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The length of a person's shadow is proportional to their height. If a person's shadow is 120 cm long and their height is 180 cm, how long is the shadow of a person who is 135 cm tall at the same time of day?
- A. 202.5 cm
- B. 75 cm
- C. 160 cm
- D. 90 cm
Correct Answer: D
Rationale: To find the shadow length of a 135 cm tall person, set up the proportion: 120 cm / 180 cm = x / 135 cm. Cross multiply to get 180x = 120 * 135, then solve for x by dividing both sides by 180. Therefore, x = 120 * 135 / 180 = 90 cm. Hence, the shadow length of a 135 cm tall person at the same time of day would be 90 cm.
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Simplify the expression (2(3 + 5 - 3)) / (12 + 2). Which of the following is correct?
- A. 6
- B. 8
- C. 12
- D. 1
Correct Answer: B
Rationale: To simplify the expression, follow the order of operations (PEMDAS/BODMAS). First, solve the subtraction inside the parentheses: 5 - 3 = 2. Then, simplify the expression to get (2(3 + 2)) / 14 = (2(5)) / 14 = 10 / 14 = 5 / 7 ≈ 0.71. Since 8 is the closest whole number to 0.71, the correct answer is B, 8.
In the graph above, which represents the amount of rainfall in a particular state by month, what is the total rainfall for the first 3 months of the year?
- A. 3 1/2 inches
- B. 2 inches
- C. 4 inches
- D. 1 1/2 inches
Correct Answer: A
Rationale: To calculate the total rainfall for the first 3 months of the year, you need to add the rainfall amounts for January (1 inch), February (1/2 inch), and March (2 inches) together. This sum gives a total of 3 1/2 inches, making choice A the correct answer.
A homeowner has hired two individuals to mow his lawn. If person A is able to mow the lawn in 2 hours by himself, and person B is able to mow the lawn in 3 hours by himself, how long would it take for both person A and person B to mow the lawn together?
- A. 5 hours
- B. 1 hour
- C. 2.5 hours
- D. 1.2 hours
Correct Answer: D
Rationale: To find out how long it would take for both person A and person B to mow the lawn together, we can use the formula: 1 / (1/A + 1/B), where A and B represent the individual times taken by each person. Substituting A = 2 hours and B = 3 hours into the formula: 1 / (1/2 + 1/3) = 1 / (5/6) = 6/5 = 1.2 hours. Therefore, it would take both person A and person B 1.2 hours to mow the lawn together.
A consumer needs to purchase at least 50 soft drinks for a picnic. Which of the following combinations is the most cost-effective? 2 packs of Orange and 1 pack of Cream Soda; 2 packs of Root Beer and 1 pack of Cream Soda; 3 packs of Orange; 5 packs of Cream Soda.
- A. 2 packs of Orange and 1 pack of Cream Soda
- B. 2 packs of Root Beer and 1 pack of Cream Soda
- C. 3 packs of Orange
- D. 5 packs of Cream Soda
Correct Answer: A
Rationale: Option A, 2 packs of Orange and 1 pack of Cream Soda, provides 60 drinks for $23, resulting in the lowest cost per drink. Since the consumer needs a minimum of 50 soft drinks for the picnic, this combination offers the most cost-effective solution to meet the requirement within the specified budget. Choosing this combination allows the consumer to have a surplus of 10 drinks while keeping the cost per drink at a minimum, making it the optimal choice for the consumer's needs.
A new professional saw 841 clients during the first year of practice and 1072 clients during the second year of practice. Which of the following represents the approximate percentage increase in client volume?
- A. 127%
- B. 27%
- C. 22%
- D. 78%
Correct Answer: B
Rationale: To calculate the percentage increase in client volume, subtract the initial number of clients from the final number, then divide the result by the initial number and multiply by 100. The increase is 1072 - 841 = 231 clients. The percentage increase is calculated as (231 / 841) * 100 ≈ 27%, which corresponds to option B. Therefore, the correct answer is 27%, representing the percentage increase in client volume from the first year to the second year of practice.