The Aftermath
Number Theory
Always Right
71
Timed questions
100
The top of one tree is 16 feet higher than the top of another tree. The heights of the two trees are in the ratio 3:4. The taller tree then falls onto a 100ft wide road from the side. What percent of the road is blockaded?
64
100
After failing to convince Brandon to put number theory problems in his Jeopardy, Ian decides that in his senior year he will make 128 number theory-themed Jeopardies everyday until the end of time. Unfortunately, Ian loses motivation and on the second day makes 64 jeopardies and 32 on the next day. On the 31st day, Ian only makes 0.000000009% of a Jeopardy. After an infinite amount of time, how many has he made?
256
100
If <B is 33 degrees, what is <A?
57
100
What's the unit digit of 3^139?
7
100
5 SECONDS TO ANSWER
13*8-7
97
200
After failing his math test, Brandon is desperate to bring his grade back up to an A. On his last 7 tests, Brandon has gotten a 98,97,98,99,100,94, and a 59 (sadly on the most recent test). What does Brandon need on his next test to get an A? (92.5 is an A)
95
200
Two different prime numbers between 4 and 18 are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained?
119
200
Using the math club favorite Stewart's formula! (b2m+c2n = amn + d2a)
Find d if c if 3, b is 4, a is 5, and m is 2.
d is sqrt (29/5)
200
At Newark Academy, 198 students voted on two issues in a school referendum with the following results: 149 voted in favor of the first issue and 119 voted in favor of the second issue. If there were exactly 9 students who voted against both issues, how many students voted in favor of both issues?
79
200
Is (13^8+9^12)>(12^9+8^13)
No
300
Everyday at school, Sophia climbs a flight of 6 stairs to practice her parkour skills. Sophia can take the stairs 1, 2, or 3 at a time. For example, Sophia could climb 3, then 1, then 2. In how many ways can Sophia climb the stairs?
24
300
An Aaron-metic sequence is a sequence in which each term after the first is obtained by adding a constant to the previous term. Each row and each column in this 5 by 5 array is an Aaron-metic sequence with five terms. What is the value of X?
31
300
Angle <ABC of triangle ABC is a right angle. The sides of ABC are the diameters of semicircles as shown. The area of the semicircle on line AB equals 8pi, and the arc of the semicircle on line AC has length 8.5pi. What is the radius of the semicircle on line BC?
7.5
300
For real numbers x and y, define x🥥y = (x +y)(x-y). What is 3🥥(4🥥5)?
-72
300
30 SECONDS TO ANSWER
Closest Team wins: How many numbers from 1-20 are factors of 362796054?
7
400
Brandon builds LEGO towers using identically shaped cubes of different colors. How many different towers with a height 8 cubes can the architect build with 2 red cubes, 3 blue cubes, and 4 green cubes? (One cube will be left out.)
1260
400
To prove number theory is the best field of math, Aaron makes his own amazing number theory problem that is definitely not an Aaron to solve: Let n be the least positive integer greater than 1000 for which gcd(63,n+120) = 21 and gcd(n+63,120) = 60
What is the sum of the digits of n?
18
400
What is the most useful formula: Stewart's Theorem?
(b2m+c2n = amn + d2a)
400
What is the sum of the prime factors of 2010?
77
400
YOU HAVE 60 SECONDS TO ANSWER THIS PROBLEM
After failing to get his last accounting job, Brandon's got another chance to make it big as a cow rancher. To get the job he's got to help his boss navigate the confusing web of cryptocurrency. If five fluxins equal 17 finches, 3 finches equal 11 flummoxes, 51 flummoxes equal 2 fiji dollars. How many fiji dollars is 21 fluxins worth?
154/15 fiji dollars
500
Julia has recently won 2 billion dollars by selling her company SmartPaperClips and Co. To choose the percent of money (between 0-1 and 0-100%) she would like to put into her savings account a fair coin is flipped. If it lands heads, then it is flipped again and the chosen number is 0 if the second flip is heads, and 1 if the second flip is tails. On the other hand, if the first coin flip is tails, then the number is chosen uniformly at random from the closed interval [0,1]. Two random numbers x and y are chosen independently in this manner. What is the probability that |x-y|>1/2?
7/16
500
Prove Ian's imposing, inspiring, innovative formula: If a is an integer, p is a prime number and a is not divisible by p, then a(p-1)mod p = 1...
Okay not really. But, find n if 1335+1105+845+275= n5
n is 144
500
In triangle ABC,<C = 90 and AB = 12. Squares ABXY and ACWZ are constructed outside of the triangle.The points X,Y,Z, and W lie on a circle. What is the perimeter of the triangle?
12 + 12sqrt(2)
500
Let P(x) be a polynomial with integer coefficients that satisfies P(23)= 10 and P(31) = 17. Given that P(n) = n+3 has two distinct integer solutions n1 and n2 find the product n1*n2.
713
500
You have two options for this question guess my (Brandon Recce)'s middle name. Hint: It begins with V
OR Do this problem in 120 SECONDS
All 20 diagonals are drawn in a regular octagon. At how many distinct points in the interior of the octagon (not on the boundary) do two or more diagonals intersect?
Answer to #1, Ask Brandon
Answer to #2, 49