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If 1 inch on a map represents 60 ft, how many yards apart are two points if the distance between the points on the map is 10 inches?
- A. 1800
- B. 600
- C. 200
- D. 2
Correct Answer: B
Rationale: If 1 inch on the map represents 60 ft, then for 10 inches on the map, the actual distance would be 10 inches x 60 ft = 600 ft. To convert this to yards, we know that 1 yard equals 3 feet. Therefore, the distance between the two points is 600 ft / 3 ft/yard = 200 yards. Choice A (1800) is incorrect because it incorrectly multiplies by 10 again instead of converting to yards. Choice C (200) is incorrect because it fails to adjust the measurement from feet to yards. Choice D (2) is incorrect as it does not consider the correct conversion factor from feet to yards.
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What is the simplest way to write the following expression? 5x - 2y + 4x + y
- A. 9x - y
- B. 9x - 3y
- C. 9x + 3y
- D. x; y
Correct Answer: A
Rationale: To simplify the given expression 5x - 2y + 4x + y, we combine like terms. Grouping the x terms together and the y terms together, we have 5x + 4x - 2y + y. Combining like terms results in 9x - y. Therefore, the simplest form of the expression is 9x - y, which corresponds to option A. Option B is incorrect because it incorrectly subtracts 3y instead of just y. Option C is incorrect because it adds 3y instead of subtracting y. Option D is incorrect as it separates x and y with a semicolon instead of an operation, providing no simplified expression.
On a highway map, the scale indicates that 1 inch represents 45 miles. If the distance on the map is 3.2 inches, how far is the actual distance in miles?
- A. 144 miles
- B. 160 miles
- C. 180 miles
- D. 200 miles
Correct Answer: A
Rationale: To find the actual distance in miles, you need to set up a proportion using the scale provided (1 inch = 45 miles). Since the distance on the map is 3.2 inches, you can set up the proportion: 1 inch / 45 miles = 3.2 inches / x miles. Cross-multiply to solve for x: 1 * x = 45 * 3.2, x = 144. Therefore, the actual distance in miles is 144. Choices B, C, and D are incorrect because they do not accurately calculate the actual distance using the scale provided.
Veronica paid an additional $3,015 for a surround sound system and $5,218 for a maintenance package. What was the total price of her new car?
- A. $50,210
- B. $48,443
- C. $43,225
- D. $40,210
Correct Answer: B
Rationale: To calculate the total price of Veronica's new car, you must sum the original price of the car with the additional costs. Veronica paid $3,015 for the surround sound system and $5,218 for the maintenance package, totaling $3,015 + $5,218 = $8,233 in additional costs. Adding this to the original price of the car, $40,210, gives $40,210 + $8,233 = $48,443. Therefore, the total price of Veronica's new car is $48,443. Choice A, $50,210, is incorrect as it does not factor in the correct additional costs. Choice C, $43,225, is incorrect because it does not include the additional costs. Choice D, $40,210, is incorrect as it only represents the original price of the car without the added expenses.
A woman wants to stack two small bookcases beneath a window that is 26 inches from the floor. The larger bookcase is 14 inches tall. The other bookcase is 8 inches tall. How tall will the two bookcases be when they are stacked together?
- A. 12 inches tall
- B. 22 inches tall
- C. 35 inches tall
- D. 41 inches tall
Correct Answer: B
Rationale: When the woman stacks the two bookcases together, the total height will be the sum of the heights of the two bookcases. Therefore, 14 inches (larger bookcase) + 8 inches (smaller bookcase) = 22 inches. So, the stacked bookcases will be 22 inches tall. Choice A is incorrect because it does not account for the total height of both bookcases. Choice C and D are incorrect as they are higher than the combined height of the two bookcases.
Approximately by what percentage are there more female staff members in City Y compared to City X?
- A. 5%
- B. 10%
- C. 15%
- D. 20%
Correct Answer: D
Rationale: To find the percentage difference in female staff members between City Y and City X, you subtract the percentage of female staff members in City X from the percentage in City Y. So, 60% (City Y) - 40% (City X) = 20%. This means there are 20% more female staff members in City Y compared to City X. Choices A, B, and C are incorrect percentages and do not accurately represent the 20% difference between the two cities.