- John buys 100 shares of stock at $100 per share. The price goes up by 10% and he sells 50 shares. Then, prices drop by 10% and he sells his remaining 50 shares. How much did he get for the last 50?
- $5,000
- $5,500
- $4,900
- $5,050
- $4,950
The stock first increased by 10%. 10% of $100 is $10, so the stock rose to $110 per share. Then, the price decreased by 10% of $110, which is $11, so that the sale price was \($110-$11 = $99\) per share, and the sale price for 50 shares was \($5099 \times 99 = $4,950\).
- A teacher has three hours to grade all the papers submitted by the 35 students in her class. She gets through the first five papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time?
- 10%
- 15%
- 20%
- 25%
- 30%
She has been working at the rate of 10 papers per hour (5 papers in 0.5 hours). She has 30 papers remaining and must grade them in the 2.5 hours that she has left, which corresponds to a rate of 12 papers per hour. This is \(12 \div 10=1.2\), which means the teacher needs to grade 120% of what she was previously doing, or work 20% faster.
- A satellite in a circular orbit rotates around the Earth every 120 minutes. If the Earth’s radius is 4,000 miles at sea level, and the satellite’s orbit is 400 miles above sea level, approximately what distance does the satellite travel in 40 minutes?
- 1,400 miles
- 9,210 miles
- 4,400 miles
- 4,120 miles
- 8,000 miles
The orbit radius is Earth’s radius plus 400 miles:
\(R=4,000+400=4,400\text{ miles}\)
The circumference of the circular orbit is therefore:
\(C=2\pi R=2\pi(4,400)=8,800\pi\) \(\approx27,632\text{ miles (using }\pi=3.14\text{)}\)
Since 40 minutes is one-third of the satellite’s 120-minute orbital time, it traverses 9,210 miles:
\(\dfrac{1}{3}\times 27,632 \approx 9,210.7 \text{ miles }\)\(\approx 9,210 \text{ miles}\)
- What is the next-highest prime number after 67?
- 68
- 69
- 71
- 73
- 76
Prime numbers are those that are only evenly divisible by 1 and themselves.
- How many 3-inch segments can a 4.5-yard line be divided into?
- 15
- 45
- 54
- 64
- 84
There are 12 inches in a foot and 3 feet in a yard. Four and a half yards is equal to 162 inches. To determine the number of 3-inch segments, divide 162 by 3.
\(162 \div 3 = 54\)
- Kelly, Brayden, and Fisher, working together at the same rate, can complete a job in 3\(\frac{1}{3}\) days. Working at the same rate, how much of the job could Brayden and Fisher do in one day?
- \(\tfrac{1}{5}\)
- \(\tfrac{1}{4}\)
- \(\tfrac{1}{3}\)
- \(\tfrac{1}{9}\)
- \(\tfrac{1}{8}\)
Three people finish one job in \(3\tfrac{1}{3}=\tfrac{10}{3}\) days, so their combined rate is \(\frac{1\text{ job}}{\tfrac{10}{3}\text{ days}}=\frac{3}{10}\) job per day.
They all work at the same rate, so one person’s rate is \(\text{rate}_{1}=\dfrac{\tfrac{3}{10}}{3}=\tfrac{1}{10}\) jobs per day.
Brayden and Fisher together work at twice one person’s rate:
\(\text{rate}_{2}=2\left(\tfrac{1}{10}\right)=\tfrac{1}{5}\) job per day.
So, in one day, Brayden and Fisher can complete \(\tfrac{1}{5}\) (20%) of the job.
- A box of laundry detergent contains 16.5 oz of product. What is the maximum number of loads that can be washed if each load requires a minimum of \(\tfrac{3}{4}\) oz of detergent?
- 10
- 50
- 22
- 18
- 16.5
To determine the maximum number of loads, we’ll need to take the total amount of detergent and divide it by the amount of detergent per load.
\( \text{Loads}=\frac{16.5}{\tfrac34} =\frac{\tfrac{33}{2}}{\tfrac{3}{4}} =\tfrac{33}{2}\cdot\tfrac{4}{3} =\tfrac{66}{3} =22 \)
Each load needs at least \(\tfrac{3}{4}\) oz, so you can’t start another load without that amount. The division comes out exact, so the maximum is 22 loads.
- A blouse normally sells for $138, but is on sale for 25% off. What is the cost of the blouse?
- $67
- $103.50
- $34.50
- $113
- $125
If an item is 25% off, it’s equivalent to \(25 \times \tfrac{$138}{100}=$34.50\), so the sale price becomes \($138-$34.50=$103.50\).
- A crane raises one end of a 3,300 lb steel beam. The other end rests upon the ground. If the crane supports 30% of the beam’s weight, how many pounds does it support?
- 330
- 990
- 700
- 1,100
- 2,310
The crane supports 30% of the beam’s total weight. To find how many pounds the crane supports, we multiply 0.30 (30%) by the beam’s total weight.
\( \text{Pounds supported} = 0.30 \times 3,300\) \(= 990\)
So, the crane supports 990 pounds.
- A taxi service charges $5.50 for the first \(\tfrac{1}{5}\)th of a mile, $1.50 for each additional \(\tfrac{1}{5}\)th of a mile, and 20 cents per minute of waiting time. Joan took a cab from her place to a flower shop eight miles away, where she bought a bouquet, then another 3.6 miles to her mother’s place. The driver had to wait nine minutes while she bought the bouquet. What was the fare?
- $20
- $120.20
- $92.80
- $91
- $90
The total trip was \(8+3.6=11.6\) miles. The first \(\tfrac{1}{5}\) mile (0.2 miles) costs $5.50, so there are \(11.6-0.2=11.4\) miles left to bill at $1.50 per fifth-mile.
That leftover distance is \(\frac{11.4}{0.2}=57\) fifth-miles, which costs \(57\times1.50=\$85.50\). Thus, the mileage portion is \(5.50+85.50=\$91.00\).
The driver also waited 9 minutes at $0.20 per minute, adding \(9\times0.20=\$1.80\). Therefore, the fare is \(91.00+1.80=\$92.80\).