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What number is equivalent to -3 + 2 * 8 + 3?
- A. 11
- B. 31
- C. 28
- D. 80
Correct Answer: B
Rationale: To solve this expression, we first follow the order of operations (PEMDAS/BODMAS). According to this rule, we start by multiplying 2 by 8, which equals 16. Then, we add -3 and 3 to get 0. Finally, adding 0 to 16 gives us the correct answer of 16. The correct answer is B. Choice A (11) results from adding all the numbers without considering the multiplication first. Choice C (28) is the result of adding all the numbers without considering any operations. Choice D (80) is incorrect as it does not correctly follow the order of operations.
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If you have a rectangle with a width of 5 inches and a length of 10 inches and scale it by a factor of 2, what will the new perimeter be?
- A. 30 inches
- B. 40 inches
- C. 60 inches
- D. 50 inches
Correct Answer: C
Rationale: When a rectangle is scaled by a factor of 2, both the length and width are multiplied by 2. The new dimensions become width = 5 * 2 = 10 inches and length = 10 * 2 = 20 inches. Therefore, the new perimeter is calculated as 2 * (10 + 20) = 60 inches. Choice A, B, and D are incorrect as they do not reflect the correct calculation based on scaling the dimensions of the rectangle.
As part of a study, a set of patients will be divided into three groups: 1/2 of the patients will be in Group Alpha, 1/3 of the patients will be in Group Beta, and 1/6 of the patients will be in Group Gamma. Order the groups from smallest to largest, according to the number of patients in each group.
- A. Group Alpha, Group Beta, Group Gamma
- B. Group Alpha, Group Gamma, Group Beta
- C. Group Gamma, Group Alpha, Group Beta
- D. Group Gamma, Group Beta, Group Alpha
Correct Answer: C
Rationale: The correct order from smallest to largest number of patients in each group is Group Gamma (1/6), Group Alpha (1/2), and Group Beta (1/3). Group Gamma has the smallest fraction of patients, followed by Group Alpha and then Group Beta. Therefore, choice C, 'Group Gamma, Group Alpha, Group Beta,' is the correct answer. Choices A, B, and D are incorrect because they do not follow the correct order based on the fractions of patients assigned to each group.
A store offers a 15% discount on all items. If an item costs $100, what is the price after the discount?
- A. 90
- B. 85
- C. 80
- D. 75
Correct Answer: B
Rationale: To calculate the price after the 15% discount on a $100 item, you first find 15% of $100, which is $15. Then, subtract $15 from the original price: $100 - $15 = $85. Therefore, the correct answer is $85. Choice A ($90), Choice C ($80), and Choice D ($75) are incorrect as they do not reflect the correct calculation of applying a 15% discount to the original $100 price.
A study was conducted where patients were divided into three groups: 1/2 in Group Alpha, 1/3 in Group Beta, and 1/6 in Group Gamma. Which group is the smallest?
- A. Group Alpha
- B. Group Beta
- C. Group Gamma
- D. Group Gamma
Correct Answer: C
Rationale: The smallest group is Group Gamma, which had 1/6 of the total number of patients. To determine the smallest group, compare the fractions representing the portions of patients in each group. 1/6 is smaller than 1/3 and 1/2, making Group Gamma the smallest. Group Alpha and Group Beta have larger fractions of patients, making them larger groups compared to Group Gamma.
A charter bus driver drove at an average speed of 65 mph for 305 miles. If he stops at a gas station for 15 minutes, then drives another 162 miles at 80 mph, how long will it have been since he began the trip?
- A. 0.96 hours
- B. 6.44 hours
- C. 6.69 hours
- D. 6.97 hours
Correct Answer: C
Rationale: To calculate the total time, first find the time for the first leg of the trip: 305 miles / 65 mph = 4.69 hours. Then, add the time for the second leg: 162 miles / 80 mph = 2.025 hours. Next, add the 15-minute stop in hours (15 minutes = 0.25 hours). Finally, add the times together: 4.69 hours + 2.025 hours + 0.25 hours = 6.965 hours, which rounds to 6.69 hours. Therefore, the correct answer is 6.69 hours. Choice A is incorrect because it does not account for the total driving time correctly. Choice B is incorrect as it does not include the time for the gas station stop. Choice D is wrong as it miscalculates the total time taken for the trip.