Integer Division and Revenue Problems

The video covers four math problems: determining if n over k is an integer, finding how many numbers equal the arithmetic mean, solving an absolute value equation, and calculating revenue from ticket sales. Each problem is analyzed using given statements to determine sufficiency for solving the problem.

In problem 103, if n and k are both integers, which of the following statements is true?

• n divided by k is always an integer.

• n divided by k is never an integer.

• n divided by k is always a fraction.

• n divided by k may or may not be an integer.

In problem 103, what additional information is needed to determine if n divided by k is an integer?

• The value of n.

• The value of k.

• Whether n is greater than k.

• None of the given statements are sufficient.

In problem 104, if none of the six numbers is less than 75, what can be concluded?

• All numbers are greater than 75.

• The average is less than 75.

• All numbers are equal to 75.

• At least one number is less than 75.

In problem 104, if none of the six numbers is greater than 75, what is the conclusion?

• At least one number is greater than 75.

• The average is greater than 75.

• All numbers are less than 75.

• All numbers are equal to 75.

In problem 105, what does statement 1 imply about x, y, and z?

• x is always positive.

• z is equal to the sum of x and y.

• x is equal to y minus z.

• y is always greater than z.

In problem 105, what does statement 2 tell us about x?

• x is negative.

• x is zero.

• x is positive.

• x is greater than y.

In problem 106, what is the equation for total revenue if x is 50%?

• PR + 0.5F = Revenue

• 0.5PR + PF = Revenue

• 0.5P + F = Revenue

• P + 0.5F = Revenue

In problem 106, what additional information is needed to solve for total revenue?

• The number of reduced price tickets.

• The number of full price tickets.

• The total number of tickets sold.

• Either the number of reduced or full price tickets.

In problem 106, if full price tickets are sold for $20 each, what is the price of reduced tickets when x is 50%?

• $5

• $10

• $15

• $20

In problem 106, what is the total number of tickets sold?

• 200

• 300

• 400

• 500