Olympiad level 1
Suppose 6 days after the day before yesterday is Thursday. What day of the week is the day after tomorrow?
Tuesday
List all of the different natural numbers that each leave a remainder of 2 when divided into 83.
3, 9, 27, 81
In a group of five children, the average weight of each child was 72 pounds. When a sixth child joined the group, the average weight of each child became 73 pounds. What was the weight of the sixth child?
78 pounds
The quotient of two numbers is 4 and their difference is 39. What is the smaller number of the two?
The larger number is 52 and the smaller number is 13.
The number 2 is the first even number, 4 is the second even number, 6 is the third even number, and so forth. What is the sum of the first twenty-five even numbers?
650
A study of 50 high school students showed that exactly 25 of them took Biology, exactly 20 of them took Chemistry, and exactly 12 of them took both subjects. How many of the 50 students took neither Biology nor Chemistry?
17 students.
From a pile of coins containing nickels (N), dimes (D), and quarters (Q), Tom picked 10 coins with a total value of $1.00. The ten coins had a different number of each of the three types and at least 1 coin of each type. How many coins of each type did he pick?
N=3
D=6
Q=1
546 is one of six three-digit numbers each of which is different and has the digits 4,5, and 6. What is the sum of these six numbers?
The sum is 3330
A school has 90 children. During the day, each child attends 4 classes. Each class has 15 children and 1 teacher. During the day, each teacher teaches 3 classes. What is the smallest number of teachers the school can have?
8 teachers
When a natural number is multiplied by itself, the result is called a perfect-square. Since 1x1=1, 2x2=4, 3x3=9 and so forth 1,4,9 and so forth are perfect-squares. What year in the 18th century (the years 1701 through 1800) was a perfect square?
1764
Betty wants to purchase a bicycle but is $23 short. Claire wants to purchase the same bicycle but is $25 short. If they combine their money, they will have just enough to buy the bicycle. What is the cost of the bicycle?
$48
ABCD is a square with diagonal AC 8 units long. How many square units are in the area of the square?
32 square units.
In the below multiplication problem, A,B,C,and D represent different digits. ABC is a three-digit number and * means multiplication. What three-digit number does ABC represent?
A B C
* D
________
1673
Find D first.
D=7
ABC = 239
Two students are needed to work in the school store during the lunch hour every day, and four students volunteer for this work. What is the greatest number of days that can be arranged in which in no pair of the four students works together more than once?
6 days
2,3,5,7,11,...are examples of prime numbers; each number has only itself and 1 as factors. Suppose the number of units in each of the length and width of a rectangle are prime numbers and the perimeter is 36 units. What is the largest number of square units the area could have?
77 square units
When Paul crossed the finish line of a 60 meter race, he was ahead of Robert by 10 meters and ahead of Same by 20 meters. Suppose Robert and Sam continue to race to the finish line without changing their rate of speed. By how many meters will Robert beat Sam?
Robert beats Sam by 12 meters.