Geometry
Area of a 3-4-5 triangle
6
What is the 15th term of the Fibonacci sequence?
610
4x-20=44
solve for x
x=16
There are five gears connected in a row, the first one is connected to the second one, the second one is connected to the third one, and so on.
If the first gear is rotating clockwise what direction is the fifth gear turning?
Clockwise
28+35
What is 63?
180
John is playing a game in which he tries to obtain the highest number possible. He must put the symbols plus, times, and minus in the following blanks, using each symbol exactly once:
2__4__6__8
John cannot use parentheses or rearrange the numbers. What is the highest possible number that John could obtain?
46
2-4+6*8
Line l is defined by 3y+12x=5. Line n is perpendicular to line l in the xy-plane. What is the slope of line n?
1/4 or 0.25
You are at an unmarked intersection ... one way is the City of Lies and another way is the City of Truth.
Citizens of the City of Lies always lie.
Citizens of the City of Truth always tell the truth.
A citizen of one of those cities (you don't know which) is at the intersection. What question could you ask to them to find the way to the City of Truth?
Which direction do you live?
188-279
What is -91?
AMC 10 Triangle Problem
20
Is 15693 divisible by 9?
NO
Divisbility rule of 9: sum of digits divisible by 9
Romania 1974
0
You have three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble.
You pick a random bag and take out one marble.
It is a white marble.
What is the probability that the remaining marble from the same bag is also white?
2/3
You are selecting marbles, not bags
Bag A, Bag A, Bag C
56*18
What is 1008?
AMC 10 Circle 4 Problem
3/28
How many multiples of 7 are between 92 and 249?
22
abc Problem
1 = 1/(abc)^2
abc = 1
Fruity Totals!
Banana = 13
Plums = 2
Apples = 6
Cherries = 4
1702/46
What is 37?
"Shear Beauty"
sqrt(250)
Prove for any integer n >= 0 that
11^(n+2)+12^(2n+1) is divisible by 133
Assume base case, n = 0
Proof for k = n+1
AIME 1997 (No calculators)
x cannot be 58
In a circle of 20 stands knights and knaves. Knights tell the truth and knaves tell the lies. You ask every person:"Is the person to your right a knight or a knave?"
You can deduce how many are knights and how many are knaves regardless of the answer. How many knights are there, and WHY?
10 each.
Knight implies the same role as their neighbor, knave implies the opposite. If changing our assumption doesn't change the answer, then there must be 10 each.
How many digits repeat for 1/17?
(paper IS allowed)
What is 16 digits?
0.0588235294117647
The length of the repeating cycle for 1/q can be at most q-1 digits