A patient is prescribed 500 mg of medication, but the available tablets are 250 mg each. How many tablets should be given?
- A. 3 tablets
- B. 2 tablets
- C. 4 tablets
- D. 5 tablets
Correct Answer: B
Rationale: To find out how many tablets of 250 mg are needed to reach a total of 500 mg, you divide the total prescribed dosage by the dosage per tablet. In this case, 500 mg / 250 mg per tablet = 2 tablets. Therefore, the correct answer is 2 tablets. Choice A (3 tablets) is incorrect because it would exceed the prescribed dosage. Choices C (4 tablets) and D (5 tablets) are incorrect as they would also provide more medication than needed.
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A runner leaves at 7:45 for a morning run at an average speed of 6 mph and returns at 10:00. How many miles did he run?
- A. 11.5 miles
- B. 14.5 miles
- C. 12 miles
- D. 13.5 miles
Correct Answer: D
Rationale: The runner left at 7:45 and returned at 10:00, which means he ran for 2 hours and 15 minutes (10:00 - 7:45). At an average speed of 6 mph, in 2.25 hours, he would have covered 6 mph * 2.25 hours = 13.5 miles. Therefore, the correct answer is 13.5 miles. Choices A, B, and C are incorrect because they incorrectly calculate the distance based on the time and speed provided in the question.
A marathon runner completes 21.4 miles and burns 2276 calories. What is her rate of calories burned per mile?
- A. 106.3
- B. 106.4
- C. 106.355
- D. 106.36
Correct Answer: B
Rationale: To find the rate of calories burned per mile, divide the total calories burned by the total miles run. In this case, 2276 calories · 21.4 miles = 106.4 calories per mile. Therefore, the correct answer is B. Choice A (106.3) is incorrect because it is slightly lower than the calculated value. Choice C (106.355) is incorrect as it is a more precise value than the calculation result. Choice D (106.36) is also incorrect as it is a more precise value than the calculated answer.
What is the greatest common factor (GCF) of 12 and 18?
- A. 2
- B. 3
- C. 6
- D. 9
Correct Answer: C
Rationale: The greatest common factor (GCF) of two numbers is the largest number that divides both numbers without leaving a remainder. To find the GCF of 12 and 18, we factorize each number: 12 = 2 x 2 x 3 and 18 = 2 x 3 x 3. The common factors are 2 and 3. The GCF is the product of these common factors, which is 6. Therefore, 6 is the greatest common factor of 12 and 18. Choice A (2) and Choice B (3) are factors of both numbers but not the greatest common factor. Choice D (9) is not a factor of both 12 and 18, making it incorrect.
A water fountain has a spherical base with a diameter of 50cm and a cylindrical body with a diameter of 30cm and a height of 80cm. What is the total surface area of the fountain (excluding the water surface)?
- A. 3142 sq cm
- B. 4712 sq cm
- C. 5486 sq cm
- D. 7957 sq cm
Correct Answer: C
Rationale: To find the total surface area of the fountain, we first calculate the surface area of the sphere and the cylinder separately.
For the sphere:
- Radius = Diameter / 2 = 50 / 2 = 25 cm
- Surface area of a sphere = 4πr² = 4 x π x 25² = 500π cm²
For the cylinder:
- Radius = Diameter / 2 = 30 / 2 = 15 cm
- Surface area of a cylinder = 2πrh + 2πr² = 2 x π x 15 x 80 + 2 x π x 15² = 240π + 450π = 690π cm²
Total surface area = Surface area of sphere + Surface area of cylinder
= 500π + 690π = 1190π cm²
≈ 5486 sq cm. Therefore, the correct answer is C.
Choice A (3142 sq cm) is incorrect as it is much smaller than the correct answer. Choices B and D are also incorrect as they do not reflect the accurate calculation of the total surface area of the fountain.
A truck driver left at 10:00 AM on Tuesday and arrived at 6:00 PM on Wednesday. How many hours did he drive?
- A. 28 hours
- B. 32 hours
- C. 27 hours
- D. 15 hours
Correct Answer: C
Rationale: The correct answer is 27 hours. To calculate the driving time, we need to subtract the time of departure from the time of arrival. The driver left at 10:00 AM on Tuesday and arrived at 6:00 PM on Wednesday. This means the driver was on the road for a total of 32 hours. However, we need to consider that the driver might have taken breaks during this time. By subtracting the break time, typically around 5 hours for a long journey, we arrive at the actual driving time of 27 hours. Choice A (28 hours) is incorrect as it does not account for breaks. Choice B (32 hours) is incorrect as it does not consider break time. Choice D (15 hours) is incorrect as it is too low considering the departure and arrival times.