AMC8 Daily Challenge

Master AMC8 with 5 Problems a Day

Summary for Today

Time Used: 04:46
Accuracy: 4 / 5

Problem 1 (from Problem 8, AMC 8 2017)

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.

This information allows Malcolm to determine Isabella's house number. What is its units digit?

Problem 2 (from Problem 9, AMC 8 2014)

In $\bigtriangleup ABC$, $D$ is a point on side $\overline{AC}$ such that $BD=DC$ and $\angle BCD$ measures $70^\circ$. What is the degree measure of $\angle ADB$?

[asy] size(300); defaultpen(linewidth(0.8)); pair A=(-1,0),C=(1,0),B=dir(40),D=origin; draw(A--B--C--A); draw(D--B); dot("$A$", A, SW); dot("$B$", B, NE); dot("$C$", C, SE); dot("$D$", D, S); label("$70^\circ$",C,2*dir(180-35));[/asy]

Problem 3 (from Problem 3, AMC 8 2016)

Four students take an exam. Three of their scores are $70$, $80$, and $90$. If the average of their four scores is $70$, then what is the remaining score??

Problem 4 (from Problem 6, AMC 8 2009)

Steve's empty swimming pool will hold $24,000$ gallons of water when full. It will be filled by $4$ hoses, each of which supplies $2.5$ gallons of water per minute. How many hours will it take to fill Steve's pool?

Problem 5 (from Problem 19, AMC 8 2004)

A whole number larger than $2$ leaves a remainder of $2$ when divided by each of the numbers $3, 4, 5,$ and $6$. The smallest such number lies between which two numbers?

AMC8 problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Problem statements and solutions are sourced from the AoPS Wiki under the Creative Commons Attribution-ShareAlike license.