Triangles, Circles, and More
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Numbers Everywhere
Mystery Questions
100
An equilateral triangle and a regular hexagon have equal perimeters. If the triangle's area is 4, what is the area of the hexagon?
6
100
A jar contains 5 different colors of gumdrops. 30% are blue, 20% are brown, 15% are red, 10% are yellow, and other 30 gumdrops are green. If half of the blue gumdrops are replaced with brown gumdrops, how many gumdrops will be brown?
42
100
Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other?
1/3
100
What is the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers?
2003
100
When is the Rose Hulman Competition?
This Saturday, November 5th
200
Isosceles triangle ABC has a base of length 5x − 8 and legs of length 6x − 5. What is the least possible integer value for x?
2
200
The taxi fare in Gotham City is $2.40 for the first 1/2 mile and additional mileage charged at the rate $0.20 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $10?
3.3
200
In one toss of two fair dice what is the probability that the product of the two numbers rolled is a prime number? Express your answer as a common fraction.
1/6
200
How many 4-digit numbers greater than 1000 are there that use the four digits of 2012?
9
200
When is the AMC 10/12 A this year?
November 10
300
What is the radius of the inscribed circle of a triangle with side lengths 9, 13, and 14?
square root of 10
300
At the theater children get in for half price. The price for 5 adult tickets and 4 child tickets is 24.50. How much would 8 adult tickets and 6 child tickets cost?
$38.50
300
In how many ways can 20 identical coins be given to 4 distinct people so that each person gets at least 2 coins?
455
300
What digit does A represent in the equation 1A × 491 = AA3A?
8
300
When is the AMC 10/12 B this year?
November 16
400
How many noncongruent integer-sided triangles with positive area and perimeter less than 15 are neither equilateral, isosceles, nor right triangles?
5
400
Marvin had a birthday on Tuesday, May 27 in the leap year 2008. In what year will his birthday next fall on a Saturday?
2017
400
An unfair coin lands on heads with a probability of 1/4. When tossed n > 1 times, the probability of exactly two heads is the same as the probability of exactly three heads. What is the value of n?
11
400
What is the smallest of four consecutive prime numbers whose sum is 220?
47
400
Who was our first guest speaker?
Dr. Cross
500
On a sheet of paper, Isabella draws a circle of radius 2, a circle of radius 3, and all possible lines simultaneously tangent to both circles. Isabella notices that she has drawn exactly k > 0 lines. How many different values of k are possible?
5
500
The line 12x + 5y = 60 forms a triangle with the coordinate axes. What is the sum of the lengths of the altitudes of this triangle?
281/13
500
Each of the 100 students in a certain summer camp can either sing, dance, or act. Some students have more than one talent, but no student has all three talents. There are 42 students who cannot sing, 
students who cannot dance, and 29 students who cannot act. How many students have two of these talents?
64
500
All the numbers 1,2,3,4,5,6,7,8,9 are written in a 3x3 array of squares, one number in each square, in such a way that if two numbers are consecutive then they occupy squares that share an edge. The numbers in the four corners add up to 18. What is the number in the center?
7
500
When are the Math Club yearbook pictures?
Tuesday, November 8th during SSRT