Arithmetic and Counting
At a conference, 5 people each shake hands with every other person exactly once. How many total handshakes occur?
Answer
10
(x+5)/3 = 7/4
x=1/4
Three people walk into a party. Then four more arrive, and three leave. After two more enter and one leaves, how many people are now at the party?
Answer
5
A group of 5 students achieved the following grades in their test: 85, 92, 88, 75, and 80. What is the mean of their grades, rounded to the nearest whole number?
Answer
86
A frog is at the bottom of a 128-meter well. Each day, it climbs up 5 meters, but each night, it slips down 3 meters. How many days will it take the frog to reach the top of the well?
Answer
64
The sum of three consecutive even integers is 84.What are the three integers?
26,28 and 30
Peter is three years older than his sister Jane. Five years ago, Peter was twice as old as Jane. What are their current ages?
Answer
Peter is 8, and Jane is 5
A heptagon (seven-sided shape) has six angles measuring 100°, 110°, 120°, 130°, 140°, and 150°. What is the measure of the seventh angle?
Answer
50 degrees
What is the sum of the first 15 positive integers?
Answer
120
A car rental company charges a fixed rental fee of $55 per day plus $0.35 per mile driven. If a person rented a car for 4 days and drove 200 miles, how much did the rental cost?
$290
In a sequence where the first term is 2, the second term is 7, and each term is obtained by adding 3 times the position number, what is the fifth term?
Answer
20
A rectangular swimming pool has a length of 12 meters and a width of 8 meters. If the length is increased by 4 meters and the width is decreased by 2 meters, what is the change in the area of the pool?
Answer
The change in the area of the pool is 0 square meters.
What is the number of ways to arrange 3 different cups on a shelf?
Answer
6
The sum of the squares of two consecutive positive even integers is 100. Find the integers.
Answer
x = 6 or x= −8
In a class of 30 students, 40% are in the drama club, 30% are in the sports club, and 20% are in both. How many students are in at least one of the clubs?
Answer
15
An aquarium has a rectangular base with a length of 20 cm, a width of 10 cm, and a height of 15 cm. If the aquarium is filled with water to a height of 6 cm, what is the volume of water in the aquarium in liters? (Note: 1 cm³ = 0.001 liters)
Answer
The volume of water in the aquarium is 1.2 liters.
A school is organizing a fundraiser with 3 different flavors of ice cream and 4 different types of toppings. How many different combinations of one ice cream flavor and one topping can be made?
Answer
12
Let f(x)=x^2−4x+5 Find the minimum value of f(x)and the value of x at which it occurs.
Answer
f(x)=1 at x=2
At a school bake sale, brownies cost $2 and cupcakes cost $3. If a total of 10 items were sold for $25, how many of each type of item were sold?
Answer
5 brownies and 5 cupcakes
A square is inscribed in a circle, and the perimeter of the square is 36 cm. The size of the circle is then doubled. What is the new diameter of the circle?
Answer
The new diameter of the circle when it’s size is doubled is approximately 18(2)^1/2 or 25.46