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 #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?

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?

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?

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?

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?

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?

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

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