This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 57

1994 AMC 8, 16
Tags: geometry , perimeter , ratio , MATHCOUNTS
The perimeter of one square is $3$ times the perimeter of another square. The area of the larger square is how many times the area of the smaller square? $\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 9$

2006 AMC 8, 13
Tags: MATHCOUNTS
Cassie leaves Escanaba at 8:30 AM heading for Marquette on her bike. She bikes at a uniform rate of 12 miles per hour. Brian leaves Marquette at 9:00 AM heading for Escanaba on his bike. He bikes at a uniform rate of 16 miles per hour. They both bike on the same 62-mile route between Escanaba and Marquette. At what time in the morning do they meet? $ \textbf{(A)}\ 10: 00 \qquad \textbf{(B)}\ 10: 15 \qquad \textbf{(C)}\ 10: 30 \qquad \textbf{(D)}\ 11: 00 \qquad \textbf{(E)}\ 11: 30$

2013 AIME Problems, 6
Tags: probability , MATHCOUNTS , AMC , AIME , number theory , relatively prime , #6
Melinda has three empty boxes and $12$ textbooks, three of which are mathematics textbooks. One box will hold any three of her textbooks, one will hold any four of her textbooks, and one will hold any five of her textbooks. If Melinda packs her textbooks into these boxes in random order, the probability that all three mathematics textbooks end up in the same box can be written as $\frac{m}{n}$, where $m$ and $n$ Are relatively prime positive integers. Find $m+n$.

1972 AMC 12/AHSME, 9
Tags: MATHCOUNTS , AMC 8 , AMC 10
Ann and Sue bought identical boxes of stationery. Ann used hers to write 1-sheet letters and Sue used hers to write 3-sheet letters. Ann used all the envelopes and had 50 sheets of paper left, while Sue used all of the sheets of paper and had 50 envelopes left. The number of sheets of paper in each box was \[ \begin{array}{rlrlrlrlrlrl} \hbox {(A)}& 150 \qquad & \hbox {(B)}& 125 \qquad & \hbox {(C)}& 120 \qquad & \hbox {(D)}& 100 \qquad & \hbox {(E)}& 80 & \end{array} \]

2014 NIMO Summer Contest, 3
Tags: MATHCOUNTS , geometry , perimeter , ratio , 3D geometry , sphere , Alcumus
A square and equilateral triangle have the same perimeter. If the triangle has area $16\sqrt3$, what is the area of the square? [i]Proposed by Evan Chen[/i]

2004 AIME Problems, 1
Tags: AMC , AIME , MATHCOUNTS
The digits of a positive integer $n$ are four consecutive integers in decreasing order when read from left to right. What is the sum of the possible remainders when $n$ is divided by $37$?

2012 Puerto Rico Team Selection Test, 6
Tags: MATHCOUNTS , number theory proposed , number theory
The increasing sequence $1; 3; 4; 9; 10; 12; 13; 27; 28; 30; 31, \ldots$ is formed with positive integers which are powers of $3$ or sums of different powers of $3$. Which number is in the $100^{th}$ position?