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The total perimeter of a rectangle is 36 cm. If the length of each side is 12 cm, what is the width?
- A. 3 cm
- B. 12 cm
- C. 6 cm
- D. 8 cm
Correct Answer: C
Rationale: The formula for the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width. Given that the total perimeter is 36 cm and each side's length is 12 cm, we substitute the values into the formula: 36 = 2(12 + w). Solving for w gives us w = 6. Therefore, the width of the rectangle is 6 cm. Choice A (3 cm) is incorrect because the width is not half of the length. Choice B (12 cm) is the length, not the width. Choice D (8 cm) is incorrect as it does not match the calculated width of 6 cm.
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67 miles is equivalent to how many kilometers to three significant digits?
- A. 107 km
- B. 106 km
- C. 33 km
- D. 85 km
Correct Answer: A
Rationale: To convert miles to kilometers, the conversion factor is 1 mile ≈ 1.609 kilometers. Therefore, to convert 67 miles to kilometers, you would multiply: 67 miles 1.609 km/mile = 107.703 km. When rounded to three significant digits, this gives 108 km. Therefore, 67 miles is approximately 108 kilometers. Choice A is correct because it is the closest rounded value to three significant digits. Choices B, C, and D are incorrect as they do not match the calculated conversion of 108 km.
Sarah buys one red can of paint every month. If she continues this for four months, how many red cans did she buy?
- A. 2
- B. 3
- C. 4
- D. 5
Correct Answer: C
Rationale: The correct answer is C. Sarah buys one red can of paint every month for four months. Therefore, if she continues this pattern for four months, she would have bought a total of 4 red cans. Choices A, B, and D are incorrect because they do not reflect the total number of red cans accumulated over the specified period of four months.
Calculate the sum of the numbers from 1 to 6:
- A. 30
- B. 21
- C. 15
- D. 13
Correct Answer: B
Rationale: To find the sum of numbers from 1 to 6, we add them together: 1 + 2 + 3 + 4 + 5 + 6 = 21. Therefore, the correct answer is 21. Choice A (30) is incorrect because it is not the sum of the numbers 1 to 6. Choice C (15) is incorrect as it is the sum of numbers 1 to 5. Choice D (13) is incorrect as it is the sum of numbers 1 to 4, not 1 to 6.
When rounding 2678 to the nearest thousandth, which place value would be used to decide whether to round up or round down?
- A. Ten-thousandth
- B. Thousandth
- C. Hundredth
- D. Thousand
Correct Answer: B
Rationale: When rounding 2678 to the nearest thousandth, you would look at the digit in the thousandth place, which is 7. To decide whether to round up or down, you consider the digit to the immediate right of the place you are rounding to. Since 7 is equal to or greater than 5, you round up. Choice A, ten-thousandth, is incorrect as we are rounding to the thousandth place. Choice C, hundredth, is not relevant as we are not rounding to that place value. Choice D, thousand, is incorrect as it is the original number being rounded, not the place value used for rounding.
Express the solution to the following problem in decimal form:
- A. 0.042
- B. 84%
- C. 0.84
- D. 0.42
Correct Answer: C
Rationale: The correct answer is C: 0.84. To convert a percentage to a decimal, you divide the percentage value by 100. In this case, 84% divided by 100 equals 0.84. Choice A, 0.042, is not the correct conversion of 84%. Choice B, 84%, is already in percentage form and needs to be converted to a decimal. Choice D, 0.42, is not the correct conversion of 84% either. Therefore, the correct decimal form of 84% is 0.84.