习题

1. John invested $10,000 in a stock that increased by 20% in value. He then sold the stock and invested the proceeds in a different stock that decreased by 10% in value. What was the final value of John's investment?

A. $11,000
B. $11,200
C. $10,800
D. $10,920
E. $10,980

Solution:

The first stock increased by 20%, so its value became 1.2 * $10,000 = $12,000.

The second stock decreased by 10%, so its value became 0.9 * $12,000 = $10,800.

Therefore, the final value of John's investment was $10,800.

Answer: C

2. A company produces 500 units of a product at a cost of $10 per unit. The company sells 400 units at a price of $15 per unit and the remaining units at a price of $8 per unit. What is the company's profit?

A. $1,000
B. $2,000
C. $3,000
D. $4,000
E. $5,000

Solution:

The total cost of producing 500 units is 500 * $10 = $5,000.

The revenue from selling 400 units at $15 per unit is 400 * $15 = $6,000.

The revenue from selling the remaining 100 units at $8 per unit is 100 * $8 = $800.

The total revenue is $6,000 + $800 = $6,800.

The profit is the revenue minus the cost, which is $6,800 - $5,000 = $1,800.

Answer: None of the above (the closest option is A, but it is not correct)

3. A train travels from A to B at a speed of 60 mph and returns from B to A at a speed of 40 mph. What is the average speed of the train for the round trip?

A. 45 mph
B. 48 mph
C. 50 mph
D. 52 mph
E. 55 mph

Solution:

Let's use the formula for average speed:

average speed = total distance / total time

Let's assume that the distance from A to B is d.

The time it takes to travel from A to B at 60 mph is d / 60.

The time it takes to travel from B to A at 40 mph is d / 40.

The total distance for the round trip is 2d.

The total time for the round trip is d / 60 + d / 40 = (2d / 120) + (3d / 120) = 5d / 120 = d / 24.

Therefore, the average speed is (2d) / (d / 24) = 48 mph.

Answer: B

4. A rectangle has a perimeter of 30 meters and an area of 36 square meters. What are the dimensions of the rectangle?

A. 3 meters by 15 meters
B. 4 meters by 9 meters
C. 5 meters by 6 meters
D. 6 meters by 6 meters
E. 8 meters by 4 meters

Solution:

Let's use the formulas for the perimeter and area of a rectangle:

perimeter = 2(length + width)

area = length * width

We have two equations and two unknowns (length and width), so we can solve for them.

From the first equation, we have:

length + width = 15

From the second equation, we have:

length * width = 36

We can use substitution to solve for one of the variables.

For example, we can solve for length in the first equation:

length = 15 - width

Then we can substitute this expression for length in the second equation:

(15 - width) * width = 36

Expanding and simplifying:

15w - w^2 = 36

Rearranging:

w^2 - 15w + 36 = 0

Factoring:

(w - 3)(w - 12) = 0

Therefore, the solutions are w = 3 and w = 12.

If w = 3, then length = 15 - 3 = 12.

If w = 12, then length = 15 - 12 = 3.

Therefore, the dimensions of the rectangle are 3 meters by 12 meters or 12 meters by 3 meters.

Answer: None of the above (the closest option is A, but it is not correct)