiplied by itself, the result is a perfect square. For example 1, 4, 9 are perfect squares because 1 x 1 = 1, 2 x 2 = 4, and 3 x 3 = 9. How many perfect squares are less than 10,000?
Problem #5
A restaurant has a total of 30 tables which are of two types. The first type seats two people at each table; the second type seats five people at each table. A total 81 people are seated when all seats are occupied. How many tables for two are there?
Tuesday, September 27, 2011
Math problems for September 30 2011
Problem #1
A slow clock loses 3 minutes every hour. Suppose the slow clock and a correct clock both show the correct time at 9 am. What time will the slow clock show when the correct clock shows 10 o'clock the evening of the same day?
Problem #2
The figure below is a 'magic square' with missing entries. When complete, the sum of the four entries in each column, each row, and each diagonal is the same. Find the value of A and the value of B.
Problem #3
The digit 3 is written at the right of a certain two-digit number thus forming a three-digit number. The new number is 372 more than the original two-digit number. What was the original two-digit number?
Problem #4
ABCD is a square with area 16 sq. meters. E and F are midpoints of sides AB and BC, respectively. What is the area of trapezoid AEFC, the shaded region?
Problem #5
Peter agreed to work after school for 8 weeks at a fixed weekly rate. But instead of being given only money, he was to be given $85 and a bicycle. However, Peter worked only 5 weeks at the fixed weekly rate and was given $25 and the bicycle. How much was the bicycle worth?
A slow clock loses 3 minutes every hour. Suppose the slow clock and a correct clock both show the correct time at 9 am. What time will the slow clock show when the correct clock shows 10 o'clock the evening of the same day?
Problem #2
The figure below is a 'magic square' with missing entries. When complete, the sum of the four entries in each column, each row, and each diagonal is the same. Find the value of A and the value of B.
Problem #3
The digit 3 is written at the right of a certain two-digit number thus forming a three-digit number. The new number is 372 more than the original two-digit number. What was the original two-digit number?
Problem #4
ABCD is a square with area 16 sq. meters. E and F are midpoints of sides AB and BC, respectively. What is the area of trapezoid AEFC, the shaded region?
Problem #5
Peter agreed to work after school for 8 weeks at a fixed weekly rate. But instead of being given only money, he was to be given $85 and a bicycle. However, Peter worked only 5 weeks at the fixed weekly rate and was given $25 and the bicycle. How much was the bicycle worth?
Friday, September 16, 2011
Math problems for Sept. 23 2011
Problem #1
The serial number of my camera is four-digit number less than 5,000 and contains the digits 2, 3, 5, and 8 but not necessarily in that order. The '3' is next to the '8', the '2' is not next to the '3', and the '5' is not next to the '2'. What is the serial number?
Problem #2
One day, Carol bought apples at 3 for 25 cents and sold all of them at 2 for 25 cents.If she made a profit of $1 that day, how many apples did she sell?
Problem #3
As shown, ABCD and AFED are squares with a common side AD of length 10 cm. Arc BD and arc DF are quarter-circles. How many square cm, are in the area of the shaded region?
Problem #4
When the same whole number is added to both the numerator and denumerator of 2/5, the value of the new fraction is 2/3. What number was added to both the numerator and denumerator?
Problem #5
The sum of the ages of three children is 32. The age of the oldest is twice the age of the youngest. The ages of the two older children differ by three years. What is the age of the youngest child?
The serial number of my camera is four-digit number less than 5,000 and contains the digits 2, 3, 5, and 8 but not necessarily in that order. The '3' is next to the '8', the '2' is not next to the '3', and the '5' is not next to the '2'. What is the serial number?
Problem #2
One day, Carol bought apples at 3 for 25 cents and sold all of them at 2 for 25 cents.If she made a profit of $1 that day, how many apples did she sell?
Problem #3
As shown, ABCD and AFED are squares with a common side AD of length 10 cm. Arc BD and arc DF are quarter-circles. How many square cm, are in the area of the shaded region?
Problem #4
When the same whole number is added to both the numerator and denumerator of 2/5, the value of the new fraction is 2/3. What number was added to both the numerator and denumerator?
Problem #5
The sum of the ages of three children is 32. The age of the oldest is twice the age of the youngest. The ages of the two older children differ by three years. What is the age of the youngest child?
Friday, September 9, 2011
Math problems for September 16
Problem #1
In the subtraction problem below, each letter represents a digit, and different letters represent different digits.
What digit C represents?
Problem #2
Each of the small boxes in the figure below is a square. The perimeter of square ABCD is 36 cm. What is the perimeter of the figure shown with darkened outline?
Problem #3
means 2 x 2 x 2 or 8
means 3 x 3 x 3 or 27
means N x N x N
Suppose
is equal to 4913. What is the value of N?
Problem #4
Carl shot 3 arrows; 2 landed in the A ring and 1 landed in circle B for a total score of 17. David also shot 3 arrows; 1 landed in A and 2 in B for a total score of 22. How many points are assigned to B?
Problem #5
In the following sequence of numbers, each number has one more 1 than the preceding number: 1, 11, 111, 1111, ... . What is the tens digit of the sum of the first 30 numbers of the sequence?
Homework
Problem #1
My age this year is a multiple of 7. Next year it will be a multiple of 5. I am more than 20 years of age but less than 80. How old will I be 6 years from now?
In the subtraction problem below, each letter represents a digit, and different letters represent different digits.
What digit C represents?
Problem #2
Each of the small boxes in the figure below is a square. The perimeter of square ABCD is 36 cm. What is the perimeter of the figure shown with darkened outline?
Problem #3
means 2 x 2 x 2 or 8
means 3 x 3 x 3 or 27
means N x N x N
Suppose
is equal to 4913. What is the value of N?
Problem #4
Carl shot 3 arrows; 2 landed in the A ring and 1 landed in circle B for a total score of 17. David also shot 3 arrows; 1 landed in A and 2 in B for a total score of 22. How many points are assigned to B?
Problem #5
In the following sequence of numbers, each number has one more 1 than the preceding number: 1, 11, 111, 1111, ... . What is the tens digit of the sum of the first 30 numbers of the sequence?
Homework
Problem #1
My age this year is a multiple of 7. Next year it will be a multiple of 5. I am more than 20 years of age but less than 80. How old will I be 6 years from now?
Saturday, May 21, 2011
9999999
Place parentheses and mathematical operations (+, -, /,*) on the left of the following equation to make it correct
9999999 = 100
9999999 = 100
Monday, May 9, 2011
Math problems for May 10 2011
Problem #1
How many times does X occurs in the diagram here.
Problem #2
The product of three counting numbers is 24. How many different sets of 3 numbers have this property if the order of the 3 numbers in a set does not matter?
Problem #3
Carol spent exactly $1 for some 5 cents stamps and some 13 cents stamps. How many 5 cents stamps did she buy?
Problem #4
In the addition problem here, there are three two-digit numbers in which different letters represent different digits. What digits do A, B, and C represent?
Problem #5
Let N be a number that divides 171 with a remainder of 6. List all the two-digit numbers that N can be.
Problem #6
The result of multiplying a counting number by itself is a square number. For example, 1, 4, and 9 are each square numbers because 1X1=1, 2X2=4, and 3X3=9. What year in the 20th century (the years 1901 through 2000) was a square number?
Problem #7
A group of 12 girls scouts had enough food to last for 8 days when they arrived in camp. However, 4 more scouts joined them without the amount of food being increased. How long will the food last if each scout is given the same daily ration as originally planned?
How many times does X occurs in the diagram here.
Problem #2
The product of three counting numbers is 24. How many different sets of 3 numbers have this property if the order of the 3 numbers in a set does not matter?
Problem #3
Carol spent exactly $1 for some 5 cents stamps and some 13 cents stamps. How many 5 cents stamps did she buy?
Problem #4
In the addition problem here, there are three two-digit numbers in which different letters represent different digits. What digits do A, B, and C represent?
Problem #5
Let N be a number that divides 171 with a remainder of 6. List all the two-digit numbers that N can be.
Problem #6
The result of multiplying a counting number by itself is a square number. For example, 1, 4, and 9 are each square numbers because 1X1=1, 2X2=4, and 3X3=9. What year in the 20th century (the years 1901 through 2000) was a square number?
Problem #7
A group of 12 girls scouts had enough food to last for 8 days when they arrived in camp. However, 4 more scouts joined them without the amount of food being increased. How long will the food last if each scout is given the same daily ration as originally planned?
Wednesday, May 4, 2011
Brain Teaser of the week
A cylinder 60 cm high has a circumference of 16 cm. A string makes exactly 5 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm?
To check the answer come back on May 12
To check the answer come back on May 12
Monday, May 2, 2011
Math problems for May 3 2011
Problem #1
The average of three numbers is 6. Let the first number be increased by 1, the second by 2, and the third by 3. What is the average of the set of increased numbers?
Problem #2
The month of January has 31 days. Suppose January 1 occurs on Monday. What day of the week is February 22 of the next month?
Problem #3
The set of stairs (see below) is constructed by placing layers of cubes on top of each other. What is the total number of cubes contained in the staircase?
Problem #4
When a counting number is multiplied by itself, the result is a square number. Some examples of square numbers are 1, 4, 9. How many square numbers between 1 and 100?
Problem #5
The product of two whole numbers is 10,000. If neither number contains a zero digit, what are the two numbers?
Problem #6
Of three numbers , two are 1/2 and 1/3. What should the third number be so that the sum of all three is 1?
Problem #7
The four-digit number A55B is divisible by 36. What is the sum of A and B?
Hint: A number is divisible by 36 if it is divisible by 9 and 4 (so it is even)
Monday, April 25, 2011
Math problems for April 26 2011
Problem #1
Person A was born on January 15, 1948.
Person B was born on January 15, 1962.
If both are alive now, in what year was person A twice as old as person B?
Problem #2
A square piece of paper is folded in half as shown and then cut into two rectangles along the fold (two rectangles are equal). The perimeter of each of the two rectangles is 18 inches. What is the perimeter of the original square?
Problem #3
My age this year is a multiple of 7. Next year it will be a multiple of 5. I am more than 20 years of age but less than 80. How old will I be 6 years from now?
Problem #4
The owner of a bicycle store had a sale on bicycles (two-wheelers) and tricycles (three-wheelers). Each cycle had two pedals. When he counted the total number of pedals of the cycles, he got 50. When he counted the total number of wheels of the cycles, he got 64. How many tricycles were offered in the sale?
Problem #5
Six people participated in a checker tournament. Each participant played exactly three games with each of the other participants. How many games were played in all?
Problem #6
A jar filled with water weighs 10 pounds. When one-half of the water is pored out, the jar and remaining water weighs five and three quarters pounds. How much does the jar weigh?
Problem #7
The average of five numbers is 18. Let the first number be increased by 1, the second number by 2, the third number by 3, the fourth number by 4, and the fifth number by 5. What is the average of the set of increased numbers?
Person A was born on January 15, 1948.
Person B was born on January 15, 1962.
If both are alive now, in what year was person A twice as old as person B?
Problem #2
A square piece of paper is folded in half as shown and then cut into two rectangles along the fold (two rectangles are equal). The perimeter of each of the two rectangles is 18 inches. What is the perimeter of the original square?
Problem #3
My age this year is a multiple of 7. Next year it will be a multiple of 5. I am more than 20 years of age but less than 80. How old will I be 6 years from now?
Problem #4
The owner of a bicycle store had a sale on bicycles (two-wheelers) and tricycles (three-wheelers). Each cycle had two pedals. When he counted the total number of pedals of the cycles, he got 50. When he counted the total number of wheels of the cycles, he got 64. How many tricycles were offered in the sale?
Problem #5
Six people participated in a checker tournament. Each participant played exactly three games with each of the other participants. How many games were played in all?
Problem #6
A jar filled with water weighs 10 pounds. When one-half of the water is pored out, the jar and remaining water weighs five and three quarters pounds. How much does the jar weigh?
Problem #7
The average of five numbers is 18. Let the first number be increased by 1, the second number by 2, the third number by 3, the fourth number by 4, and the fifth number by 5. What is the average of the set of increased numbers?
Thursday, April 21, 2011
Friday, April 15, 2011
Math problems for April 29 2011
Problem #1
The average of five numbers is 18. Let the first number be increased by 1, the second number by 2, the third number by 3, tho fourth number by 4, and the fifth by 5. what is the average of the set of increased numbers?
The average of five numbers is 18. Let the first number be increased by 1, the second number by 2, the third number by 3, tho fourth number by 4, and the fifth by 5. what is the average of the set of increased numbers?
Monday, April 11, 2011
Math problems for April 12 2011
Problem #1
Suppose two days ago was Sunday. What day of the week will 365 days from today then be?
Problem #2
What should the starting number be in that diagram?
Problem #3
A rectangulat tile is 2 inches by 3 inches. What is the least number of tiles that are needed to completely cover a square region 2 feet on each side?
Problem #4
Six arrows land on target shown here. Each arrow is in one of the regions of the target. Which of the following total scores is possible? 16, 19, 26, 31, 41, 44?
Problem #5
A total of 350 pounds of cheese is packaged into boxes each containing 1 3/4 pounds of cheese. Each box is then sold for $1.75. What is the total selling price of all of the boxes of cheese?
Problem #6
A circular track is 1000 yards in circumference. Cyclists A, B, and C start at the same place and time, and race around the track at the following rates per minute: A at 700 yards, B at 800 yards, and C at 900 yards. What is the least amount of minutes it must take for all three to be together again.
Problem #7
$1200 is divided among four brothers so that each gets $100 more than the brother who is his next younger brother. How much does the youngest brother gets?
Suppose two days ago was Sunday. What day of the week will 365 days from today then be?
Problem #2
What should the starting number be in that diagram?
Problem #3
A rectangulat tile is 2 inches by 3 inches. What is the least number of tiles that are needed to completely cover a square region 2 feet on each side?
Problem #4
Six arrows land on target shown here. Each arrow is in one of the regions of the target. Which of the following total scores is possible? 16, 19, 26, 31, 41, 44?
Problem #5
A total of 350 pounds of cheese is packaged into boxes each containing 1 3/4 pounds of cheese. Each box is then sold for $1.75. What is the total selling price of all of the boxes of cheese?
Problem #6
A circular track is 1000 yards in circumference. Cyclists A, B, and C start at the same place and time, and race around the track at the following rates per minute: A at 700 yards, B at 800 yards, and C at 900 yards. What is the least amount of minutes it must take for all three to be together again.
Problem #7
$1200 is divided among four brothers so that each gets $100 more than the brother who is his next younger brother. How much does the youngest brother gets?
Monday, April 4, 2011
Math problems for April 4 2011
Problem#1
A train is moving at the rate of 1 mile in 1 minute and 20 seconds. If the train continues at this rate, how far will it travel in one hour?
Problem #2
Six dollars were exchanged for nickels and dimes. The number of nickels was the same as the number of dimes. How many nickels were there in the change?
Problem #3
In the multiplication example below, A, B, and H are different digits. What is the sum of A, B, and H?
Problem #4
If a number is divided by 3 and 5, the remainder is 1. If it is divided by 7, there is no reminder. What number between 1 and 100 satisfies the above condition?
Problem #5
Mrs. Winthorp went to a store , spent half of her money and then $10 more. She went to a second store, spent half of her remaining money and then $10 more. But she then had no money left. How much money did she have to begin with when she went to the first store.
Problem #6
Alice and Betty each wants to buy the same kind of ruler. But Alice is 22 cents short and Betty is 3 cents short. When they combine their money, they still do not have enough money. What is the most the ruler can cost?
A train is moving at the rate of 1 mile in 1 minute and 20 seconds. If the train continues at this rate, how far will it travel in one hour?
Problem #2
Six dollars were exchanged for nickels and dimes. The number of nickels was the same as the number of dimes. How many nickels were there in the change?
Problem #3
In the multiplication example below, A, B, and H are different digits. What is the sum of A, B, and H?
Problem #4
If a number is divided by 3 and 5, the remainder is 1. If it is divided by 7, there is no reminder. What number between 1 and 100 satisfies the above condition?
Problem #5
Mrs. Winthorp went to a store , spent half of her money and then $10 more. She went to a second store, spent half of her remaining money and then $10 more. But she then had no money left. How much money did she have to begin with when she went to the first store.
Problem #6
Alice and Betty each wants to buy the same kind of ruler. But Alice is 22 cents short and Betty is 3 cents short. When they combine their money, they still do not have enough money. What is the most the ruler can cost?
Monday, March 28, 2011
Math problems for March 29 2011
Problem #1 Arrange the digits 1, 1, 2, 2, 3, 3, as a six-digit number in which the 1s are separated by one digit, the 2s are separated by two digits, and the 3s are separated by three digits. Problem #2 Each of the boxes in the figure below is a square. Using the lines of the figure, how many different squares can be traced?
Problem #4 The perimeter of a rectangle is 20 feet and the foot-measure of each side is a whole number. How many rectangles with different shapes satisfy these conditions?
Problem #3
In a math contest of 10 problems, 5 points was given for each correct answer and 2 points was deducted for each incorrect answer.If Nancy answered all 10 problems and scored 29 points, how many correct answers did she have?
Problem #4 The perimeter of a rectangle is 20 feet and the foot-measure of each side is a whole number. How many rectangles with different shapes satisfy these conditions?
Problem #5
When Anne, Betty, and Cynthia compared the amount of money each had, they discovered that Anne and Betty together had $12, Betty and Cynthia together had $18, and Anne and Cinthia together had $10.
Who had the least amount of money, and how much was it?
Problem #6 Three water pipes are used to fill a swimming pool. The first pipe alone takes 8 hours to fill the pool, the second pipe alone takes 12 hours to fill the pool, and the third pipe alone takes 24 hours to fill the pool. If all three pipes are open at the same time, how long will it take to fill the pool?Monday, March 21, 2011
Math problems for March 19 2011
Problem #1
A dollar was changed into 16 coins consisting of just nickels and dimes.
How many coins of each kind were in the change?
Problem #2
In the multiplication problem below, different letters stand for different digits, and ABC and DBC each represent a three-digit number.
What does DBC represent?
Problem #3
The product of two numbers is 144 and their difference is 10.
What is the sum of the two numbers?
Problem #4
If I start with 2 and count by 3s until I reach 449, I will get: 2, 5, 8,11, ...,449 where 2 is the first number, 5 is the second number and so forth. If 449 is Nth number, what is the value of N?
Problem #5
A man drives from his home at 30 miles per hour to the shopping center which is 20 miles from his home. On the return trip he encounters heavy traffic and averages 12 miles per hour. How much time does the man take to drive to and from the shopping center.
Problem #6
The XYZ club collected a total of $1.21 from its members with each member contributing the same amount. If each member paid for his or her share with 3 coins, how many nickels were contributed?
A dollar was changed into 16 coins consisting of just nickels and dimes.
How many coins of each kind were in the change?
Problem #2
In the multiplication problem below, different letters stand for different digits, and ABC and DBC each represent a three-digit number.
What does DBC represent?
Problem #3
The product of two numbers is 144 and their difference is 10.
What is the sum of the two numbers?
Problem #4
If I start with 2 and count by 3s until I reach 449, I will get: 2, 5, 8,11, ...,449 where 2 is the first number, 5 is the second number and so forth. If 449 is Nth number, what is the value of N?
Problem #5
A man drives from his home at 30 miles per hour to the shopping center which is 20 miles from his home. On the return trip he encounters heavy traffic and averages 12 miles per hour. How much time does the man take to drive to and from the shopping center.
Problem #6
The XYZ club collected a total of $1.21 from its members with each member contributing the same amount. If each member paid for his or her share with 3 coins, how many nickels were contributed?
Sunday, March 13, 2011
Math problems for March 15 2011
Problem #1
A camera and case together cost $100. If the camera costs $90 more than the case, how much does the case cost?
Problem #2
Below are three views of the same cube.
What letter is on the face opposite (1) H, (2) X, and (3)Y?
Problem #3
I have exactly ten coins whose total value is $1.
If three of the coins are quarters, what are the remaining coins?
Problem #4
If the digits A, B, and C are added, the sum is the two-digit number AB as shown below.
What is the value of C?
A + B + C = AB
Problem #5
The sum of the weights of Tom and Bill is 138 pounds and one boy is 34 pounds heavier than the other. How much does the heavier boy weigh?
Problem #6
When I open my math book, there are two pages which face me and the product of the two page numbers is 1806.
What are the two page numbers?
Problem #7
In the addition problem below A, B, and C are digits. If C is placed in the tens column instead of the units column as shown at the far right, the sum is 97.
What are the values of A, B, and C?
Problem #8
One loaf of bread and six rolls cost $1.80. At the same prices, two loaves of bread and four rolls cost $2.40. How much does one loaf of bread cost?
A camera and case together cost $100. If the camera costs $90 more than the case, how much does the case cost?
Problem #2
Below are three views of the same cube.
What letter is on the face opposite (1) H, (2) X, and (3)Y?
Problem #3
I have exactly ten coins whose total value is $1.
If three of the coins are quarters, what are the remaining coins?
Problem #4
If the digits A, B, and C are added, the sum is the two-digit number AB as shown below.
What is the value of C?
A + B + C = AB
Problem #5
The sum of the weights of Tom and Bill is 138 pounds and one boy is 34 pounds heavier than the other. How much does the heavier boy weigh?
Problem #6
When I open my math book, there are two pages which face me and the product of the two page numbers is 1806.
What are the two page numbers?
Problem #7
In the addition problem below A, B, and C are digits. If C is placed in the tens column instead of the units column as shown at the far right, the sum is 97.
What are the values of A, B, and C?
Problem #8
One loaf of bread and six rolls cost $1.80. At the same prices, two loaves of bread and four rolls cost $2.40. How much does one loaf of bread cost?
Tuesday, March 1, 2011
3rd grade: Optional homework for March 1 2011 class
Problem #1
Julius Caesar wrote the Roman Numerals I, II, III, IV, and V in a certain order from left to right. He wrote I before III but after IV. He wrote II after IV but before I. He wrote V after II but before III. If V was not the third numeral, in what order did Caesar write the five numerals from left to right?
Problem #2
In the multiplication problem below, each blank space represents a missing digit.
Find the product.
Problem #3
Thirteen plums weigh as much as two apples and one pear. Four plums and one apple have the same weight as one pear.
How many plums have the weight of one pear?
Problem #4
During a school year, a student was given an award of 25 cents for each math test he passed and was fined 50 cents for each math test he failed. At the end of the school year, the student had passed 7 times as many tests as he had failed, and received $3.75.
How many tests did he fail?
Julius Caesar wrote the Roman Numerals I, II, III, IV, and V in a certain order from left to right. He wrote I before III but after IV. He wrote II after IV but before I. He wrote V after II but before III. If V was not the third numeral, in what order did Caesar write the five numerals from left to right?
Problem #2
In the multiplication problem below, each blank space represents a missing digit.
Find the product.
Problem #3
Thirteen plums weigh as much as two apples and one pear. Four plums and one apple have the same weight as one pear.
How many plums have the weight of one pear?
Problem #4
During a school year, a student was given an award of 25 cents for each math test he passed and was fined 50 cents for each math test he failed. At the end of the school year, the student had passed 7 times as many tests as he had failed, and received $3.75.
How many tests did he fail?
Saturday, February 26, 2011
3rd grade: Math problems for March 1 2011
Problem #1
If 24 gallons of water are poured into an empty tank, then 3/4 of the tank is filled.
How many gallons does a full tank hold?
To see solution click here
Problem #2
A train can hold 78 passengers. The train starts out empty and picks up 1 passenger at the first stop, 2 passengers at the second stop, 3 passengers at the third stop, and so forth.
After how many stops will the train be full?
To see solution click here
Problem #3
The number of two-dollar bills I need to pay for a purchase is 9 more than the number of five-dollar bills I need to pay for the same purchase.
What is the cost of the purchase?
To see solution click here
Problem #4
The last Friday of a particular month is on the 25th day of the month.
What day of the week is the first day of the month?
Here is the video with almost correct solution. Please find the error.
See here
Problem #5
The age of a man is the same as his wife's age with the digits reversed. The sum of their ages is 99 and the man is 9 years older than his wife.
How old is the man?
To see solution click here
Problem #6
D is the sum of the odd numbers from 1 through 99 inclusive, and N is the sum of the evn numbers from 2 through 98 inclusive:
D = 1+3+5+ ...+99
and
N = 2+4+6+...+98
Which is greater, D or N, and by how much?
If 24 gallons of water are poured into an empty tank, then 3/4 of the tank is filled.
How many gallons does a full tank hold?
To see solution click here
Problem #2
A train can hold 78 passengers. The train starts out empty and picks up 1 passenger at the first stop, 2 passengers at the second stop, 3 passengers at the third stop, and so forth.
After how many stops will the train be full?
To see solution click here
Problem #3
The number of two-dollar bills I need to pay for a purchase is 9 more than the number of five-dollar bills I need to pay for the same purchase.
What is the cost of the purchase?
To see solution click here
Problem #4
The last Friday of a particular month is on the 25th day of the month.
What day of the week is the first day of the month?
Here is the video with almost correct solution. Please find the error.
See here
Problem #5
The age of a man is the same as his wife's age with the digits reversed. The sum of their ages is 99 and the man is 9 years older than his wife.
How old is the man?
To see solution click here
Problem #6
D is the sum of the odd numbers from 1 through 99 inclusive, and N is the sum of the evn numbers from 2 through 98 inclusive:
D = 1+3+5+ ...+99
and
N = 2+4+6+...+98
Which is greater, D or N, and by how much?
Monday, February 21, 2011
Optional homework for February vacation
Problem #1
You have a red bag (where you can put 600 gram of sugar), a napkin, a box( which contains 1 kilogram and 100 gram of sugar), and a blue bag,(where you can put as much sugar as you want).
How to fill the blue bag with 1 kilogram of sugar.
Hints:
1 kilogram = 1000 grams
You can put any amount of sugar on the napkin and use it inside of any bag or the box
See solution here
Problem #2
The apartment building has 5 floors. 4 people live in this building. Each of them live on separate floor (from second to fifth). These people are entering elevator on the first floor at the same time. Elevator needs to stop on only one floor (from which all these people will go home). If a person walks down 1 floor he/she gets 1 point. If a person walks up 1 floor he/she gets 2 points. What floor elevator should stop so total number of points for all 4 people is minimal?
Problem #3
We know that 51/A - 12 is the whole number and greater than 0. What value is A?
You have a red bag (where you can put 600 gram of sugar), a napkin, a box( which contains 1 kilogram and 100 gram of sugar), and a blue bag,(where you can put as much sugar as you want).
How to fill the blue bag with 1 kilogram of sugar.
Hints:
1 kilogram = 1000 grams
You can put any amount of sugar on the napkin and use it inside of any bag or the box
See solution here
Problem #2
The apartment building has 5 floors. 4 people live in this building. Each of them live on separate floor (from second to fifth). These people are entering elevator on the first floor at the same time. Elevator needs to stop on only one floor (from which all these people will go home). If a person walks down 1 floor he/she gets 1 point. If a person walks up 1 floor he/she gets 2 points. What floor elevator should stop so total number of points for all 4 people is minimal?
Problem #3
We know that 51/A - 12 is the whole number and greater than 0. What value is A?
Monday, February 14, 2011
3rd grade: Math problems for February 15 2011
Problem #1
Suppose five days before the day after tomorrow was Wednesday.
What day of the week was yesterday?
Problem #2
X and Y are two different numbers selected from the first fifty counting numbers from 1 to 50 inclusive.
What is the largest value that
(X+Y)/(X-Y) can have?
Problem #3
If 20 is added to one-third of a number, the result is the double of the number.
What is the number?
Problem #4
Suppose five days before the day after tomorrow was Wednesday.
What day of the week was yesterday?
Problem #2
X and Y are two different numbers selected from the first fifty counting numbers from 1 to 50 inclusive.
What is the largest value that
(X+Y)/(X-Y) can have?
Problem #3
If 20 is added to one-third of a number, the result is the double of the number.
What is the number?
Problem #4
The counting numbers are arranged in four columns as shown below. Under which column letter will 101 appear?
A...B...C...D
1....2...3...4
8....7...6...5
9..10.11.12
..........14.13
Problem #5
In the 'magic square' below, the four numbers in each column, in each row, and in each of the two diagonals, have the same sum. What value should N have?
? ? 7 12
N 4 9 ?
? 5 16 3
8 11 ? ?
Problem #6
In the addition problem below, each letter stands for a digit and different letters stand for different digits.
What digits do the letters H, E, and A each represents.
HE
HE
HE
HE
+
HE
___
AH
The same written in different way: HE + HE +HE+HE=AH
In the addition problem below, each letter stands for a digit and different letters stand for different digits.
What digits do the letters H, E, and A each represents.
HE
HE
HE
HE
+
HE
___
AH
The same written in different way: HE + HE +HE+HE=AH
Tuesday, February 8, 2011
Optional homework for Math class Feb. 8 2011
Problem #1
In the multiplication problem below, A and B stand for different digits. Find A and B.
AB
X
BA
_____
114
304
_____
3154
Problem #2
100 pounds of chocolate is packaged into boxes each containing 1 1/4 pounds of chocolate. Each box is then sold for $1.75. What is the total selling price for all of the boxes of chocolate?
Problem #3
P and Q represents numbers, and
P * Q means (P + Q)/2.
What is the value of 3 * (6 * 8)?
In the multiplication problem below, A and B stand for different digits. Find A and B.
AB
X
BA
_____
114
304
_____
3154
Problem #2
100 pounds of chocolate is packaged into boxes each containing 1 1/4 pounds of chocolate. Each box is then sold for $1.75. What is the total selling price for all of the boxes of chocolate?
Problem #3
P and Q represents numbers, and
P * Q means (P + Q)/2.
What is the value of 3 * (6 * 8)?
Monday, February 7, 2011
3rd grade: Math problems for February 8 2011
Problem #1
The four-digit numeral 3AA1 is divisible by 9.
What digit does A represents?
Rule: A number is divisible by 9 if sum of its digits
is divisible by 9.
Examples:
9 has one digit 9 is divisible by 9
18 has two digits, 1 and 8 => 1 + 8 = 9 is divisible by 9
900 has three digits, 9, 0, 0. 9 + 0 + 0 = 9 is divisible by 9
Problem #2
Suppose all the counting numbers are arranged in columns as
shown below.
Under what column-letter will 100 appear?
A B C D E F G
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 _ _ _
Problem #3
A boy has the following seven coins in his pocket: 2 pennies,
2 nickels, 2 dimes, and 1 quarter. He takes out two coins, records
the sum of their values, and then puts them back with the other
coins. He continues to take out two coins, record the sum of their
values, and then put them back.
How many different sums can he record at most.
Problem #4
In a group of 30 students, 8 take French, 12 take Spanish and
3 take both languages.
How many students of the group take neither French nor Spanish?
Problem #5
Glen, Harry, and Kim each have a different favorite sport among
tennis, baseball, and soccer. Glen doe not like baseball or soccer.
Harry does not like baseball. Name the favorite sport of each person.
Problem #6
In the 'magic-square' below, five more numbers can be placed in the
boxes so that the sum of the three numbers in each row, in each
column, and in each diagonal is always the same.
What value should X have?
The four-digit numeral 3AA1 is divisible by 9.
What digit does A represents?
Rule: A number is divisible by 9 if sum of its digits
is divisible by 9.
Examples:
9 has one digit 9 is divisible by 9
18 has two digits, 1 and 8 => 1 + 8 = 9 is divisible by 9
900 has three digits, 9, 0, 0. 9 + 0 + 0 = 9 is divisible by 9
Problem #2
Suppose all the counting numbers are arranged in columns as
shown below.
Under what column-letter will 100 appear?
A B C D E F G
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 _ _ _
Problem #3
A boy has the following seven coins in his pocket: 2 pennies,
2 nickels, 2 dimes, and 1 quarter. He takes out two coins, records
the sum of their values, and then puts them back with the other
coins. He continues to take out two coins, record the sum of their
values, and then put them back.
How many different sums can he record at most.
Problem #4
In a group of 30 students, 8 take French, 12 take Spanish and
3 take both languages.
How many students of the group take neither French nor Spanish?
Problem #5
Glen, Harry, and Kim each have a different favorite sport among
tennis, baseball, and soccer. Glen doe not like baseball or soccer.
Harry does not like baseball. Name the favorite sport of each person.
Problem #6
In the 'magic-square' below, five more numbers can be placed in the
boxes so that the sum of the three numbers in each row, in each
column, and in each diagonal is always the same.
What value should X have?
| 15 | __ | 35 |
| 50 | __ | __ |
| 25 | X | __ |
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