Algebra
While eating out, Mike and Joe each tipped their server $2. Mike tipped 10% of his bill and Joe tipped 20% of his bill. What was the difference, in dollars, between their bills?
10 dollars
For how many (not necessarily positive) integers n is 4000*(⅖)^n an integer?
9
How many integers between 2020 and 2400 have four distinct digits arranged in increasing order? (For example, 2347 is one integer.).
15
Bob is tiling the floor of his 12 foot by 16 foot living room. He plans to place one-foot by one-foot square tiles to form a border along the edges of the room and to fill in the rest of the floor with two-foot by two-foot square tiles. How many tiles will he use?
87 tiles
Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn't know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are true."
(1) It is prime.
(2) It is even.
(3) It is divisible by 7.
(4) One of its digits is 9.
What is Isabella’s house number?
91
It takes Anna 30 minutes to walk uphill 1 km from her home to school, but it takes her only 10 minutes to walk from school to her home along the same route. What is her average speed, in km/hr, for the round trip?
3 km/h
Charles was born in a year between 1300 and 1400. Louis was born in a year between 1400 and 1500. Each was born on 6 April in a year that was a perfect square. Each lived for 110 years. In what year while they were both alive were their ages both perfect squares on 7 April?
1469
The Fibonacci sequence 1,1,2,3,5,8,13,21, etc. starts with two 1s, and each term afterwards is the sum of its two predecessors. Which one of the ten digits is the last to appear in the unit position of a number in the Fibonacci sequence?
6
The midpoints of the four sides of a rectangle are (-3,0), (2,0), (5,4) and (0,4) What is the area of the rectangle?
40
Five children, Amelia, Bob, Charlie, Devin and Edwin, were in the classroom when one of them broke a window. The teacher asked each of them to make a statement about the event, knowing three of them always lie and two always tell the truth. Their statements were as follows:
Amelia: “Charlie did not break it, nor did Devin.”
Bob: “I didn’t break it, nor did Devin.”
Charlie: “I didn’t break it, but Edwin did.”
Devin: "Amelia or Edwina broke it."
Edwin: “Charlie broke it.”
Who broke the window?
Charlie
The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse?
0 dimes
There are a number of eggs in a box. If we take 3 eggs each time, 1 is left in the end; if 5 are taken each time, 2 are left in the end; if we take 7 each time, 3 are left in the end. How many eggs are in the box at least?
52
A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selected?
3/10
Two congruent circles centered at points A and B each pass through each other’s center. The line containing both A and B is extended to intersect the circles at points C and D. THe circles intersect at two points, one of which is E. What is the measure of angle CED?
120
In a round-robin tournament with 6 teams, each team plays one game against each other team, and each game results in one team winning and one team losing. At the end of the tournament, the teams are ranked by the number of games won. What is the maximum number of teams that could be tied for the most wins at the end of the tournament?
5 teams
Sally has five red cards numbered 1 through 5 and four blue cards numbered 3 through 6. She stacks the cards so that the colors alternate and so that the number on each red card divides evenly into the number on each neighboring blue card. What is the sum of the numbers on the middle three cards?
12
Mary chose an even four-digit number n. She wrote down all the divisors of n in increasing order from left to right: 1, 2, …, n/2, n. At some point, Mary wrote 323 as a divisor of n. What is the smallest possible value of the divisor written to the right of 323?
340
A coin is biased in such a way that on each toss the probability of heads is ⅔ and the probability of tails is 1/3. The outcomes of the tosses are independent. A player has the choice of playing Game A or Game B. In Game A she tosses the coin three times and wins if all three outcomes are the same. In Game B she tosses the coin four times and wins if both the outcomes of the first and second tosses are the same and the outcomes of the third and fourth tosses are the same. What are the chances to win each game (MUST ANSWER WITH BOTH)
Game A - 27/81
Game B - 25/81
A 1X2 rectangle is inscribed in a semicircle with longer sides on the diameter. What is the area of the semicircle?
π (pi)
Kiran has a box containing three different types of fruit: apples, pears, and bananas. In the box, 21 pieces of fruit are not apples, 25 pieces of fruit are not pears, and 28 pieces of fruit are not bananas. How many pieces of fruit are in the box?
37
The table below displays some of the results of last summer's Frostbite Falls Fishing Festival, showing how many contestants caught n fish for various values of n:
n 0 1 2 3 ... 13 14 15
Number of Contestants 9 5 7 23... 5 2 1
who caught n fish
In the newspaper story covering the event, it was reported that
(a) the winner caught 15 fish
(b) those who caught 3 or more fish averaged 6 fish each
(c) those who caught 12 or fewer fish averaged 5 fish each
What was the total number of fish caught during the festival?
943 fish
N is a natural number without repeating digits, and N is divisible by each of its digits. What is the maximum value of N?
9867312
Tina randomly selects two distinct numbers between 1 and 5 (inclusive), and Sergio randomly selects a number between 1 and 10 (inclusive). What is the probability that Sergio's number is larger than the sum of the two numbers chosen by Tina?
2/5
Right triangle ABC has leg lengths AB = 20 and BC = 21. Including AB and BC, how many line segments with integer length can be drawn from vertex B to a point on hypotenuse ?
13
A town has 2017 houses. Of these 2017 houses, 1820 have a dog, 1651 have a cat, and 1182 have a turtle. If x is the largest possible number of houses that have a dog, a cat, and a turtle, and y is the smallest possible number of houses that have a dog, a cat, and a turtle, then what is x - y?
563