# Difference between revisions of "2019 AMC 8 Problems"

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== Problem 19 == | == Problem 19 == | ||

+ | In a tournament there are six team taht play each other twice. A team earns <math>3</math> points for a win, <math>1</math> point for a draw, and <math>0</math> points for a loss. After all the games have been played it turns out that the top three teams earned the same number of total points. What is the greatest possible number of total points for each of the top three teams? | ||

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+ | <math>\textbf{(A) }22\qquad\textbf{(B) }23\qquad\textbf{(C) }24\qquad\textbf{(D) }26\qquad\textbf{(E) }30</math> | ||

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== Problem 20 == | == Problem 20 == | ||

== Problem 21 == | == Problem 21 == |

## Revision as of 14:16, 20 November 2019

## Contents

- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25

## Problem 1

Ike and Mike go into a sandwich shop with a total of to spend. Sandwiches cost each and soft drinks cost each. Ike and Mike plan to buy as many sandwiches as they can and use the remaining money to buy soft drinks. Counting both soft drinks and sandwiches, how many items will they buy?

## Problem 2

Three identical rectangles are put together to form rectangle , as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is feet, what is the area in square feet of rectangle ?

## Problem 3

3. Which of the following is the correct order of the fractions , , and , from least to greatest?

## Problem 4

Quadrilateral is a rhombus with perimeter meters. The length of diagonal is meters. What is the area in square meters of rhombus ?

## Problem 5

A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise behind. Confident that he will win, the hare stops to take a nap. Meanwhile, the tortoise walks at a slow steady pace for the entire race. The hare awakes and runs to the finish line, only to find the tortoise already there. Which of the following graphs matches the description of the race, showing the distance traveled by the two animals over time from start to finish? [img]https://latex.artofproblemsolving.com/e/f/9/ef92362133ad95b0788184ff802df2094337d377.png[/img] [img width="65" height="5"]https://latex.artofproblemsolving.com/6/8/2/682b63fdba98e33c13055463223d6c8ea409cf23.png[/img]

## Problem 6

There are grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point is in the center of the square. Given that point is randomly chosen among the other 80 points, what is the probability that the line is a line of symmetry for the square?

## Problem 7

Shauna takes five tests, each worth a maximum of points. Her scores on the first three tests are , , and . In order to average for all five tests, what is the lowest score she could earn on one of the other two tests?

## Problem 8

Gilda has a bag of marbles. She gives 20% of them to her friend Pedro. Then Gilda gives 10% of what is left to another friend, Ebony. Finally, Gilda gives 25% of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?

## Problem 9

Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are cm in diameter and cm high. Felicia buys cat food in cylindrical cans that are cm in diameter and cm high. What is the ratio of the volume one of Alex's cans to the volume one of Felicia's cans?

## Problem 10

## Problem 11

The eighth grade class at Lincoln Middle School has students. Each student takes a math class or a foreign language class or both. There are eigth graders taking a math class, and there are eight graders taking a foreign language class. How many eigth graders take a math class and a foreign language class?

## Problem 12

## Problem 13

A is a number that has the same value when read from left to right or from right to left. (For example 12321 is a palindrome.) Let be the least three-digit integer which is not a palindrome but which is the sum of three distinct two-digit palindromes. What is the sum of the digits of ?

## Problem 14

Isabella has coupons that can be redeemed for free ice cream cones at Pete's Sweet Treats. In order to make the coupons last, she decides that she will redeem one every days until she has used them all. She knows that Pete's is closed on Sundays, but as she circles the dates on her calendar, she realizes that no circled date falls on a Sunday. On what day of the week does Isabella redeem her first coupon?

MondayTuesdayWednesdayThursdayFriday

## Problem 15

On a beach people are wearing sunglasses and people are wearing caps. Some people are wearing both sunglasses and caps. If one of the people wearing a cap is selected at random, the probability that this person is is also wearing sunglasses is . If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?

## Problem 16

Qiang drives miles at an average speed of miles per hour. How many additional miles will he have to drive at miles per hour to average miles per hour for the entire trip?

## Problem 17

What is the value of the product

## Problem 18

The faces of each of two fair dice are numbered , , , , , and . When the two dice are tossed, what is the probability that their sum will be an even number?

## Problem 19

In a tournament there are six team taht play each other twice. A team earns points for a win, point for a draw, and points for a loss. After all the games have been played it turns out that the top three teams earned the same number of total points. What is the greatest possible number of total points for each of the top three teams?

## Problem 20

## Problem 21

## Problem 22

## Problem 23

## Problem 24

## Problem 25

Alice has apples. In how many ways can she share them with Becky and Chris so that each of the people has at least apples?

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.