Q. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer paid $70, how many miles did they drive?
A.
100 miles
B.
150 miles
C.
200 miles
D.
250 miles
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Solution
Let the number of miles driven be m. The total cost is given by: 50 + 0.20m = 70. Solving for m gives 0.20m = 20, so m = 100 miles.
Correct Answer:
A
— 100 miles
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Q. A farmer has chickens and cows. If there are 20 heads and 56 legs in total, how many cows are there?
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Solution
Let the number of chickens be c and the number of cows be k. We have the equations: c + k = 20 and 2c + 4k = 56. Solving these gives k = 10.
Correct Answer:
B
— 10
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Q. A number is increased by 25% and then decreased by 20%. If the final result is 96, what was the original number?
A.
80
B.
90
C.
100
D.
110
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Solution
Let the original number be x. The equation is: x * 1.25 * 0.8 = 96. Simplifying gives x = 96 / 1 = 120, so the original number is 100.
Correct Answer:
C
— 100
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Q. A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 cm, what is the width?
A.
4 cm
B.
6 cm
C.
8 cm
D.
10 cm
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Solution
Let the width be w cm. Then the length is 3w cm. The perimeter is given by: 2(length + width) = 48. Thus, 2(3w + w) = 48. Simplifying gives 8w = 48, so w = 6 cm.
Correct Answer:
B
— 6 cm
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Q. A school has a total of 300 students. If the ratio of boys to girls is 3:2, how many girls are there?
A.
120
B.
150
C.
180
D.
200
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Solution
Let the number of boys be 3x and the number of girls be 2x. Then, 3x + 2x = 300. This gives 5x = 300, so x = 60. Therefore, the number of girls is 2x = 120.
Correct Answer:
B
— 150
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Q. A train travels 60 km at a certain speed and returns at 90 km/h. If the total time for the journey is 4 hours, what is the speed of the train on the way to the destination?
A.
30 km/h
B.
40 km/h
C.
50 km/h
D.
60 km/h
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Solution
Let the speed of the train on the way to the destination be x km/h. The time taken to travel to the destination is 60/x hours and the time taken to return is 60/90 hours. The total time is given by: 60/x + 60/90 = 4. Solving for x gives x = 40 km/h.
Correct Answer:
B
— 40 km/h
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Q. If 5 times a number decreased by 3 equals 12, what is the number?
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Solution
Let the number be x. The equation is: 5x - 3 = 12. Adding 3 to both sides gives 5x = 15, so x = 3.
Correct Answer:
C
— 4
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Q. If 5x + 2y = 20 and y = 2, what is the value of x?
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Solution
Substitute y = 2 into 5x + 2(2) = 20. This gives 5x + 4 = 20. Subtract 4: 5x = 16. Divide by 5: x = 16/5 = 3.2.
Correct Answer:
C
— 4
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Q. If a rectangle has a length of (x + 2) and a width of (x - 3), what is the area?
A.
x^2 - x - 6
B.
x^2 + x - 6
C.
x^2 - 6
D.
x^2 + 6
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Solution
Area = Length × Width = (x + 2)(x - 3) = x^2 - 3x + 2x - 6 = x^2 - x - 6.
Correct Answer:
A
— x^2 - x - 6
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Q. If a rectangle has a length of 3x and a width of 2x, what is its area?
A.
5x^2
B.
6x^2
C.
7x^2
D.
8x^2
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Solution
Area = Length × Width = 3x × 2x = 6x^2.
Correct Answer:
B
— 6x^2
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Q. Solve for x: 2x - 4 = 10.
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Solution
2x - 4 = 10. Add 4 to both sides: 2x = 14. Divide by 2: x = 7.
Correct Answer:
B
— 5
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Q. Solve for y: 2y - 4 = 10.
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Solution
2y - 4 = 10. Add 4 to both sides: 2y = 14. Divide by 2: y = 7.
Correct Answer:
B
— 7
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Q. The sum of two numbers is 20, and their difference is 4. What are the two numbers?
A.
10 and 10
B.
12 and 8
C.
14 and 6
D.
16 and 4
Show solution
Solution
Let the two numbers be x and y. We have the equations: x + y = 20 and x - y = 4. Adding these gives 2x = 24, so x = 12. Substituting back gives y = 8.
Correct Answer:
B
— 12 and 8
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Q. What is the solution to the equation 2(x - 3) = 4?
A.
x = 1
B.
x = 2
C.
x = 4
D.
x = 7
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Solution
2(x - 3) = 4. Divide by 2: x - 3 = 2. Add 3: x = 5.
Correct Answer:
D
— x = 7
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Q. What is the solution to the inequality 2x + 5 > 15?
A.
x < 5
B.
x > 5
C.
x < 10
D.
x > 10
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Solution
2x + 5 > 15. Subtract 5 from both sides: 2x > 10. Divide by 2: x > 5.
Correct Answer:
B
— x > 5
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Q. What is the solution to the inequality 5x - 3 < 12?
A.
x < 3
B.
x < 2
C.
x > 3
D.
x > 2
Show solution
Solution
5x - 3 < 12. Add 3 to both sides: 5x < 15. Divide by 5: x < 3.
Correct Answer:
A
— x < 3
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