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?

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?

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.)

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?

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?

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?

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?