# Difference between revisions of "2016 AMC 8 Problems"

m (Someone put "bruh" on the solution thing so i changed it back.) |
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In rectangle <math>ABCD</math>, <math>AB=6</math> and <math>AD=8</math>. Point <math>M</math> is the midpoint of <math>\overline{AD}</math>. What is the area of <math>\triangle AMC</math>? | In rectangle <math>ABCD</math>, <math>AB=6</math> and <math>AD=8</math>. Point <math>M</math> is the midpoint of <math>\overline{AD}</math>. What is the area of <math>\triangle AMC</math>? | ||

+ | |||

+ | <asy>draw((0,4)--(0,0)--(6,0)--(6,8)--(0,8)--(0,4)--(6,8)--(0,0)); | ||

+ | label("$A$", (0,0), SW); | ||

+ | label("$B$", (6, 0), SE); | ||

+ | label("$C$", (6,8), NE); | ||

+ | label("$D$", (0, 8), NW); | ||

+ | label("$M$", (0, 4), W); | ||

+ | label("$4$", (0, 2), W); | ||

+ | label("$6$", (3, 0), S);</asy> | ||

<math>\textbf{(A) }12\qquad\textbf{(B) }15\qquad\textbf{(C) }18\qquad\textbf{(D) }20\qquad \textbf{(E) }24</math> | <math>\textbf{(A) }12\qquad\textbf{(B) }15\qquad\textbf{(C) }18\qquad\textbf{(D) }20\qquad \textbf{(E) }24</math> |

## Latest revision as of 11:21, 11 May 2021

## 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

The longest professional tennis match lasted a total of 11 hours and 5 minutes. How many minutes is that?

## Problem 2

In rectangle , and . Point is the midpoint of . What is the area of ?

## Problem 3

Four students take an exam. Three of their scores are and . If the average of their four scores is , then what is the remaining score?

## Problem 4

When Cheenu was a boy he could run miles in hours and minutes. As an old man he can now walk miles in hours. How many minutes longer does it take for him to travel a mile now compared to when he was a boy?

## Problem 5

The number is a two-digit number.

• When is divided by , the remainder is .

• When is divided by , the remainder is .

What is the remainder when is divided by ?

## Problem 6

The following bar graph represents the length (in letters) of the names of 19 people. What is the median length of these names?

## Problem 7

Which of the following numbers is not a perfect square?

## Problem 8

Find the value of the expression

## Problem 9

What is the sum of the distinct prime integer divisors of ?

## Problem 10

Suppose that means What is the value of if

## Problem 11

Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is

## Problem 12

Jefferson Middle School has the same number of boys and girls. of the girls and of the boys went on a field trip. What fraction of the students on the field trip were girls?

## Problem 13

Two different numbers are randomly selected from the set and multiplied together. What is the probability that the product is ?

## Problem 14

Karl's car uses a gallon of gas every miles, and his gas tank holds gallons when it is full. One day, Karl started with a full tank of gas, drove miles, bought gallons of gas, and continued driving to his destination. When he arrived, his gas tank was half full. How many miles did Karl drive that day?

## Problem 15

What is the largest power of that is a divisor of ?

## Problem 16

Annie and Bonnie are running laps around a -meter oval track. They started together, but Annie has pulled ahead because she runs faster than Bonnie. How many laps will Annie have run when she first passes Bonnie?

## Problem 17

An ATM password at Fred's Bank is composed of four digits from to , with repeated digits allowable. If no password may begin with the sequence then how many passwords are possible?

## Problem 18

In an All-Area track meet, sprinters enter a meter dash competition. The track has lanes, so only sprinters can compete at a time. At the end of each race, the five non-winners are eliminated, and the winner will compete again in a later race. How many races are needed to determine the champion sprinter?

## Problem 19

The sum of consecutive even integers is . What is the largest of these consecutive integers?

## Problem 20

The least common multiple of and is , and the least common multiple of and is . What is the least possible value of the least common multiple of and ?

## Problem 21

A top hat contains 3 red chips and 2 green chips. Chips are drawn randomly, one at a time without replacement, until all 3 of the reds are drawn or until both green chips are drawn. What is the probability that the 3 reds are drawn?

## Problem 22

Rectangle below is a rectangle with . The area of the "bat wings" (shaded area) is

## Problem 23

Two congruent circles centered at points and each pass through the other circle's center. The line containing both and is extended to intersect the circles at points and . The circles intersect at two points, one of which is . What is the degree measure of ?

## Problem 24

The digits , , , , and are each used once to write a five-digit number . The three-digit number is divisible by , the three-digit number is divisible by , and the three-digit number is divisible by . What is ?

## Problem 25

A semicircle is inscribed in an isosceles triangle with base and height so that the diameter of the semicircle is contained in the base of the triangle as shown. What is the radius of the semicircle?

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