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A circle has an area of 121π in². Which of the following is the circumference of the circle in terms of pi (π)?
- A. 11π in
- B. 22π in
- C. 44π in
- D. 5.5π in
Correct Answer: B
Rationale: To find the circumference of the circle, we first need to determine the radius. Given that the area of the circle is 121π in², we use the formula for the area of a circle (A = πr²) to find the radius squared. So, r² = 121, which means the radius (r) is 11 in. The circumference of a circle is calculated using the formula 2πr. Substituting the radius value of 11 in, we get 2π(11) = 22π in. Therefore, the correct answer is 22π in. Choice A (11π in), Choice C (44π in), and Choice D (5.5π in) are incorrect because they do not correctly calculate the circumference based on the given area of the circle.
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A bucket can hold 2500 mL. How many liters can the bucket hold?
- A. 0.25 L
- B. 25 L
- C. 2.5 L
- D. 250 L
Correct Answer: C
Rationale: To convert milliliters (mL) to liters (L), you divide by 1000 since 1000 mL is equivalent to 1 liter. Therefore, 2500 mL is equal to 2.5 liters (2500 mL · 1000 = 2.5 L). Choice A (0.25 L) is incorrect as it represents a conversion error by a factor of 10. Choice B (25 L) is incorrect as it incorrectly multiplies instead of dividing by 1000. Choice D (250 L) is incorrect as it overestimates the conversion by a factor of 100.
A consumer recently purchased a new car and paid $48,000. This amount is $2,000 less than twice what the consumer's friend paid for their car. Which of the following is the amount that the friend paid for their car?
- A. $23,000
- B. $46,000
- C. $25,000
- D. $50,000
Correct Answer: C
Rationale: To find the amount the friend paid, you can set up the equation 2x - 2000 = 48000, where x represents the amount the friend paid. Solving this equation gives x = $25,000. Therefore, the friend paid $25,000. Choice A ($23,000) is incorrect because it does not account for the $2,000 difference mentioned in the question. Choice B ($46,000) is incorrect because it is double the amount needed. Choice D ($50,000) is incorrect as it does not consider the $2,000 less mentioned in the question.
What is the result when the number 1 is raised to ANY power?
- A. One
- B. Itself
- C. Zero
- D. Two
Correct Answer: A
Rationale: The correct answer is A: 'One.' When the number 1 is raised to any power, the result is always 1. This is a fundamental mathematical property where any number raised to the power of 0 equals 1. Choices B, C, and D are incorrect. Choice B 'Itself' is vague and does not provide a clear mathematical result. Choice C 'Zero' is incorrect as 1 raised to any power is not zero. Choice D 'Two' is incorrect as the result of raising 1 to any power is always 1, not 2.
What is the GCF (greatest common factor)?
- A. The largest factor that all the numbers share
- B. The smallest factor that all the numbers share
- C. The largest multiple that all the numbers share
- D. The smallest multiple that all the numbers share
Correct Answer: A
Rationale: The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. This factor represents the highest number that can evenly divide each of the numbers in the set without any remainder. Choice B, 'The smallest factor that all the numbers share,' is incorrect because the GCF is the greatest, not the smallest, factor. Choices C and D, 'The largest multiple that all the numbers share' and 'The smallest multiple that all the numbers share,' are also incorrect as the GCF refers to factors, not multiples.
What is the least common multiple? What is the least common factor?
- A. The smallest number that both numbers multiply into; the smallest number that divides evenly into both
- B. The largest number that both numbers multiply into; the smallest number that divides evenly into both
- C. The smallest number that both numbers divide into evenly; the smallest number that multiplies into both
- D. The smallest number that both numbers divide into evenly; the smallest number that both multiply into
Correct Answer: A
Rationale: The least common multiple is the smallest number that both numbers multiply into, which means it is the smallest number that both numbers can be evenly divided by without leaving a remainder. The least common factor, on the other hand, is the smallest number that divides both numbers without leaving a remainder. Therefore, choice A is correct as it accurately defines the least common multiple and factor. Choices B, C, and D are incorrect because they provide inaccurate definitions or mix up the concepts of multiplication and division in relation to finding the least common multiple and factor.