Question Bank

When the positive integer $n$ is divided by 9, the remainder is 5. What is the remainder when $3n + 8$ is divided by 9?

When the digits of a two-digit positive integer are reversed, the resulting integer is 36 greater than the original integer. What is the positive difference between the two digits?

If $27^{x} = 9^{\,x+4}$, what is the value of $x$?

If the integer $N = 3^{43} \times 7^{22}$, what is the units digit of $N$?

A salesperson earns a commission of 10 percent on the first $800 of weekly sales and 25 percent on all sales beyond $800. In a week her total commission was $455. What were her total sales for the week, in dollars?

A profit of $70{,}000 is shared by a firm's 3 partners and 8 employees. If each partner receives twice as much as each employee, how much does each partner receive?

For which value of $k$ does the equation $x^2 - 6x + k = 0$ have exactly one real solution?

A farmer will use 40 meters of fencing to enclose a rectangular pen on three sides, with an existing wall forming the fourth side. What is the greatest possible area of the pen, in square meters? (Note: The area of a rectangle equals its length multiplied by its width.)

How many integers $x$ satisfy both $-5 < 2x - 1 \le 7$ and $x \ne 1$?

How many integers $n$ satisfy $|n - 3| < 5$?

After a price was reduced by 25 percent and the reduced price was then lowered by an additional 10 percent, the final price was $81. What was the original price?

At a company, 60 percent of the employees are engineers and the rest are designers. If 30 percent of the engineers and 65 percent of the designers work remotely, what percent of all the employees work remotely?

A cyclist rides 36 kilometers from home to a town at an average speed of 18 kilometers per hour and immediately rides back along the same route at an average speed of 12 kilometers per hour. What is the cyclist's average speed, in kilometers per hour, for the round trip?

Working together at their constant rates, pipes A and B fill an empty tank in 6 hours. Working alone, pipe A fills the same tank in 10 hours. How many hours does pipe B alone take to fill the tank?

Over her first $n$ games of a season, a bowler averaged 140 points per game. After scoring 188 points in her next game, her average for the season rose to 146 points per game. What is the value of $n$?

The five numbers 4, 9, 10, 13, and $x$ have an average (arithmetic mean) equal to their median. Which of the following could be the value of $x$?

A box contains 30 batteries, exactly 6 of which are defective. Two are drawn at random without replacement. What is the probability that BOTH are defective?

Using each letter of LEVEL exactly once, how many distinct 5-letter arrangements can be formed in which the two L's are NOT next to each other?

In a theater, the first row has 14 seats, and each subsequent row has 3 more seats than the row in front of it. If the theater has 25 rows, how many seats are in the last row?

A bacteria culture starts with 50 cells and triples in size every 4 hours. After how many hours will the culture first exceed 10,000 cells?