Question Bank

When $9^{48}$ is divided by 10, what is the remainder?

If $n = (19)^{17} + (18)^{14}$, what is the units digit of $n$?

If $5^x - 5^{x-2} = (24)(5^y)$, what is $y$ in terms of $x$?

If $d = \frac{1}{2^{8} \times 5^{7}}$ is expressed as a terminating decimal, how many nonzero digits will $d$ have?

If Marco loses 9 kilograms, he will weigh three times as much as his brother. Together they now weigh 277 kilograms. What is Marco's present weight, in kilograms?

Last year a town council consisting of only Green and Liberal members had 18 more Green members than Liberal members. This year the council has the same number of members as last year, but it has 5 fewer Green members than last year. If this year the number of Green members is $\frac{5}{8}$ of the number of council members, how many members does the council have this year?

The cost $C$, in dollars, to remove $p$ percent of a certain contaminant from a reservoir is estimated by using the formula $C = \frac{20,000p}{100 - p}$. According to this estimate, how much more would it cost to remove 98 percent of the contaminant from the reservoir than it would cost to remove 75 percent of the contaminant?

At her regular hourly rate, Mira had estimated the labour cost of a repair job as $180, and she was paid that amount. However, the job took 6 hours longer than she had estimated and, consequently, she earned $5 per hour less than her regular hourly rate. What was the time Mira had estimated for the job, in hours?

If $[x]$ denotes the least integer greater than or equal to $x$ and $\left[\frac{x}{4}\right] = 0$, which of the following could be the value of $x$?

If $1 < a < b < c$, which of the following has the greatest value?

A furniture dealer bought a cabinet for $360 and then set the selling price equal to the purchase price plus a markup that was 40 percent of the selling price. If the dealer sold the cabinet at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the cabinet?

The present ratio of players to coaches at a sports academy is 20 to 1. If the number of players were to increase by 88 and the number of coaches were to increase by 10, the ratio of players to coaches would then be 12 to 1. What is the present number of coaches?

After cycling to a trailhead, Dana plans to walk east along a canal path, turn around, and return to the trailhead by the same path. After walking 8.5 kilometres east, she decides to walk for only 88 minutes more. If Dana walks at a constant rate of 8 minutes per kilometre, how many kilometres farther east can she walk and still be able to return to the trailhead in 88 minutes?

Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of $x$ units of Product R in 7 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of $3x$ units of Product R in 6 days?

Rafael is 2 centimetres shorter than Amira, and Bianca is 5 centimetres taller than Rafael. If Bianca's height is 158 centimetres, what is the median height, in centimetres, of these three people?

For the positive numbers $n$, $n+1$, $n+2$, $n+8$, $n+9$, the mean is how much greater than the median?

In a carton of 14 light bulbs, a total of 2 are faulty. If a customer buys 2 bulbs selected at random from the carton, what is the probability that neither bulb will be faulty?

There are 7 pens in a drawer, of which 2 are fountain pens and 5 are ballpoints. How many possible selections of 3 pens from this drawer include at least one fountain pen?

A state produced 840 million pounds of milk in 2011 and 2.2 billion pounds in 2016. Approximately how many more million gallons of milk did it produce in 2016 than in 2011? (1 billion = $10^9$, and 1 gallon of milk weighs 8.6 pounds.)

Let $M = \frac{1}{101} + \frac{1}{102} + \frac{1}{103} + \cdots + \frac{1}{200}$, the sum of the reciprocals of every integer from 101 through 200. Which of the following must be true?