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A macaroni and cheese recipe calls for 1/2 cup of flour for every 1 cup 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. 4 cups
- C. 3 8/15 cups
- D. 6 cups
Correct Answer: B
Rationale: To determine the amount of milk needed for 2 cups of flour, set up the proportion: 1 cup of milk / 1/2 cup of flour = x / 2 cups of flour. Cross multiply to get 2 cups of milk = 1 cup of flour * 2 cups of flour. Therefore, x = 4 cups of milk. The chef would need 4 cups of milk for the larger batch.
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What is the area of the largest circle that can fit entirely inside a rectangle measuring 8 centimeters by 10 centimeters?
- A. 18Ï€ cm^2
- B. 16Ï€ cm^2
- C. 8Ï€ cm^2
- D. 10Ï€ cm^2
Correct Answer: B
Rationale: To find the largest circle that fits inside the given rectangle, the circle's diameter should match the shorter side of the rectangle, which is 8 cm. The radius of the circle is half the diameter, making it 4 cm. The area of a circle is determined using the formula A = πr^2, where r is the radius. Substituting r = 4 cm, we get A = π*(4)^2 = 16π cm^2. Therefore, the correct answer is 16π cm^2, as this is the maximum area circle that can fit entirely inside the given rectangle.
An athlete runs 4 miles in 28 minutes and then changes pace to run the next 4 miles in 32 minutes. Overall, what is the average time in minutes it takes the athlete to run 1 mile?
- A. 7.5 minutes
- B. 7 minutes
- C. 8.5 minutes
- D. 8 minutes
Correct Answer: A
Rationale: To calculate the average time per mile, we add the total time taken for both parts (28 minutes + 32 minutes = 60 minutes) and divide it by the total distance covered (8 miles). This gives us 60 minutes / 8 miles = 7.5 minutes per mile. Therefore, the correct answer is 7.5 minutes, representing the average time it takes the athlete to run 1 mile.
A recipe calls for 2 1/2 cups of flour to yield 36 cookies. How much flour will be needed to make 90 cookies using the same recipe?
- A. 6 1/2 cups
- B. 10 1/2 cups
- C. 5 1/2 cups
- D. 4 1/2 cups
Correct Answer: A
Rationale: To determine the amount of flour needed for 90 cookies using the same recipe, set up a proportion: (90 cookies / 36 cookies) * 2.5 cups = 6.25 cups, which simplifies to 6 1/2 cups of flour. Therefore, to make 90 cookies, you will need 6 1/2 cups of flour, based on the original recipe's ratio of flour to cookies.
What is the best decimal approximation of 10 times the positive square root of 207?
- A. 100
- B. 44.7
- C. 200
- D. 89.4
Correct Answer: D
Rationale: To find the decimal approximation of 10 times the positive square root of 207, we first approximate the square root of 207 to be around 14.4. Multiplying this by 10 gives us 144. Among the choices, 89.4 is the closest value to this approximation, making it the correct answer. Therefore, the best decimal approximation of 10 times the positive square root of 207 is 89.4.
A couple dining at a restaurant receives a bill for $38.40. They wish to leave a 15% gratuity. What is the estimated gratuity amount?
- A. $4.00
- B. $5.76
- C. $5.00
- D. $7.00
Correct Answer: B
Rationale: To calculate a 15% gratuity on a $38.40 bill, you multiply $38.40 by 0.15 (15%). This calculation results in $5.76, which is the estimated gratuity amount. Therefore, the correct answer is $5.76 (Choice B). Leaving a 15% gratuity is a common practice to show appreciation for the service provided by the restaurant staff.