1. Train Chase
A train leaves the station at 2:00 PM traveling at 50 mph. Another train leaves the same station at 3:00 PM, traveling at 75 mph. At what time will the second train catch up to the first train?
2. Dividing Apples
Max has 84 apples. He gives ⅓ of them to his friend and then gives ½ of the remaining apples to his sister. How many apples does Max have left?
3. Tricky Multiplication
What is the product of the smallest two-digit even number and the largest single-digit odd number?
4. Book Reading Puzzle
Maria reads 12 pages a day on weekdays and 20 pages a day on weekends. If her book has 260 pages and she starts reading on a Monday, how many days will it take her to finish the book?
5. Age Riddle
Two years ago, Lisa was 4 times as old as her brother Tim. Now, Lisa is 12 years old. How old is Tim now?
6. Odd Sum
What is the sum of all odd numbers between 50 and 100, inclusive?
7. Sharing Money
John, Maria, and Sarah have $240 altogether. John has twice as much money as Maria, and Sarah has $40 more than Maria. How much money does each person have?
8. Rectangle Puzzle
The perimeter of a rectangle is 36 cm. If its length is 3 times its width, what are the dimensions of the rectangle?
9. Cutting Rope
You have a 90-foot-long rope that you need to cut into equal pieces of 7 feet each. How many full pieces can you cut, and how much rope will remain?
10. Chocolate Bars
Emily has 5 chocolate bars. She eats 1/3 of the first bar, 1/4 of the second, 1/2 of the third, and 1/6 of the fourth. How much chocolate does she have left after eating from the four bars?
11. Fraction Puzzle
Tim has ⅓ of a pizza, Maria has ⅖ of another pizza, and John has ⅚ of a third pizza. Who has the most pizza, and by how much?
12. Time and Distance
A bus leaves the station at 10:15 AM, traveling at 40 miles per hour. Another bus leaves at 11:00 AM, traveling at 50 miles per hour. How long will it take for the second bus to catch up to the first bus?
13. Triangle Puzzle
The perimeter of a triangle is 36 cm. One side is twice as long as the shortest side, and the third side is 3 cm longer than the shortest side. What are the lengths of the three sides?
14. Marble Sharing
Liam has twice as many marbles as Jake. Jake has 8 more marbles than Sara. Altogether, they have 62 marbles. How many marbles does each person have?
15. Age Difference
Jack is 12 years older than his brother. If in 6 years, Jack will be twice as old as his brother, how old is each person now?
16. Pizza Sharing
Five friends share 4 pizzas equally. How much pizza does each friend get, and how much pizza is left?
17. Sum of Multiples
What is the sum of all multiples of 3 between 1 and 100?
18. Distance Problem
Sarah runs 12 kilometers in the morning and 8 kilometers in the afternoon every day. How many days will it take her to run a total of 100 kilometers?
19. Water Tank
A water tank can be filled in 6 hours when using one pipe. Another pipe can fill the tank in 4 hours. How long will it take to fill the tank if both pipes are used together?
20. Speed Puzzle
A car travels 180 miles in 3 hours. Another car travels 240 miles in 4 hours. Which car is traveling faster, and by how much?
21. Candy Problem
Julie has 64 candies. She gives 1/4 of them to her friend and eats 1/3 of the remaining candies. How many candies does she have left?
22. Clock Hands
At what time between 5:00 and 6:00 will the minute hand and hour hand of a clock overlap?
23. Sharing Cookies
A baker made 240 cookies. He sold ⅝ of the cookies and gave ⅓ of the remaining cookies to a school. How many cookies does the baker have left?
24. Classroom Puzzle
In a class of 30 students, ⅔ of them play soccer, and ⅘ of those who play soccer also play basketball. How many students play both soccer and basketball?
25. Money Puzzle
Tom has 5 times as much money as Jane, and together they have $84. How much money does each person have?
26. Filling Jars
You have 8 small jars that hold 4 candies each and 6 large jars that hold 8 candies each. How many candies are there in total?
27. Cutting Cake
A cake is cut into 16 equal pieces. If 7/8 of the cake is eaten, how many pieces remain?
28. Frog Jumps
A frog can jump 3 feet forward and 2 feet backward. If the frog jumps 10 times, how far forward does it go?
29. Fraction Puzzle
If 2/5 of a number is 24, what is the number?
30. Sharing Pizza
Mike has 5/8 of a pizza, and his friend Jake has 3/4 of another pizza. Who has more pizza, and by how much?
31. Train Speed
A train travels 120 miles in 2 hours. If it continues at the same speed, how far will it travel in 5 hours?
32. Perimeter Puzzle
The perimeter of a rectangle is 56 cm. If its length is 4 cm longer than its width, what are the dimensions of the rectangle?
33. Tricky Sequence
What is the next number in the sequence: 2, 7, 14, 23, 34, __?
34. Sharing Candy
Two friends have a total of 72 candies. If one friend has 16 more candies than the other, how many candies does each friend have?
35. Dividing Chocolate
A chocolate bar has 24 pieces. If ⅓ of the chocolate is given to a friend, and ⅛ is eaten by you, how many pieces remain?
36. Travel Puzzle
A car travels at 60 miles per hour for 3 hours. It then slows down and travels at 40 miles per hour for 2 hours. What is the total distance traveled?
37. Sum of Even Numbers
What is the sum of all even numbers between 50 and 100, inclusive?
38. Cutting Ribbon
A ribbon that is 72 inches long is cut into pieces that are each 7 inches long. How many full pieces can be cut, and how much ribbon will remain?
39. Age Puzzle
Two years ago, Ella was twice as old as her brother. Now, Ella is 14 years old. How old is her brother?
40. Pizza Fractions
You have 3/5 of a pizza, and your friend has 7/10 of another pizza. Who has more pizza, and by how much?
41. Tricky Multiplication
What is the product of the largest two-digit number and the smallest two-digit number?
42. Dividing Money
A total of $360 is divided among 3 friends. If the first friend gets twice as much as the second, and the third gets half as much as the second, how much money does each friend get?
43. Train Timing
Two trains leave the same station, one traveling east at 50 mph and the other traveling west at 60 mph. How far apart will they be after 4 hours?
44. Sharing Cookies
A baker made 300 cookies. He sold ¾ of the cookies and gave ⅓ of the remaining cookies to a friend. How many cookies does the baker have left?
45. Ball Puzzle
A ball bounces to ⅓ of its original height every time it hits the ground. If the ball is dropped from a height of 27 feet, how high will it bounce after 3 bounces?
46. Classroom Problem
In a class of 25 students, ⅗ are girls. If ⅖ of the girls play soccer, how many girls in the class play soccer?
47. Number Puzzle
What is the smallest number that is divisible by both 8 and 12?
48. Tricky Fractions
If ⅖ of a number is 30, what is ⅘ of the same number?
49. Percentage Problem with Subjects:
At Oakdale School, all 5th graders must take either art or music, but not both. If 55% of the 5th graders take art and 40% of those taking music also take French, what percent of the 5th graders are taking music but not French?
50. Cube Slicing Problem:
If a large cube is sliced into smaller equal-sized cubes, which of the following quantities could be the number of smaller cubes?
a) 8
b) 27
c) 64
d) 125
e) 150
51. Distance Ratio Problem:
In a line segment, point J is three times as far from point L as N is from J. J is also nine times as far from point C as N is from C. If N to C measures 180 feet, what is the distance from J to L?
52. Fraction Reduction Problem:
Let (X) = X + 5 if X is even, and (X) = X – 2 if X is odd. Find the value of (8) – (11) in simplest form.
Line Segment and Midpoint Problem:
Points P, Q, R, and S lie on a straight line, though not necessarily in that order. Point P is the midpoint of QR. If QR = 18 inches, RS = 6 inches, and QS = 14 inches, what is the length of PS?
Overlapping Rectangles Area Problem:
Two rectangles, one with dimensions 10 by 15 and the other with dimensions 8 by 12, overlap to form a square-shaped intersection. What is the area of the intersecting square if each side is 5 units long?
Triangle Perimeter Problem:
In an equilateral triangle, points A, B, and C are on the sides so that A is on side PQ, B is on side QR, and C is on side RP. If PA = QB = RC = 4 units and each side of the triangle is 12 units, find the perimeter of triangle ABC.
Sequence Value
A sequence starts at 3, and each next term is 2 more than the previous term. What is the 7th term in the sequence?
The sequence Sn is defined such that S1 = 3 and S(n+1) = 2S_n – 1. Find S_4.
Algebraic Expression Problem:
Simplify the expression (3^2 + 3) × (3^4 – 3^2).
Fraction Addition
What is the sum of 3/4 and 2/5 in simplest form?
Volume of a Cube
Find the volume of a cube with a side length of 7 units.
Average Speed
If a car travels 60 miles in 1.5 hours, what is its average speed in miles per hour?
Ratio Problem
In a classroom, the ratio of boys to girls is 3:4. If there are 12 boys, how many girls are there?
Mistake in Calculation
Jamie made a mistake in a math problem. He multiplied by 4 instead of adding 4. Jamie’s answer was 32. What is the correct answer?
Distance Between Numbers
There are two numbers that are three times as far from 10 as they are from 4. What are those two numbers?
Adjusted Price with Increased Quantity
A bag of apples originally contained 10 apples and was selling for $5.00. The store added more apples to the bag but kept the price the same. Now, the price of a dozen apples (12 apples) is $4.00. How many apples were added to the bag?
Ladder Rungs Movement
Sam started on the 5th rung of a ladder. He went up 4 rungs, then down 6 rungs, and then up 5 rungs. He is now on the 2nd rung from the top. How many rungs does the ladder have?
Age Difference Problem
Sarah is 5 times as old as Liam. Liam is 20 years younger than Sarah. How old is Sarah?
Playing Time for Team Members
A soccer team has 12 players, but only 8 can play on the field at once. The season has 24 games. The coach decides that each player will play the same number of complete games. How many complete games will each player play?
Fraction Problem
In the expression 3×a−b2×c\frac{3 \times a – b}{2 \times c}2×c3×a−b, if a=5a = 5a=5, b=7b = 7b=7, and c=4c = 4c=4, what is the result in simplest form?
Mistake in Calculation
Sally made a mistake in a math problem. She divided by 5 instead of multiplying by 5. Sally’s answer was 4. What is the correct answer?
Distance Between Numbers
Find two numbers that are twice as far from 9 as they are from 5. What are those two numbers?
Price Adjustment with Added Quantity
A bag containing 8 lemons was priced at $4.00. The manager added some more lemons to the bag without changing the price. Now, the price per lemon has dropped to $0.50. How many lemons are in the bag now?
Ladder Positioning Problem
Leo started on the 4th rung of a ladder. He climbed up 5 rungs, then down 3 rungs, and then up 4 rungs. He is now on the 3rd rung from the top of the ladder. How many rungs does the ladder have?
Age Comparison Problem
Emma is twice as old as John. John is 15 years younger than Emma. How old is John?
Team Rotation for Equal Playtime
A volleyball team has 10 players, but only 6 can play at a time. The season has 30 games. The coach wants each player to play the same number of complete games. How many complete games will each player play?
Pattern and Sequence Prediction
What is the next number in the sequence: 5, 10, 15, 20, __?
Correcting a Mistaken Operation
Tom accidentally subtracted 8 instead of adding 8 in a problem. His answer was 12. What should the correct answer be?
Comparing Ages
Michael is 4 times as old as Amy. Amy is 18 years younger than Michael. How old is Michael?
Rung Movements on a Ladder
Jack was on the 6th rung of a ladder. He went up 3 rungs, down 2 rungs, and then up 5 rungs. He is now 2 rungs from the top. How many rungs does the ladder have?
Calculating New Total After Price Change
A bundle of 15 bananas was sold for $3.00. After adding some bananas, the total price remained the same, but now the price per banana is $0.20. How many bananas are in the new bundle?
Equivalent Fraction Conversion
In the expression (2a+3b)/4c, if a=3 b=6 and c=5, what is the simplified result?
Birthday Problem
Lucas’s birthday was on Tuesday, March 3. His sister’s birthday is exactly 6 weeks later, also on a Tuesday in April. There are 31 days in March. What is the date of his sister’s birthday?
Girls and Boys in a Class Test
The average score of girls in a test is 72%, and the average score of boys is 66%. The overall average score of the class is 69%. What percentage of the class are boys?
Class Composition in a Test
In a test, the average score of girls is 88%, and the average score of boys is 80%. The average score of the whole class is 83%. What percentage of the class are girls?
Weight Distribution in a Group
The average weight of boys in a group is 65 kg, and the average weight of girls is 55 kg. The average weight of the whole group is 60 kg. What percentage of the group are boys?
Team Scores in a Quiz Competition
In a quiz competition, Team A has an average score of 90 points, and Team B has an average score of 75 points. The overall average score of all participants is 82.5 points. What percentage of the participants are from Team A?
Player Heights in a Sports Meet
The average height of male players in a team is 180 cm, and the average height of female players is 165 cm. The average height of all players is 172.5 cm. What percentage of the players are male?
Basketball Tournament
In a basketball tournament, Team A scored 3 points more than Team B. Team B scored 5 points more than Team C. Altogether, the three teams scored a total of 150 points. How many points did Team B score?
Evan was born on his grandfather’s 60th birthday. In how many years will Evan’s grandfather be 4 times as old as Evan will be then?
Buses leaving City A and going to City B pass a bus traveling at the same speed coming in the opposite direction every 10 minutes. How many buses arrive in City B from City A in one hour?
The difference between two positive numbers is 56. One of the numbers is 34. Find the quotient if the other number is divided by 7.