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What defines an integer?
- A. A whole number (not a fraction or decimal!) that can be positive, negative, or zero
- B. A number with a decimal point
- C. A fraction
- D. A percentage
Correct Answer: A
Rationale: An integer is a whole number that can be positive, negative, or zero. It does not include fractions or decimals. Choice B, 'A number with a decimal point,' is incorrect because integers do not have decimal points. Choice C, 'A fraction,' is incorrect because integers are not expressed as ratios of two integers. Choice D, 'A percentage,' is incorrect because integers are not necessarily related to proportions out of 100.
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If x represents the width of a rectangle and the length is six less than two times the width, which of the following expressions represents the length of the rectangle in terms of x?
- A. 2x-6
- B. 6-2x
- C. 6x-2
- D. 3x-4
Correct Answer: A
Rationale: To find the expression representing the length of the rectangle in terms of x, we need to consider that the length is six less than two times the width. If we denote the width as x, the length can be expressed as 2x - 6. Therefore, the correct expression is 2x-6 (choice A). Choice B, 6-2x, represents the width subtracted from 6, not the length. Choice C, 6x-2, is not derived from the given information about the relationship between the width and length. Choice D, 3x-4, is not consistent with the relationship provided in the question.
3(x-2)=12. Solve the equation above for x. Which of the following is the correct answer?
- A. 6
- B. -2
- C. -4
- D. 2
Correct Answer: A
Rationale: To solve the equation 3(x-2)=12, first distribute the 3: 3x - 6 = 12. Next, isolate x by adding 6 to both sides: 3x = 18. Finally, divide by 3 to find x: x = 6. Therefore, the correct answer is A (6). Choice B (-2) is incorrect as it does not satisfy the equation. Choice C (-4) is also incorrect as it does not satisfy the equation. Choice D (2) is incorrect as it does not satisfy the equation either.
What defines a composite number?
- A. A number with only two factors
- B. A number that is a fraction
- C. A number with more than 2 factors
- D. A number with exactly two factors
Correct Answer: C
Rationale: A composite number is a positive integer greater than one that has more than two factors. Choice A is incorrect because a number with only two factors is a prime number. Choice B is incorrect as being a fraction does not define a composite number. Choice D is incorrect because a number with exactly two factors is a prime number, not a composite number.
A homeowner has hired two people to mow his lawn. If person A is able to mow the lawn in 2 hours by herself and person B is able to mow the lawn in 3 hours by himself, what is the amount of time it would take for both person A and B to mow the lawn together?
- A. 5 hours
- B. 2.5 hours
- C. 1.2 hours
- D. 1 hour
Correct Answer: C
Rationale: To find the combined work rate, you add the individual work rates: 1/2 + 1/3 = 5/6. This means that together, they can mow 5/6 of the lawn per hour. To determine how long it would take for both A and B to mow the entire lawn, you take the reciprocal of 5/6, which gives you 6/5 or 1.2 hours. Therefore, it would take 1.2 hours for person A and person B to mow the lawn together. Choice A (5 hours) is incorrect because it does not consider the combined efficiency of both workers. Choice B (2.5 hours) is incorrect as it does not reflect the correct calculation based on the combined work rates of the two individuals. Choice D (1 hour) is incorrect as it doesn't consider the fact that the combined rate is less than the individual rate of person A alone, thus taking longer than 1 hour.
How do you convert pounds to kg and kg to pounds?
- A. Multiply by 2.2 for pounds; divide by 2.2 for kg
- B. Multiply by 2 for pounds; divide by 2 for kg
- C. Multiply by 1.8 for pounds; divide by 1.8 for kg
- D. Multiply by 1.5 for pounds; divide by 1.5 for kg
Correct Answer: A
Rationale: To convert pounds to kg, you need to divide by 2.2, not multiply. Similarly, to convert kg to pounds, you should multiply by 2.2. Therefore, choice A is correct. Choices B, C, and D are incorrect because they provide incorrect conversion factors for pounds and kg, leading to inaccurate results.