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What is a common denominator?
- A. A shared multiple of two denominators
- B. A shared factor of two numerators
- C. A number that is the same in all fractions
- D. A number that divides evenly into both fractions
Correct Answer: A
Rationale: A common denominator is a shared multiple of the denominators in a set of fractions. It is necessary when adding or subtracting fractions to have a common denominator to ensure that the fractions can be combined accurately. Choice B is incorrect because the common denominator is related to the denominators, not the numerators. Choice C is incorrect because while the common denominator is the same in all fractions being added or subtracted, it is not necessarily a number that is the same in all fractions. Choice D is incorrect because a common denominator is a multiple of the denominators, not a number that divides evenly into both fractions.
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If a box of 55 syringes costs $660.00, what is the cost of four syringes?
- A. $51.00
- B. $26.00
- C. $32.00
- D. $48.00
Correct Answer: D
Rationale: To find the cost of one syringe, divide the total cost by the number of syringes: $660.00 · 55 = $12. Therefore, the cost of four syringes is 4 x $12 = $48. Choices A, B, and C are incorrect because they do not correctly calculate the cost per syringe or the total cost of four syringes.
If (D) is the distance traveled and (R) is the rate of travel, which of the following represents the relationship between D and R for the equation D=2R?
- A. D is twice as much as R
- B. R is twice as much as D
- C. R is two times D
- D. D is two more than R
Correct Answer: A
Rationale: The equation D=2R means that D equals 2 times R, which translates to D being twice the value of R. Therefore, choice A, 'D is twice as much as R,' is the correct representation of the relationship between D and R. Choice B, 'R is twice as much as D,' incorrectly reverses the roles of D and R. Choice C, 'R is two times D,' incorrectly states the relationship between R and D. Choice D, 'D is two more than R,' does not accurately reflect the relationship presented in the equation.
As a company's stocks increase, production, sales, and investments also increase. Which of the following is the independent variable?
- A. Sales
- B. Stocks
- C. Production
- D. Investments
Correct Answer: B
Rationale: The independent variable in this scenario is 'Stocks.' An independent variable is the one that is manipulated or controlled by the experimenter. In this case, stocks are the factor that is changing and influencing the other variables - production, sales, and investments. Production, sales, and investments are dependent on the changes in stocks; hence, they are the dependent variables. While production, sales, and investments may increase as a result of changes in stocks, the stocks themselves are the driving force behind these changes, making them the independent variable.
What is a prime number?
- A. A number divisible by only 1 and itself
- B. A number divisible by 2 and 3
- C. A number divisible by any number
- D. A number with exactly three factors
Correct Answer: A
Rationale: The correct answer is A: 'A number divisible by only 1 and itself.' A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. This definition aligns with choice A. Choice B is incorrect because not all prime numbers are divisible by 2 and 3. Choice C is incorrect as prime numbers are not divisible by any number other than 1 and themselves. Choice D is incorrect because a prime number has exactly two factors, 1 and itself, not three factors.
How do you find the least common multiple?
- A. List all multiples of the numbers, then find the smallest common one
- B. List all factors of the numbers, then find the largest common one
- C. Divide the largest number by the smallest
- D. Multiply the two numbers together
Correct Answer: A
Rationale: The correct way to find the least common multiple is to list all the multiples of each number and then identify the smallest common multiple. Choice A is correct because it describes the correct process. Listing factors, as suggested in choice B, helps in finding the greatest common factor, not the least common multiple. Dividing the largest number by the smallest, as mentioned in choice C, does not help find the least common multiple. Multiplying the two numbers together, as stated in choice D, results in their least common multiple when the numbers have no common factors.