Continental Math League (CML) Practice Questions
Grades 4, 5 & 6
150 Free CML Practice Problems – Prepare for Continental Math League competitions with challenging multi-step problems designed to match actual CML contest difficulty. Perfect for students in grades 4, 5, and 6!
📚 What’s Included:
- ✅ 150 CML-style practice questions covering all topics
- ✅ Multi-step problem solving to build critical thinking
- ✅ Downloadable PDF for offline practice
- ✅ Answer spaces for student work
- ✅ Organized by difficulty – Basic to Advanced
📝 Section 1: Foundational CML Questions (1–40)
Start with these fundamental problems to build confidence. These questions cover basic CML topics including arithmetic, algebra, geometry, and word problems.
1) Emma made a mistake in a division problem. She added 8 instead of dividing by 8. Emma’s answer was 35. The correct answer to the problem is _____.
2) A fruit seller had 300 apples. He sold 125 apples on Monday, 75 apples on Tuesday, and the rest equally on Wednesday and Thursday. How many apples did he sell on Wednesday?
3) The sum of three consecutive integers is 51. What is the smallest of these integers?
4) A rectangle has a length that is twice its width. If the perimeter of the rectangle is 48 cm, what is the length of the rectangle?
5) If 5x = 20, what is the value of x + 3?
6) A car travels 60 miles in 1 hour. At this rate, how far will it travel in 4.5 hours?
7) The product of two consecutive integers is 240. What is the sum of these integers?
8) A triangle has sides of lengths 7 cm, 24 cm, and x cm. If the perimeter of the triangle is 50 cm, what is the value of x?
9) If the area of a square is 64 cm², what is the length of one side of the square?
10) A book costs $15. If you buy 3 books and pay with a $50 bill, how much change will you receive?
11) What is the value of 8^2 – 4^3?
12) A cylinder has a radius of 3 cm and a height of 10 cm. What is the volume of the cylinder? (Use π = 3.14)
13) If a shirt costs $20 and is on sale for 25% off, what is the sale price of the shirt?
14) A train leaves a station and travels at a speed of 80 km/h. How far will the train travel in 2.5 hours?
15) The sum of the angles in a triangle is 180 degrees. If one angle is 90 degrees and another is 45 degrees, what is the third angle?
16) A recipe calls for 2 cups of flour for every 3 cups of sugar. If you have 8 cups of sugar, how many cups of flour do you need?
17) If 7y – 4 = 24, what is the value of y?
18) A pool is filled with water at a rate of 15 gallons per minute. How many gallons will be needed to fill the pool in 2 hours?
19) The length of a rectangle is 3 times its width. If the perimeter of the rectangle is 48 cm, what is the width?
20) If 5a = 15, what is the value of 2a + 3?
21) A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If you drive 150 miles, what is the total cost?
22) The area of a triangle is 24 cm². If the base of the triangle is 8 cm, what is the height?
23) A box contains 3 red balls, 5 blue balls, and 2 green balls. If one ball is picked at random, what is the probability that it is blue?
24) If the time is 3:15 PM now, what will be the time 2 hours and 45 minutes from now?
25) A store sells pencils for $0.50 each and erasers for $0.75 each. If you buy 10 pencils and 4 erasers, how much do you spend?
26) The difference between a number and 15 is 7. What is the number?
27) A recipe requires 3/4 cup of sugar. If you want to make half the recipe, how much sugar do you need?
28) If 9x = 63, what is the value of x – 2?
29) A train travels 90 miles in 1.5 hours. What is its average speed in miles per hour?
30) The sum of the angles in a quadrilateral is 360 degrees. If three angles are 90 degrees, 85 degrees, and 75 degrees, what is the fourth angle?
31) A box has a length of 10 cm, a width of 5 cm, and a height of 2 cm. What is the volume of the box?
32) If the cost of 5 meters of ribbon is $15, what is the cost of 2 meters of ribbon?
33) A car’s value depreciates by 15% each year. If the car is worth $20,000 now, what will it be worth in one year?
34) The length of a rectangle is 4 cm more than its width. If the perimeter of the rectangle is 28 cm, what is the length?
35) If 3x + 5 = 20, what is the value of x?
36) A cyclist travels 12 miles in 1 hour. At this rate, how far will the cyclist travel in 3.5 hours?
37) The product of three consecutive integers is 210. What is the middle integer?
38) A box contains 2 red balls, 3 blue balls, and 5 green balls. If one ball is picked at random, what is the probability that it is not blue?
39) If the time is 6:45 AM now, what will be the time 3 hours and 15 minutes from now?
40) A store sells notebooks for $1.25 each and folders for $0.75 each. If you buy 8 notebooks and 6 folders, how much do you spend?
🎯 Section 2: Advanced CML Challenge Questions (41–150)
Challenge yourself with these advanced multi-step problems! These questions require deeper mathematical reasoning and are designed to prepare you for the most difficult CML contest problems.
41) If 3 × 4^n = 768, what is the value of n?
42) The sum of five consecutive integers is 105. What is the product of the largest and smallest of these integers?
43) A number is increased by 25% and then decreased by 20%. The result is 100. What was the original number?
44) What is the smallest positive integer that leaves a remainder of 3 when divided by 7, a remainder of 5 when divided by 9, and a remainder of 4 when divided by 11?
45) The product of three consecutive integers is 210. What is the sum of these three integers?
46) If 2^a × 3^b = 72, where a and b are positive integers, what is the sum of all possible values of a + b?
47) What is the sum of all two-digit multiples of 9?
48) Maya has 3 dimes, 7 nickels, and 12 pennies. In how many different ways can she make 43 cents using at least one of each type of coin?
49) If 7k + 3 is divisible by 10, what is the sum of all possible values of the last digit of k?
50) How many integers between 100 and 999 have exactly two identical digits?
Set B: Fractions, Decimals, and Percentages
51) Greg spent 1/4 of his money on lunch and 2/5 of the remainder on a book. If he has $21 left, how much did he start with?
52) A container is 2/3 full of water. When 12 gallons of water are added, it becomes 5/6 full. What is the capacity of the container in gallons?
53) What fraction of 3/4 is 9/16?
54) If 40% of a number is 64, what is 75% of the same number?
55) A recipe calls for 3/4 cup of flour for every 2/3 cup of sugar. How many cups of flour are needed for 10 cups of sugar?
56) When a decimal is rounded to the nearest tenth, the result is 7.4. What is the smallest possible value of this decimal?
57) In a class, 3/8 of the students are boys and the rest are girls. If 1/4 of the boys and 1/3 of the girls wear glasses, what fraction of the class wears glasses?
58) The price of a computer was reduced by 20% during a sale. After the sale, the price was increased by 20%. The final price was $576. What was the original price before the sale?
59) What is the value of 34 + 23 × 38?
60) A tank is 1/4 full of water. After 45 gallons are added, the tank is 3/5 full. What is the capacity of the tank in gallons?
Set C: Geometry and Measurement
61) A rectangular garden has a perimeter of 42 feet and an area of 108 square feet. What are the dimensions of the garden?
62) A cylindrical can has a radius of 3 inches and a height of 8 inches. How many cubic inches of water will the can hold? (Use π = 3.14)
63)
In the figure, square ABCD has side length 8 cm. Point P is on BC
such that BP = 3 cm. What is the area of triangle APD in square centimeters?
such that BP = 3 cm. What is the area of triangle APD in square centimeters?
64) A 12 ft by 16 ft rectangular floor is to be covered with square tiles that are each 8 inches on a side. How many tiles are needed?
65) The circumference of a circle is 24π inches. What is its area in square inches?
66) The volume of a cube is 125 cubic centimeters. What is its surface area in square centimeters?
67)
The figure below is formed by joining five identical squares. If each square has an area of 16 square centimeters, what is the perimeter of the entire figure?
68) The length of a rectangle is 4 cm more than its width. If the area of the rectangle is 96 square cm, what is its perimeter?
69) A triangular prism has equilateral triangular bases with sides of 6 cm. If the height of the prism is 10 cm, what is its volume in cubic centimeters? (Use √3 = 1.73)
70) The length of a rectangular field is 3 times its width. If 270 meters of fencing is needed to enclose the field, what is the length of the field in meters?
Set D: Ratios, Proportions, and Rates
71) At a school, the ratio of boys to girls is 4:5. If there are 36 students in the class, how many more girls than boys are there?
72) Lisa can paint a fence in 5 hours. Tom can paint the same fence in 3 hours. How long would it take them to paint the fence working together?
73) A car travels 210 miles in 3.5 hours. At this rate, how far will it travel in 5 hours?
74) In a bag of marbles, the ratio of red to blue to green marbles is 3:5:7. If there are 45 red marbles, how many marbles are in the bag?
75) If 9 workers can build a wall in 12 days, how many days would it take 6 workers to build the same wall, assuming all workers work at the same rate?
76) Two pipes can fill a tank in 12 minutes and 15 minutes respectively. A third pipe can empty the tank in 10 minutes. How many minutes will it take to fill the tank if all three pipes are open?
77) A boat travels 24 miles downstream in 2 hours and 24 miles upstream in 3 hours. What is the speed of the boat in still water?
78) At a party, the ratio of adults to children was 5:3. After 10 adults left, the ratio became 1:1. How many children were at the party?
79) A recipe calls for 3 cups of flour and 2 cups of sugar to make 36 cookies. How many cups of sugar are needed to make 60 cookies?
80) If 7 shirts cost $84, how much would 11 shirts cost at the same price per shirt?
Set E: Patterns and Sequences
81) What is the next number in the sequence: 3, 7, 15, 31, 63, ___?
82) In a pattern, each term after the first is found by multiplying the previous term by 2 and then subtracting 5. If the 3rd term is 25, what is the 1st term?
83) What is the 10th term in the sequence 5, 8, 11, 14, …?
84) The first five terms of a sequence are 2, 6, 18, 54, 162. What is the product of the 6th and 7th terms?
85) The sum of the first n terms of a sequence is n². What is the 7th term of this sequence?
86) Olivia makes $10 on the first day of her job. Each day after that, she makes $5 more than the day before. How much will she make on the 12th day?
87) A pattern starts with 3 dots. Each step after that adds 4 more dots than were added in the previous step. How many dots will be in the 8th step?
88) What is the sum of the first 20 terms in the sequence 3, 6, 9, 12, …?
89) In the sequence 1, 3, 7, 15, 31, …, each term after the first is found by multiplying the previous term by what number and then adding what number?
90) The first few terms of a sequence are 1, 8, 27, 64, 125. What is the value of the 9th term minus the 8th term?
Set F: Logic and Problem Solving
91) Alan, Beth, and Carlos each have some marbles. Alan has twice as many as Beth, and Carlos has 5 more than Alan. If they have 37 marbles in total, how many marbles does Beth have?
92) A father is 30 years older than his son. In 6 years, the father will be 3 times as old as his son. How old is the son now?
93) Three friends ordered a large pizza for $18. Sam paid 1/3 of the cost, Tim paid $2 more than Sam, and Jordan paid the rest. How much did Jordan pay?
94)
How many different triangles can be formed by connecting three of the points shown in the figure?
95) A bakery sells chocolate chip cookies for $1.25 each and oatmeal cookies for $1.50 each. If Maya buys 20 cookies for $27, how many chocolate chip cookies did she buy?
96) Five friends are seated in a row. Amy must sit next to Bob. Charlie must sit next to David. Eddie must sit at one end. How many different seating arrangements are possible?
97) In a bag, there are 3 red marbles, 5 blue marbles, and 7 green marbles. If two marbles are drawn without replacement, what is the probability that both are the same color? Express your answer as a fraction in lowest terms.
98) Sophia has 8 different books she wants to arrange on a shelf. If she always keeps her 3 math books together and her 2 science books together, how many different arrangements are possible?
99) Julia, Kai, and Leo run a race. If Julia is twice as likely to win as Kai, and Kai is three times as likely to win as Leo, what is the probability that Julia wins the race?
100) A combination lock has 3 dials, each with the digits 0 through 9. How many different combinations are possible if no digit can be used more than once?
Set G: Number Theory and Algebraic Thinking
101) What is the least common multiple of 18, 24, and 30?
102) If x + y = 10 and xy = 21, what is the value of x² + y²?
103) A positive number is 12 less than its square. What is the sum of all possible values of this number?
104) When a two-digit number is multiplied by the sum of its digits, the result is 144. What is this two-digit number?
105) Find the largest three-digit number that is divisible by 7, 11, and 13.
106) If a * b = a + b + ab, what is the value of 3 * 4?
107) What is the greatest common factor of 2^5 × 3^3 × 5 and 2^3 × 3^2 × 5^2?
108) How many three-digit numbers are divisible by both 4 and 5?
109) If a + 2b = 19 and 3a – b = 8, what is the value of a × b?
110) The sum of the squares of three consecutive even integers is 116. What is the middle integer?
Additional Challenge Questions
111) Noah has 8 coins in his pocket that total $1.70. If he only has nickels, dimes, and quarters, how many of each coin does he have?
112) A rectangular sheet of paper has length 18 inches and width 12 inches. The four corners are cut out, each being a square with sides of length 3 inches. What is the area of the resulting shape?
113) The average (arithmetic mean) of five consecutive integers is n. What is the average of the next five consecutive integers?
114) What is the remainder when 7^100 is divided by 10?
115) The hour and minute hands of a clock form a right angle at what time between 3:00 and 4:00?
116)
A square piece of paper is folded along a diagonal. What fraction of the original area is now exposed?
117) If x² + y² = 25 and xy = 12, what is the value of (x + y)²?
118) On a farm, the ratio of chickens to cows to pigs is 5:2:3. If there are 150 legs in total, how many animals are on the farm?
119) Two trains leave stations 350 miles apart and travel toward each other. One train travels at 60 mph and the other at 50 mph. After how many hours will they meet?
120) What is the last digit of 3^87?
Set H: Advanced Critical Thinking Problems
121) The Chess Club and Drama Club at Lincoln School are selling tickets for their performances. Chess Club tickets cost $5 for adults and $3 for students. Drama Club tickets cost $7 for adults and $4 for students. The Chess Club sold twice as many adult tickets as student tickets and collected $330. The Drama Club sold the same number of adult tickets as the Chess Club but half as many student tickets, and collected $385. How many student tickets did the Chess Club sell?
122)
A regular hexagon ABCDEF is divided into 6 triangles by drawing lines from the center O to each vertex.
Point P is on side AB such that AP = 1/3 × AB. Points Q and R are on sides BC and CD, respectively,
such that BQ = 1/3 × BC and CR = 1/3 × CD. If the area of the hexagon is 24 square units,
what is the area of triangle PQR in square units?
Point P is on side AB such that AP = 1/3 × AB. Points Q and R are on sides BC and CD, respectively,
such that BQ = 1/3 × BC and CR = 1/3 × CD. If the area of the hexagon is 24 square units,
what is the area of triangle PQR in square units?
123) Ms. Chen’s class is putting together a time capsule. There are 24 students in the class, and each student contributes exactly one item. The ratio of books to toys to photographs is 2:3:5. If there are 3 more toys than books, and twice as many photographs as toys, how many books are in the time capsule?
124) The Martinez family is driving to their vacation destination. They travel for 2 hours at 45 mph, then increase their speed to 60 mph for the next 3 hours. Due to traffic, they have to decrease their speed to 40 mph for the final hour of their trip. If they traveled a total of 290 miles, how many miles did they drive at 60 mph?
125)
A pizza with a diameter of 12 inches is cut into 8 equal slices. Carla eats 3 slices, and Ben eats 2 slices.
If a slice costs $1.50, what is the price per square inch of the pizza? (Use π = 3.14)
If a slice costs $1.50, what is the price per square inch of the pizza? (Use π = 3.14)
126) Farmer Johnson has cows, pigs, and chickens on his farm. He counts 35 heads and 94 legs in total. If he has 3 more pigs than cows, how many of each animal does he have?
127)
Five points A, B, C, D, and E lie on a circle. Angles ABC, BCD, and CDE are all equal to 60°.
What is the measure of angle DEA in degrees?
What is the measure of angle DEA in degrees?
128) A store offers a 20% discount on all items. During a special sale, customers receive an additional 15% off the discounted price. Jeremy purchases a bike that normally costs $240. The sales tax rate is 7%, which is applied after all discounts. How much does Jeremy pay for the bike, including tax?
129) For a school fundraiser, students sell boxes of chocolate bars. Small boxes contain 8 bars and cost $12. Large boxes contain 15 bars and cost $20. The fundraising committee wants to purchase a total of 300 chocolate bars while spending exactly $430. How many large boxes should they buy?
130)
Three identical squares with side length 6 cm are arranged as shown in the figure below.
What is the perimeter of the entire shape in centimeters?
What is the perimeter of the entire shape in centimeters?
Set I: Integrated Mathematical Reasoning
131) A museum charges $8 per adult ticket and $5 per child ticket. One day, they sold 240 tickets and collected $1,655. After analyzing their visitor data, the museum found that the number of adult visitors was 25 more than twice the number of children who came in groups. If 40 children came individually (not in groups), how many children came in groups?
132) Julian has a collection of cubes with edge lengths of 1 cm, 2 cm, and 3 cm. He has twice as many 2 cm cubes as 1 cm cubes, and the number of 3 cm cubes is half the number of 1 cm cubes. If the total volume of all the cubes is 180 cubic cm, how many cubes does Julian have in total?
133)
A square with side length 12 cm is cut into four identical L-shaped pieces as shown.
What is the perimeter of each L-shaped piece in centimeters?
What is the perimeter of each L-shaped piece in centimeters?
134) The Science Club is conducting an experiment with a mixture containing water, salt, and sugar. The initial mixture is 80% water, 15% salt, and 5% sugar by weight. They add 30 grams of salt and 10 grams of sugar to the mixture, which increases the total weight by 20%. After this addition, salt makes up 25% of the new mixture by weight. What was the weight of the initial mixture in grams?
135) Three friends decide to invest in a small business. Alex invests $4000, Bianca invests $6000, and Carlos invests $5000. They agree that 40% of the profits will be shared equally, and the remaining 60% will be divided in proportion to the amount each person invested. If the business makes a profit of $9000, how much more money does Bianca receive than Alex?
136)
A rectangular tank has a base measuring 80 cm by 60 cm. It contains water to a depth of 30 cm.
A solid metal cube with edge length 20 cm is placed in the tank, causing the water level to rise.
By how many centimeters does the water level rise?
A solid metal cube with edge length 20 cm is placed in the tank, causing the water level to rise.
By how many centimeters does the water level rise?
137) A digital timer counts down from a starting number of seconds to zero. When the timer is at the 5-minute mark, Rita notices that 2/3 of the total time has already elapsed. When the timer reaches the 2-minute mark, Rita calculates that 5/6 of the total time has elapsed. How many minutes was the timer initially set for?
138)
A standard number cube (with faces numbered 1 through 6) is rolled three times.
The sum of the three numbers is 10.
If the first roll gave an even number and the second roll gave an odd number,
what is the probability that the third roll gave the number 3?
The sum of the three numbers is 10.
If the first roll gave an even number and the second roll gave an odd number,
what is the probability that the third roll gave the number 3?
139) A bookshelf contains 40 books arranged in a single row. The books are either fiction or non-fiction. There are 3 more fiction books than non-fiction books. No two non-fiction books are next to each other, and no more than two fiction books are adjacent to each other. How many possible arrangements of these books are there on the shelf?
140) A community garden is divided into square plots. Each plot is 4 meters by 4 meters. The garden is surrounded by a fence that forms a rectangle with dimensions 28 meters by 20 meters. The paths between plots and around the perimeter are 2 meters wide. How many complete 4×4 plots can fit in the garden?
Set J: Real-World Problem Solving
141) The water level in a reservoir decreases by 3 inches each week during a drought. After the water level drops to a certain point, water restrictions are imposed, and the weekly decrease slows to 2 inches per week. If the reservoir’s water level was initially 68 inches, and it took 27 weeks for the reservoir to become completely dry, after how many weeks were the water restrictions imposed?
142)
A baker is packaging cookies in rectangular boxes. Each cookie has a diameter of 2 inches and is 1/2 inch thick.
The box’s interior dimensions are 8 inches × 6 inches × 2 inches. The cookies must be packed in a single layer.
What is the maximum number of cookies that can fit in one box?
The box’s interior dimensions are 8 inches × 6 inches × 2 inches. The cookies must be packed in a single layer.
What is the maximum number of cookies that can fit in one box?
143) The Thompson family is comparing their electricity bills for the past year. In the winter months (December through February), they use an average of 1200 kilowatt-hours (kWh) per month. In the spring (March through May) and fall (September through November), they use 800 kWh per month. In the summer (June through August), they use 1500 kWh per month. If their electricity costs 12¢ per kWh for the first 800 kWh in a month and 15¢ per kWh for any additional usage, what is their total electricity cost for the year?
144)
A bicycle wheel has a diameter of 28 inches. The cyclist rides at a constant speed of 12 miles per hour.
How many revolutions does the wheel make in 10 minutes? (Use π = 3.14 and 1 mile = 5280 feet)
How many revolutions does the wheel make in 10 minutes? (Use π = 3.14 and 1 mile = 5280 feet)
145) A recycling center pays 5¢ for each aluminum can and 10¢ for each glass bottle. Sophia and Daniel collect recyclables together. Sophia collects twice as many cans as Daniel, but only half as many bottles. Together they collect 150 items and receive $10.50. How many bottles did Daniel collect?
146)
A rectangular swimming pool is 12 meters long and 8 meters wide. A walkway of uniform width
surrounds the pool. If the total area of the pool and walkway together is 198 square meters,
what is the width of the walkway in meters?
surrounds the pool. If the total area of the pool and walkway together is 198 square meters,
what is the width of the walkway in meters?
147) In a science experiment, a culture of bacteria doubles in size every 3 hours. If the culture initially contains 500 bacteria, how many bacteria will be present after 18 hours?
148)
A large pizza has a diameter of 16 inches and costs $20. A medium pizza has a diameter of 12 inches
and costs $15. A small pizza has a diameter of 8 inches and costs $10. Which size pizza has the best value
in terms of cost per square inch of pizza? (Use π = 3.14)
and costs $15. A small pizza has a diameter of 8 inches and costs $10. Which size pizza has the best value
in terms of cost per square inch of pizza? (Use π = 3.14)
149) A train departs from Station A at 9:15 AM traveling at 50 miles per hour. A second train leaves from Station B, which is 250 miles away, at 10:45 AM traveling toward Station A at 70 miles per hour. The first train stops for a 25-minute break at 11:00 AM, then continues at the same speed. At what time do the two trains meet?
150)
A toy company manufactures model cars with a scale of 1:24, meaning each model is 1/24 the size of the actual car.
If a real car is 15 feet long, 6 feet wide, and 5 feet tall, what is the volume of the model car in cubic inches?
(1 foot = 12 inches)
If a real car is 15 feet long, 6 feet wide, and 5 feet tall, what is the volume of the model car in cubic inches?
(1 foot = 12 inches)
🎓 Section 3: Progressive Practice by Grade Level (151–250)
Questions organized by grade level with increasing difficulty. Master each level before advancing!
� Grade 4 Level: Building Foundations (Questions 151-175)
Focus: Basic operations, simple fractions, introductory geometry, and word problems
151) If you multiply a number by 8 and then subtract 15, you get 57. What is the number?
152) A baker makes 48 cupcakes. She puts them into boxes of 6. If she sells 5 boxes, how many cupcakes does she have left?
153) What is the perimeter of a rectangle with a length of 12 cm and a width of 7 cm?
154) Tommy has $35. He buys 3 books for $8 each. How much money does he have left?
155) If 7 × N = 84, what is the value of N ÷ 2?
156) A square garden has a perimeter of 36 meters. What is the area of the garden?
157) What is the sum of all even numbers between 10 and 20, including both 10 and 20?
158) A movie starts at 2:45 PM and lasts for 1 hour and 35 minutes. What time does it end?
159) If 3/4 of a number is 36, what is the whole number?
160) A box contains 5 red marbles, 8 blue marbles, and 7 green marbles. What fraction of the marbles are blue?
161) What is 456 + 789 – 234?
162) A farmer has 72 eggs. He puts them into cartons that hold 12 eggs each. How many cartons does he need?
163) If the temperature is 68°F in the morning and rises by 15 degrees, then drops by 8 degrees in the evening, what is the evening temperature?
164) What is the next number in the pattern: 5, 10, 20, 40, _____?
165) A triangle has sides of length 9 cm, 12 cm, and 15 cm. What is its perimeter?
166) Lucy saves $5 each week. How many weeks will it take her to save $75?
167) What is 25 × 16?
168) A book has 240 pages. Jason reads 1/3 of the book on Monday and 1/4 of the book on Tuesday. How many pages has he read in total?
169) If 4 pencils cost $6, what is the cost of 10 pencils?
170) What is the area of a triangle with a base of 10 cm and a height of 8 cm?
171) A classroom has 28 students. If 3/7 of them are boys, how many girls are in the class?
172) What is 144 ÷ 12 + 8 × 3?
173) A rectangle has an area of 48 square meters and a width of 6 meters. What is its length?
174) If today is Wednesday, what day will it be 100 days from now?
175) A bakery sells cookies for $2 each and brownies for $3 each. If Maria buys 5 cookies and 4 brownies, how much does she spend?
🎯 Grade 5 Level: Intermediate Challenges (Questions 176-215)
Focus: Decimals, percentages, complex fractions, multi-step problems, and basic algebra
176) If 3x + 7 = 28, what is the value of 2x?
177) A shirt originally costs $45. If it’s on sale for 20% off, what is the sale price?
178) What is 3.5 × 2.4?
179) A car travels 180 miles in 3 hours. At this same speed, how far will it travel in 5 hours?
180) What is 2/3 + 3/4? (Express your answer as a mixed number in simplest form)
181) A rectangular prism has dimensions of 5 cm × 4 cm × 3 cm. What is its volume?
182) The average of five numbers is 24. If four of the numbers are 20, 25, 22, and 28, what is the fifth number?
183) A circle has a radius of 7 cm. What is its circumference? (Use π = 3.14)
184) If 5/8 of a class are girls and there are 15 girls, how many students are in the class?
185) What is 15% of 240?
186) A number is multiplied by 6, then 18 is added to the product. The result is 90. What is the number?
187) What is the least common multiple (LCM) of 12 and 18?
188) A store sells pens in packs of 8 and pencils in packs of 12. What is the smallest number of items you can buy to get an equal number of pens and pencils?
189) If 4/5 of a number is 64, what is 3/8 of that number?
190) A rectangular garden is 15 meters long and 8 meters wide. A path 2 meters wide runs around the outside of the garden. What is the area of the path?
191) What is 7.8 – 3.45 + 2.6?
192) The sum of three consecutive even numbers is 84. What is the largest of these numbers?
193) A train travels at 75 km/h for 2.5 hours, then at 90 km/h for 1.5 hours. What is the total distance traveled?
194) If a square has an area of 121 square centimeters, what is its perimeter?
195) What is the greatest common factor (GCF) of 48 and 72?
196) A recipe calls for 2 1/2 cups of flour. If you want to make 3 times the recipe, how many cups of flour do you need?
197) If 8 workers can complete a job in 12 days, how many days would it take 6 workers to complete the same job?
198) What is 40% of 80 plus 25% of 60?
199) A cylinder has a radius of 4 cm and a height of 10 cm. What is its volume? (Use π = 3.14)
200) The ratio of boys to girls in a school is 3:4. If there are 210 students in total, how many are boys?
201) What is 2.5² + 3.5² – 4²?
202) A store increases the price of an item by 25%, then decreases the new price by 20%. If the original price was $80, what is the final price?
203) How many diagonals does a hexagon have?
204) If the perimeter of an equilateral triangle is 45 cm, what is its area? (Use √3 ≈ 1.73)
205) A number is divided by 7, then 5 is subtracted. The result is 8. What is the number?
206) What is 3/5 of 2/3 of 150?
207) A baseball team won 60% of its games. If they won 18 games, how many games did they play in total?
208) What is the sum of all multiples of 7 between 10 and 70?
209) A rectangle has a length that is 4 cm more than twice its width. If the perimeter is 56 cm, what is the length?
210) If 12% of a number is 36, what is 35% of that number?
211) A bag contains 5 red, 7 blue, and 8 green marbles. If you draw 2 marbles at random without replacement, and both are blue, how many blue marbles remain in the bag?
212) What is the median of the following numbers: 12, 18, 15, 20, 14, 22, 16?
213) A square and a circle have the same perimeter/circumference of 40 cm. Which has the greater area, and by how much? (Use π = 3.14)
214) If 5^x = 125, what is the value of 3^x?
215) A water tank can be filled by pipe A in 6 hours and by pipe B in 8 hours. If both pipes are opened together, how long will it take to fill the tank?
🚀 Grade 6 Level: Advanced Problem Solving (Questions 216-250)
Focus: Ratios, proportions, negative numbers, coordinate geometry, and complex multi-step reasoning
216) If 2x – 5 = 3x + 7, what is the value of x?
217) A map uses a scale of 1:50,000. If two cities are 7.5 cm apart on the map, what is the actual distance between them in kilometers?
218) What is the value of (-3) × (-4) + (-5) × 2?
219) A store sells a product at a 30% markup. If the selling price is $65, what was the cost to the store?
220) What is the distance between points A(2, 3) and B(6, 6) on a coordinate plane?
221) The product of two consecutive odd integers is 195. What is the sum of these two integers?
222) A cone has a radius of 6 cm and a height of 8 cm. What is its volume? (Use π = 3.14)
223) If the ratio of a:b is 2:3 and the ratio of b:c is 4:5, what is the ratio of a:c?
224) What is |−8| + |5| − |−3|?
225) A triangle has angles in the ratio 2:3:4. What is the measure of the largest angle?
226) If 40% of x is equal to 60% of y, and y = 80, what is the value of x?
227) A number is increased by 25%, then decreased by 25%. What is the net percent change from the original number?
228) What is the surface area of a cube with edge length 5 cm?
229) The average of 6 numbers is 45. If one of the numbers is removed, the average becomes 42. What number was removed?
230) If 3^(2x) = 81, what is the value of 2^(x+1)?
231) A rectangular prism has a length of 10 cm, width of 6 cm, and height of 8 cm. What is its surface area?
232) Two numbers are in the ratio 5:7. If their sum is 132, what is the smaller number?
233) What is the value of x if (x/4) + 7 = (x/3) – 2?
234) A spherical ball has a radius of 9 cm. What is its volume? (Use π = 3.14)
235) If the temperature drops from 5°C to −12°C, by how many degrees did it drop?
236) A car’s value depreciates by 15% each year. If the car is worth $20,000 now, what will it be worth after 2 years?
237) What is the mode and range of the data set: 12, 15, 18, 12, 20, 15, 12, 25?
238) A right triangle has legs of length 9 cm and 12 cm. What is the length of its hypotenuse?
239) If 5 machines can produce 300 items in 6 hours, how many items can 8 machines produce in 9 hours?
240) What is the slope of a line passing through points (3, 5) and (7, 13)?
241) A mixture contains milk and water in the ratio 7:3. If there are 35 liters of milk, what is the total volume of the mixture?
242) If x² = 144 and x > 0, what is the value of (x + 3)(x – 5)?
243) A pentagon has three angles of 110° each. If the remaining two angles are equal, what is the measure of each?
244) What is 2^5 + 3^3 – 4^2?
245) A train travels from City A to City B at 60 km/h and returns at 80 km/h. What is its average speed for the entire round trip?
246) If the area of a trapezoid is 96 cm², the height is 8 cm, and one parallel side is 10 cm, what is the length of the other parallel side?
247) A box contains cards numbered 1 through 50. If a card is drawn at random, what is the probability that it shows a number that is both a multiple of 3 and a multiple of 4?
248) If (a + b)/2 = 15 and (a – b)/2 = 5, what is the value of a?
249) A rectangular solid has a volume of 360 cm³. If its length is 10 cm and its width is 6 cm, what is its total surface area?
250) In a school election, candidate A received 45% of the votes, candidate B received 35% of the votes, and candidate C received the remaining votes. If candidate C received 120 votes, how many students voted in total?
📊 Section 3 Summary: 100 Additional Practice Questions
🎯 Grade-by-Grade Progression:
- Questions 151-175 (Grade 4): Foundation building with basic operations, simple fractions, and introductory problem-solving
- Questions 176-215 (Grade 5): Intermediate challenges with decimals, percentages, ratios, and multi-step reasoning
- Questions 216-250 (Grade 6): Advanced topics including negative numbers, coordinate geometry, complex algebra, and sophisticated problem-solving
💡 Practice Strategy: Start with your grade level, then progress to more challenging problems. Mastering each level builds the foundation for success in CML competitions!
�📖 Answer Key & Solutions
Answers to these questions are available in the complete answer key document.
Note on Questions 121-150: These advanced questions are designed to develop critical thinking skills needed for CML competitions. They require multi-step solution processes, incorporate multiple mathematical concepts, and often involve real-world applications.
Note on Questions 151-250: These grade-specific questions provide progressive practice aligned with educational standards for grades 4-6. Each level builds upon previous knowledge while introducing new concepts at an appropriate pace.
🏆 CML Competition Success Tips
- Practice Regularly: Work through 5-10 problems daily to build consistency
- Time Yourself: CML contests are timed – practice under time pressure
- Show Your Work: Develop clear problem-solving strategies
- Review Mistakes: Learn from errors to avoid repeating them
- Master Fundamentals: Strong basic skills are essential for advanced problems
- Think Multi-Step: Break complex problems into manageable parts
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