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Math Olympiad

1

How to find the sum of the first n natural numbers?

2

If 20 is added to one third of a number the result is double that number. What is the number?

3

How do you calculate the sum of sequences starting from various natural numbers?

4

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 ?

5

A car needs 1 minute 30 seconds to travel a distance of 1 mile. At this rate,how many miles will the car travel in 1 hour ?

6

A phone and case together cost $100. If the phone cost $90 more than the case, how much would the case cost ?

7

The sum of the weights of Adam and Alex is 138 pounds and one boy is 34 pounds heavier than the other .How much does the heavier boy weigh ?

10

A train travels 1 mile in 1 minute and 30 seconds. At this rate how many miles will this train travel in 1 hour? 

8

One day , Alex 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 he sell ?

9

If 16 is added to one-third of a number the result is three times that number. What is the number?

11

If x is divided by y, the result is 3/4. If y is divided by z , the result is 5/6. What is the result when x is divided by z ?

12

A certain natural number is divisible by 3 and also by 5. When the number is divided by 7, the remainder is 4. What is the smallest number that satisfies these conditions ?

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13

The sum of the ages of three children is 32. The age of the oldest is twice the age of the youngest. The age of the two children differ by three years. What is the age of the youngest child?

14

A jar filled with water weighs 10 pounds. When half of the water is poured out, the jar and the remaining water weigh 5.75 pounds. How much does the jar alone weigh?

15

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 largest of the two numbers?

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