1. What is the least common multiple (LCM) of 6 and 8?
The LCM of 6 and 8 is 24.

2. Solve the equation: 3x + 4 = 16.
To solve the equation, subtract 4 from both sides: 3x = 12. Then divide both sides by 3: x = 4.

3. If two numbers are in the ratio 3:5 and their sum is 64, what are the numbers?
Let the two numbers be 3x and 5x. Their sum is 64, so 3x + 5x = 64. Combining like terms, we get 8x = 64. Dividing by 8, x = 8. Therefore, the numbers are 3(8) = 24 and 5(8) = 40.

4. What is the square root of 100?
The square root of 100 is 10.

5. A car travels 240 miles in 4 hours. What is its average speed?
Average speed is calculated by dividing the total distance by the total time. In this case, the average speed of the car is 240 miles/4 hours = 60 miles per hour.

6. If a man sells a product for $80, which is a 20% profit on the cost price, what is the cost price of the product?
Let the cost price of the product be x. Since the selling price is 120% (100% + 20%) of the cost price, we can form the equation: x * 120% = $80. Solving for x, we find that x = $80 / 120% = $66.67.

7. Convert 3/8 into a decimal.
To convert a fraction to a decimal, divide the numerator by the denominator. In this case, 3 divided by 8 equals 0.375.

8. If 5 workers can complete a job in 10 days, how many workers are needed to complete the same job in 5 days?
The amount of work done is inversely proportional to the number of workers. Therefore, the product of the number of workers and the time required to complete the job is constant. In this case, 5 workers * 10 days = x workers * 5 days. Solving for x, we find that x = (5 workers * 10 days) / 5 days = 10 workers.

9. If a shirt originally cost $60 and is now on sale for 25% off, what is the sale price?
To find the sale price, multiply the original price by (100% – discount percentage). In this case, the sale price is $60 * (100% – 25%) = $60 * 75% = $45.

10. A rectangle has a length of 8 inches and a diagonal of 10 inches. What is the width of the rectangle?
Using the Pythagorean theorem, we can find the width of the rectangle. Let the width be x. The equation becomes: x^2 + 8^2 = 10^2. Solving for x, we get x^2 + 64 = 100, x^2 = 36, and x = 6. Therefore, the width of the rectangle is 6 inches.

11. Simplify the expression: (2^3 × 3^2) ÷ (2^2 × 3^3).
Using the laws of exponents, we can simplify the expression. (2^3 × 3^2) ÷ (2^2 × 3^3) = (8 × 9) ÷ (4 × 27) = 72 ÷ 108 = 2/3.

12. If 1/8 of a number is 10, what is the number?
Let the number be x. We can form the equation: (1/8)x = 10. Solving for x, we find that x = 10 * 8 = 80.

13. If the sum of two numbers is 52 and their difference is 12, what are the numbers?
Let the two numbers be x and y. We can form the equations: x + y = 52 and x – y = 12. Adding the two equations together, we get 2x = 64. Dividing by 2, x = 32. Substituting x into one of the equations, we find y = 20. Therefore, the numbers are 32 and 20.

14. A tub can be filled in 6 hours. It takes 4 hours to empty the tub. How long will it take to fill the tub if both the filling and emptying processes are done simultaneously?
The rate of filling is 1/6 of the tub per hour, while the rate of emptying is 1/4 of the tub per hour. The net rate when both processes are done simultaneously is 1/6 – 1/4 = 1/12 of the tub per hour. Therefore, it will take 12 hours to fill the tub when both processes are done simultaneously.

15. What is 25% of 80?
To find a percentage of a number, multiply the number by the percentage as a decimal. Therefore, 25% of 80 is 0.25 * 80 = 20.

16. If a quarter of a number is 15, what is the number?
Let the number be x. We can form the equation: (1/4)x = 15. Solving for x, we find that x = 15 * 4 = 60.

17. A recipe calls for 2 cups of flour and makes 12 cookies. How many cups of flour are needed to make 30 cookies?
The ratio of cups of flour to cookies is 2:12. To find the number of cups of flour needed for 30 cookies, we can set up the proportion: 2 cups / 12 cookies = x cups / 30 cookies. Cross-multiplying, we get 12x = 2 * 30, and solving for x gives x = (2 * 30) / 12 = 5 cups.

18. If a train travels at a speed of 60 miles per hour, how many miles will it travel in 2.5 hours?
To find the distance traveled, multiply the speed by the time. Therefore, the train will travel 60 miles per hour * 2.5 hours = 150 miles.

19. Solve the equation: 2(x + 4) = 18.
To solve the equation, distribute the 2 to the terms inside the parentheses: 2x + 8 = 18. Then subtract 8 from both sides: 2x = 10. Finally, divide both sides by 2: x = 5.

20. A store is having a 30% off sale. If an item originally costs $50, what is the sale price?
To find the sale price, multiply the original price by (100% – discount percentage). In this case, the sale price is $50 * (100% – 30%) = $50 * 70% = $35.

1. What is the difference between simple interest and compound interest?
Simple interest is calculated only on the principal amount, whereas compound interest is calculated on both the principal amount and accumulated interest.

2. Explain the concept of permutation and combination.
Permutation is the arrangement of objects in a specific order, while combination is the selection of objects without considering their order.

3. How do you calculate the probability of an event?
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

4. What is a logarithm?
A logarithm is the power to which a base must be raised to produce a given number. It is the inverse operation of exponentiation.

5. What is the difference between a parameter and a statistic?
A parameter is a numerical measurement that characterizes a population, whereas a statistic is a numerical measurement that characterizes a sample.

6. What is the concept of standard deviation?
Standard deviation is a measure of the dispersion or variability of a set of values. It indicates how much the values deviate from the average.

7. Explain the concept of correlation and covariance.
Correlation measures the strength and direction of the relationship between two variables, while covariance measures their joint variability.

8. How do you solve a quadratic equation?
A quadratic equation can be solved using the quadratic formula or by factoring the equation into two binomial terms.

9. What is the concept of vectors?
Vectors are quantities that have both magnitude and direction. They are often used in mathematics and physics to represent physical quantities.

10. How do you find the nth term of an arithmetic sequence?
The nth term of an arithmetic sequence can be found using the formula: nth term = first term + (n-1) * common difference.

11. Explain the concept of limits in calculus.
Limits are used to define the behavior of a function as the input approaches a certain value. It determines the value of the function at that particular point.

12. What is the concept of integration in calculus?
Integration is the reverse process of differentiation. It calculates the area under a curve by summing infinitely many small rectangles.

13. How do you solve a system of linear equations?
A system of linear equations can be solved by substitution, elimination, or matrix methods.

14. Explain the concept of factorials.
Factorials are the products of all positive integers less than or equal to a given positive integer. It is denoted by the exclamation mark (!).

15. What is the concept of exponential growth and decay?
Exponential growth is a mathematical term that describes the rapid increase of a quantity over time. Exponential decay, on the other hand, describes the rapid decrease of a quantity over time.

16. How do you find the derivative of a function?
The derivative of a function measures how the function changes as the input changes. It can be found using the rules of differentiation.

17. What is the concept of rational numbers?
Rational numbers are numbers that can be expressed as a ratio of two integers. They can be written in fraction or decimal form.

18. Explain the concept of matrices and determinants.
Matrices are rectangular arrays of numbers, and determinants are a numerical value associated with a matrix. They are used to solve systems of linear equations.

19. How do you calculate the area and perimeter of a triangle?
The area of a triangle can be calculated using the formula 0.5 * base * height, and the perimeter can be found by adding the lengths of all three sides.

20. What is the concept of logarithmic differentiation?
Logarithmic differentiation is a method used to differentiate functions that are products, quotients, or powers by taking the natural logarithm of both sides of the equation and then differentiating.