# CMM Assessment Problems

### Charlotte Math Meetup Assessment Problems

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