2007 iTest Problems
Contents
[hide]- 1 Multiple Choice Section
- 1.1 Problem 1
- 1.2 Problem 2
- 1.3 Problem 3
- 1.4 Problem 4
- 1.5 Problem 5
- 1.6 Problem 6
- 1.7 Problem 7
- 1.8 Problem 8
- 1.9 Problem 9
- 1.10 Problem 10
- 1.11 Problem 11
- 1.12 Problem 12
- 1.13 Problem 13
- 1.14 Problem 14
- 1.15 Problem 15
- 1.16 Problem 16
- 1.17 Problem 17
- 1.18 Problem 18
- 1.19 Problem 19
- 1.20 Problem 20
- 1.21 Problem 21
- 1.22 Problem 22
- 1.23 Problem 23
- 1.24 Problem 24
- 1.25 Problem 25
- 2 Short Answer Section
- 2.1 Problem 26
- 2.2 Problem 27
- 2.3 Problem 28
- 2.4 Problem 29
- 2.5 Problem 30
- 2.6 Problem 31
- 2.7 Problem 32
- 2.8 Problem 33
- 2.9 Problem 34
- 2.10 Problem 35
- 2.11 Problem 36
- 2.12 Problem 37
- 2.13 Problem 38
- 2.14 Problem 39
- 2.15 Problem 40
- 2.16 Problem 41
- 2.17 Problem 42
- 2.18 Problem 43
- 2.19 Problem 44
- 2.20 Problem 45
- 2.21 Problem 46
- 2.22 Problem 47
- 2.23 Problem 48
- 2.24 Problem 49
- 2.25 Problem 50
- 3 Ultimate Question
Multiple Choice Section
Problem 1
A twin prime pair is a set of two primes such that is greater than . What is the arithmetic mean of the two primes in the smallest twin prime pair?
Problem 2
Find if and satisfy and .
Problem 3
An abundant number is a natural number that's proper divisors sum is greater than the number. Which one of the following natural numbers is an abundant number?
Problem 4
Star flips a quarter four times. Find the probability that the quarter lands heads exactly twice.
Problem 5
Compute the sum of all twenty-one terms of the geometric series .
Problem 6
Find the units digit of the sum
Problem 7
An equilateral triangle with side length has the same area as a square with side length . Find .
Problem 8
Joe is right at the middle of a train tunnel and he realizes that a train is coming. The train travels at a speed of 50 miles per hour, and Joe can run at a speed of 10 miles per hour. Joe hears the train whistle when the train is a half mile from the point where it will enter the tunnel. At that point in time, Joe can run toward the train and just exit the tunnel as the train meets him. Instead, Joe runs away from the train when he hears the whistle. How many seconds does he have to spare (before the train is upon him) when he gets to the tunnel entrance?
Problem 9
Suppose that and are positive integers such that , the geometric mean of and is greater than , and the arithmetic mean of and is less than . How many pairs satisfy these conditions?
Problem 10
My grandparents are Arthur, Bertha, Christoph, and Dolores. My oldest grandparent is only years older than my youngest grandparent. Each grandfather is two years older than his wife. If Bertha is younger than Dolores, what is the difference between Bertha’s age and the mean of my grandparents’ ages?