Isabella’s house has $3$ bedrooms. Each bedroom is $12$ feet long, $10$ feet wide, and $8$ feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy $60$ square feet in each bedroom. How many square feet of walls must be painted?
A college student drove his compact car $120$ miles home for the weekend and averaged $30$ miles per gallon. On the return trip the student drove his parents’ SUV and averaged only $20$ miles per gallon. What was the average gas mileage, in miles per gallon, for the round trip?
The point $O$ is the center of the circle circumscribed about $\triangle ABC,$ with $\angle BOC=120^\circ$ and $\angle AOB=140^\circ,$ as shown. What is the degree measure of $\angle ABC?$
At Frank’s Fruit Market, $3$ bananas cost as much as $2$ apples, and $6$ apples cost as much as $4$ oranges. How many oranges cost as much as $18$ bananas?
The $2007$ AMC $12$ contests will be scored by awarding $6$ points for each correct response, $0$ points for each incorrect response, and $1.5$ points for each problem left unanswered. After looking over the $25$ problems, Sarah has decided to attempt the first $22$ and leave the last $3$ unanswered. How many of the first $22$ problems must she solve correctly in order to score at least $100$ points?
Triangle $ABC$ has side lengths $AB=5,$ $BC=6,$ and $AC=7.$ Two bugs start simultaneously from $A$ and crawl along the sides of the triangle in opposite directions at the same speed. They meet at point $D.$ What is $BD?$
Tom’s age is $T$ years, which is also the sum of the ages of his three children. His age $N$ years ago was twice the sum of their ages then. What is $\frac{T}{N}?$
Some boys and girls are having a car wash to raise money for a class trip to China. Initially $40\%$ of the group are girls. Shortly thereafter two girls leave and two boys arrive, and then $30\%$ of the group are girls. How many girls were initially in the group?
The angles of quadrilateral $ABCD$ satisfy $\angle A=2\angle B=3\angle C=4\angle D.$ What is the degree measure of $\angle A,$ rounded to the nearest whole number?
A teacher gave a test to a class in which $10\%$ of the students are juniors and $90\%$ are seniors. The average score on the test was $84.$ The juniors all received the same score, and the average score of the seniors was $83.$ What score did each of the juniors receive on the test?
A traffic light runs repeatedly through the following cycle: green for $30$ seconds, then yellow for $3$ seconds, and then red for $30$ seconds. Leah picks a random three-second time interval to watch the light. What is the probability that the color changes while she is watching?
Point $P$ is inside equilateral $\triangle ABC.$ Points $Q,$ $R,$ and $S$ are the feet of the perpendiculars from $P$ to $\overline{AB},$ $\overline{BC},$ and $\overline{CA},$ respectively. Given that $PQ=1,$ $PR=2,$ and $PS=3,$ what is $AB?$
Each face of a regular tetrahedron is painted either red, white, or blue. Two colorings are considered indistinguishable if two congruent tetrahedra with those colorings can be rotated so that their appearances are identical. How many distinguishable colorings are possible?
Let $a,$ $b,$ and $c$ be digits with $a\ne0.$ The three-digit integer $\overline{abc}$ lies one third of the way from the square of a positive integer to the square of the next larger integer. The integer $\overline{acb}$ lies two thirds of the way between the same two squares. What is $a+b+c?$
Rhombus $ABCD,$ with side length $6,$ is rolled to form a cylinder of volume $6$ by taping $\overline{AB}$ to $\overline{DC}.$ What is $\sin(\angle ABC)?$
The parallelogram bounded by the lines $y=ax+c,$ $y=ax+d,$ $y=bx+c,$ and $y=bx+d$ has area $18.$ The parallelogram bounded by the lines $y=ax+c,$ $y=ax-d,$ $y=bx+c,$ and $y=bx-d$ has area $72.$ Given that $a,$ $b,$ $c,$ and $d$ are positive integers, what is the smallest possible value of $a+b+c+d?$
