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What is 31% of 426?
- A. 425.69
- B. 0.07
- C. 13.7
- D. 132.06
Correct Answer: D
Rationale: To find 31% of 426, you multiply 426 by 0.31 (which represents 31% in decimal form). The calculation is 426 * 0.31 = 132.06. Therefore, the correct answer is D, 132.06.
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A macaroni and cheese recipe calls for 1/3 cup of flour for every 1 1/5 cups of milk. To make a bigger batch, the chef uses 2 cups of flour. Which of the following would be the amount of milk needed for the bigger batch?
- A. 2 2/5 cups
- B. 7 1/5 cups
- C. 6 cups
- D. 3 8/15 cups
Correct Answer: B
Rationale: To determine the amount of milk needed for the bigger batch, we first establish the ratio of flour to milk, which is 1/3 : 1 1/5. Converting 1 1/5 to an improper fraction gives us 6/5. Therefore, the ratio becomes 1:6/5 = 1:1.2. If the chef uses 2 cups of flour, the calculation would be 2 x 1.2 = 2.4 cups of milk needed. This is equivalent to 2 2/5 cups. Hence, the correct answer is 7 1/5 cups.
A child has a bottle full of pennies, nickels, dimes, and quarters. There are twice as many quarters as pennies, four times as many nickels as pennies, and five times as many dimes as nickels. How many more dimes does the child have than quarters?
- A. 10 times as many
- B. 4 times as many
- C. 5 times as many
- D. 29 times as many
Correct Answer: D
Rationale: Let's assign a value to the number of pennies. If we say there is 1 penny, then there are 2 quarters (twice as many as pennies), 4 nickels (four times as many as pennies), and 20 dimes (five times as many as nickels). The number of dimes is 20, and the number of quarters is 2. The difference between the number of dimes and quarters is 20 - 2 = 18. Therefore, the child has 18 more dimes than quarters, which is 18 times as many, not 29 times as many as stated in the original answer choice.
What is the value of x in the equation below? 18x - 4 = -10
- A. x = -2 or x = 1
- B. x = -1/3 or x = 2
- C. x = -1/2 or x = 3/2
- D. x = -3/2 or x = 1/2
Correct Answer: B
Rationale: To solve the equation 18x - 4 = -10, first, add 4 to both sides to get 18x = -6. Then, divide by 18 to isolate x, which gives x = -1/3. Therefore, the correct answer is x = -1/3 or x = 2. It's crucial to double-check the solutions in relation to the original equation to ensure accuracy. The error in the original solution is the incorrect value provided for x = -1 which should have been x = -1/3 instead. Hence, the correct solution is x = -1/3 or x = 2.
A person weighed 180 lb. Three months later, they weighed 160 lb. What is the percentage of weight the person lost over 3 months? (Round to the nearest percent.)
- A. 13%
- B. 20%
- C. 10%
- D. 5%
Correct Answer: B
Rationale: To calculate the percentage of weight lost, subtract the final weight from the initial weight, divide by the initial weight, and multiply by 100. In this case: (180 - 160) / 180 * 100 = 20%, which rounds to the nearest percent as 20%. Therefore, the person lost 20% of their initial weight over the three months. This calculation represents the relative decrease in weight from the initial weight to the final weight, indicating that the person lost 20% of their initial weight during the three-month period.
One gallon of cleaning solution requires 6 oz of ammonia. If the maintenance department needs 120 gallons of solution to clean all the floors, how much ammonia is needed?
- A. 20 oz
- B. 20 gallons
- C. 720 oz
- D. 720 gallons
Correct Answer: C
Rationale: To calculate the total amount of ammonia needed, you must multiply the amount of ammonia required for one gallon of solution by the total number of gallons needed. With 6 oz of ammonia per gallon, multiplying 6 oz by 120 gallons gives you a total of 720 oz of ammonia needed. Therefore, 720 oz of ammonia are required to clean all the floors.