CML Advanced Practice – Part 2
Questions 51-100 | Grades 4-6
Continuation of Advanced CML Practice – This section covers age problems, distance-rate-time, probability, counting, and more advanced topics.
⏰ Word Problems – Age & Time
51) A clock gains 3 minutes every hour. If it is set correctly at 9:00 AM, what time will the clock show when the actual time is 3:00 PM?
52) Maria is 4 years older than her brother. In 5 years, the sum of their ages will be 32. How old is Maria now?
53) A father is 3 times as old as his son. In 12 years, he will be twice as old as his son. How old is the father now?
54) The sum of Tom’s age and Jerry’s age is 45. Tom is 5 years older than Jerry. How old is Jerry?
🚗 Word Problems – Distance, Rate & Time
55) A car travels 240 miles in 4 hours. If it continues at the same speed, how many miles will it travel in 7 hours?
56) Two trains leave the same station at the same time, traveling in opposite directions. One travels at 60 mph and the other at 80 mph. After how many hours will they be 420 miles apart?
57) A pool can be filled by pipe A in 6 hours and by pipe B in 9 hours. How long would it take to fill the pool if both pipes are used together? (Express as a decimal)
58) A cyclist rides uphill at 8 mph and downhill at 12 mph. If the total distance is 40 miles and the ride takes 4 hours, how many miles were uphill?
🧪 Word Problems – Mixtures & Ratios
59) A recipe calls for 3 cups of flour for every 2 cups of sugar. If you use 9 cups of flour, how many cups of sugar do you need?
60) A solution is 30% acid. How many liters of pure acid must be added to 20 liters of this solution to make it 50% acid?
61) The ratio of boys to girls in a class is 3:5. If there are 24 students total, how many are girls?
62) A 40-liter mixture of alcohol and water is 25% alcohol. How much water must be added to make it 20% alcohol?
🔢 Digit & Number Problems
63) The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 27 more than the original. What is the original number?
64) How many three-digit positive integers have digits that sum to 6?
65) A two-digit number is 4 times the sum of its digits. If the tens digit is 3 more than the units digit, what is the number?
66) How many two-digit numbers have the property that the sum of their digits is 9?
67) What is the largest three-digit number that is divisible by 17?
🎲 Counting & Combinations
68) How many ways can you arrange the letters in the word MATH?
69) A committee of 3 people must be chosen from a group of 8 people. How many different committees can be formed?
70) In how many ways can 5 people sit in a row if two particular people must sit next to each other?
71) How many different 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition?
72) How many ways can you choose 2 books from a shelf of 10 books?
73) In how many ways can the letters A, B, C, D be arranged in a circle?
🎯 Probability
74) If you roll two dice, what is the probability of getting a sum of 7? (Express as a fraction in lowest terms)
75) A bag contains 5 red balls and 3 blue balls. What is the probability of drawing 2 red balls in succession without replacement?
76) What is the probability of flipping a coin 3 times and getting exactly 2 heads?
77) A card is drawn from a standard deck. What is the probability it is either a heart or a face card?
➗ Divisibility & Multiples
78) How many two-digit numbers are divisible by both 3 and 4?
79) How many positive three-digit integers are multiples of 13?
80) What is the smallest positive integer that is divisible by 2, 3, 4, 5, and 6?
81) How many integers between 1 and 200 are divisible by 7 but not by 3?
📐 Pythagorean Theorem & Right Triangles
82) A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?
83) A ladder 20 feet long leans against a wall. If the bottom of the ladder is 12 feet from the wall, how high up the wall does the ladder reach?
84) What is the distance between points (2, 5) and (8, 13)?
85) A rectangle has dimensions 6 by 8. What is the length of its diagonal?
📊 Average, Median & Mode
86) The arithmetic mean of three numbers is 24. If two of the numbers are 18 and 22, what is the third number?
87) Find the median of the set: {12, 15, 9, 23, 18, 11, 20}
88) The average of 6 numbers is 15. If one number is removed, the average becomes 14. What was the removed number?
89) What is the mode of the data set: {3, 7, 5, 3, 9, 5, 3, 2}?
🧩 Miscellaneous Challenge Problems
90) How many ways can you make change for 50 cents using only nickels, dimes, and quarters?
91) A clock shows 3:00. What is the angle between the hour and minute hands?
92) How many squares (of any size) are on a standard 8×8 chessboard?
93) If today is Wednesday, what day of the week will it be 100 days from now?
94) How many diagonals does a regular octagon have?
95) What is the sum of all interior angles of a hexagon?
96) A number becomes 50 when rounded to the nearest ten. What is the smallest possible value of this number?
97) How many different positive divisors does 2⁴ × 3³ × 5² have?
98) If f(x) = 2x + 3, what is f(f(5))?
99) A square and a regular hexagon have the same perimeter. If the square has side length 12, what is the side length of the hexagon?
100) What is the smallest positive integer that leaves a remainder of 2 when divided by 3, 4, and 5?
📖 Answer Key (Questions 51-100)
Check your answers below. Show all work for full understanding!
51) 3:18 PM
52) 15
53) 36
54) 20
55) 420
56) 3
57) 3.6
58) 16
59) 6
60) 8
61) 15
62) 10
63) 47
64) 28
65) 36
66) 9
67) 986
68) 24
69) 56
70) 48
71) 120
72) 45
73) 6
74) 1/6
75) 5/14
76) 3/8
77) 11/26
78) 8
79) 69
80) 60
81) 19
82) 15
83) 16
84) 10
85) 10
86) 32
87) 15
88) 20
89) 3
90) 10
91) 90°
92) 204
93) Friday
94) 20
95) 720°
96) 49.5
97) 60
98) 29
99) 8
100) 62
🎉 Congratulations on completing all 100 advanced CML problems!
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