CFAT Problem Solving 1 — Questions and Answers
Question 1: A lamp's watt rating is 60. After 10 hours of operation, how many kWh does it consume?
- 0.6 kWh (Correct answer)
- 0.06 kWh
- 6 kWh
- 16 kWh
Correct answer: 0.6 kWh
To calculate energy consumption in kilowatt-hours (kWh), multiply the power in watts by the time in hours, then divide by 1000. Here, (60 Watts * 10 Hours) / 1000 = 600 / 1000 = 0.6 kWh. This conversion is essential for understanding electricity usage.
Question 2: A pair of identically dense balls, one big and one small, are rolled in the same direction at the same pace. What will happen to the bigger ball when they collide?
- Be propelled backward
- Jump over the small ball
- Continue Forward (Correct answer)
- Be propelled backward
Correct answer: Continue Forward
This scenario involves principles of momentum and inertia. The larger ball, despite having the same density and initial speed, possesses greater mass and therefore greater momentum than the smaller ball. Upon collision, the larger ball will transfer some momentum to the smaller ball, but its own greater inertia will cause it to continue moving forward, albeit potentially at a slightly reduced speed, rather than being propelled backward.
Question 3: A swimming pool measuring 22 feet long, 10 feet broad, and 5 feet tall holds how many cubic feet of water?
- 1100 (Correct answer)
- 5500
- 550
- 2200
Correct answer: 1100
The volume of a rectangular prism, such as a swimming pool, is calculated by multiplying its length, width (broad), and height (tall). So, Volume = 22 feet * 10 feet * 5 feet = 1100 cubic feet. This is a straightforward application of the volume formula.
Question 4: A pie is sliced so that one piece, one-quarter of the pie, is twice the size of the other portions. How many pieces of pie are cut?
- 4
- 8
- 3
- 7 (Correct answer)
Correct answer: 7
First, one piece is 1/4 of the pie. The remaining 3/4 of the pie is divided into smaller portions. Since the large piece (1/4) is twice the size of the other portions, each small portion is (1/4) / 2 = 1/8 of the pie. The remaining 3/4 of the pie consists of (3/4) / (1/8) = 6 small pieces. Adding the one large piece, there are a total of 1 + 6 = 7 pieces.
Question 5: Rose buys 7 apples, gives three to Samantha, and then gives Gary half of what is left. How many apples does Gary receive?
- 1
- 2 (Correct answer)
- 4
- 3
Correct answer: 2
Rose starts with 7 apples. After giving 3 to Samantha, she has 7 - 3 = 4 apples remaining. She then gives Gary half of these remaining apples, which is 4 / 2 = 2 apples. Therefore, Gary receives 2 apples.
Question 6: If one officer is assigned to every 16 privates in the army, how many officers are there in a regiment of 1,105 officers and privates?
- 65 (Correct answer)
- 69
- 62
- 67
Correct answer: 65
The ratio of officers to privates is 1:16, meaning each group of 1 officer and 16 privates totals 17 people. To find the number of officers in a regiment of 1,105 people, divide the total number of people by the size of one such group: 1105 / 17 = 65. Thus, there are 65 officers.
Question 7: If a child can run 10 metres while a car travels 30 metres, how far can the child run if the automobile travels 66 metres?
- 22 (Correct answer)
- 25
- 12
- 15
Correct answer: 22
This is a ratio problem. The child runs 10 meters for every 30 meters the car travels, establishing a 1:3 ratio. If the car travels 66 meters, the child will run one-third of that distance. Therefore, the child runs (1/3) * 66 meters = 22 meters.
Question 8: Employees at a discounted appliance store get an extra 20% off the lowest price on any item. If an employee buys a dishwasher during a 15% discount sale, how much will he pay if the appliance was originally $450?
- $292.50
- $280.90
- $306.00 (Correct answer)
- $287.00
Correct answer: $306.00
First, calculate the price after the 15% discount: $450 * (1 - 0.15) = $450 * 0.85 = $382.50. Then, apply the employee's 20% discount to this new price: $382.50 * (1 - 0.20) = $382.50 * 0.80 = $306.00. The employee will pay $306.00.
Question 9: A car's selling price is $12,590, which is 20% off its original price. What was the initial price?
- $14,990.90
- $15,737.50 (Correct answer)
- $15,108.00
- $14,310.40
Correct answer: $15,737.50
If the selling price of $12,590 is 20% off the original price, it means the selling price represents 80% (100% - 20%) of the original price. To find the original price, divide the selling price by 0.80. So, $12,590 / 0.80 = $15,737.50.
Question 10: A box contains 28 blue pencils and 7 black pencils. What is the ratio of the black and blue pens?
- 1:4 (Correct answer)
- 1:9
- 2:7
- 1:8
Correct answer: 1:4
The question asks for the ratio of black pencils to blue pencils. There are 7 black pencils and 28 blue pencils. The ratio is 7:28. To simplify, divide both numbers by their greatest common divisor, which is 7, resulting in a simplified ratio of 1:4.
Question 11: If Jenny can paint a property in 4 hours and Mark can paint the same house in 6 hours, how long will it take for both of them to paint the house?
- 3 hours and 12 minutes
- 4 hours and 10 minutes
- 3 hours and 44 minutes
- 2 hours and 24 minutes (Correct answer)
Correct answer: 2 hours and 24 minutes
Jenny's rate is 1/4 house per hour, and Mark's rate is 1/6 house per hour. When working together, their combined rate is 1/4 + 1/6 = 3/12 + 2/12 = 5/12 house per hour. To find the total time, take the reciprocal of the combined rate: 1 / (5/12) = 12/5 hours. Converting 12/5 hours to hours and minutes gives 2 hours and (2/5 * 60) = 24 minutes, so 2 hours and 24 minutes.
CFAT Problem Solving 1
A lamp's watt rating is 60.
After 10 hours of operation, how many kWh does it consume?