The following 7 problems are from past assignments. They can be roughly used for assessment purpose. A student who can correctly answer at least 5 of these 7 problems may fit well into CMM Level M. A student who can correctly answer at least 3 of the 5 level E problems may fit well into CMM level E.
2nd Assignment (Due: 8:00pm ET, March 28, 2020)
Note: The answer to each problem should be a number. Please also report how many minutes it takes you to finish each problem. Do not rush.
1. (M) An integer is chosen at random from the set {41, 42, 43, ..., 67}. What's the probability that the chosen number is one more than a multiple or 4 or one more than a multiple of 5? (Please express the answer as a decimal number rounded to hundredth.)
2. (E) What's the total number of different ways that the blanks of "__ 3 __ 9" can be filled in so that the resulting four-digit number is a multiple of 33?
3. (E) In an up-and-down counting number, the digits increase to a maximum digit and then decrease. This maximum is not the first or last digit. (A few examples: 1247321 is an up-and-down counting number; 12477321 is not an up-and-down counting number; 13557321 is not an up-and-down counting number.) How many different 4-digit up-and-down numbers are there in which the maximum digit is 6 and at least one of the digits is a 3?
1st Assignment (Due: 8:00pm ET, March 23, 2020)
Note: The answer to each problem should be a number. Please also report how many minutes it takes you to finish each problem.
1. (E) Calculate 498 x 498 without using a calculator. (You may use a paper and pencil if you have to. Think about the fastest way to do it.)
2. (E) The whole numbers 3, 4, 5, 6, 12 and 13 are arranged, without repetition, in a horizontal row so that the sum of any two numbers in adjoining positions is a perfect square. Find the sum of the middle two numbers.
3. (E) Starting at the same time on opposite shores of a lake, two boats cross back and forth for 35 minutes without stopping. One boat needs 5 minutes to cross the lake. The other boat needs 7 minutes. What is the number of times during the 35 minutes that the faster boat passes the slower boat going in the same or opposite direction?
4. (M) Team A and Team B play a series of games until one of them has won two games. No game ends in a tie. In any single game, the probability that Team A win is 70%. What is the probability that they play exactly 2 games?
Key
Assignment 1
0.41
7
65
Assignment 2
248004
25
7
0.58