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Solve for x: 3(x - 4) = 18.
- A. x = 10
- B. x = 12
- C. x = 5
- D. x = 3
Correct Answer: A
Rationale: To solve the equation, begin by distributing the 3 on the left side: 3x - 12 = 18. Next, add 12 to both sides to isolate x: 3x = 30. Finally, divide by 3 to determine the value of x: x = 10. Therefore, the correct answer is x = 10. Choice B, x = 12, is incorrect as the correct value of x is 10, not 12. Choice C, x = 5, is incorrect as it does not satisfy the equation after substitution. Choice D, x = 3, is incorrect as it does not fulfill the equation when substituted back.
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A female ran a 24-mile course. Her first 6 miles she ran in 1 hour. The second set of 6 miles in 1.2 hours. The third set of 6 miles in 1.5 hours. The fourth set of 6 miles in 1.6 hours. How long did it take her to complete the course?
- A. 5 hours
- B. 5.3 hours
- C. 4 hours
- D. 6 hours
Correct Answer: B
Rationale: To find the total time, add the times for each set of 6 miles: 1 + 1.2 + 1.5 + 1.6 = 5.3 hours. Therefore, it took her 5.3 hours to complete the 24-mile course. Choice A, 5 hours, is incorrect because the total time is slightly more than that. Choice C, 4 hours, is incorrect as it doesn't account for the total time taken. Choice D, 6 hours, is incorrect as it's an overestimation of the actual time taken.
Find x if 40:5 = 60:x.
- A. 12
- B. 7
- C. 1
- D. 8
Correct Answer: B
Rationale: To find x in the proportion 40:5 = 60:x, set up the equation: 40/5 = 60/x. Cross-multiply to solve for x: 40x = 60 * 5 => 40x = 300. Divide by 40 to isolate x: x = 300 / 40 = 7.5. However, x should be a whole number since it represents a quantity, so x = 7. Therefore, the correct answer is 7 (B). Choices A, C, and D are incorrect as they do not satisfy the proportion equation.
7 is divisible by which of the following numbers?
- A. 2 only
- B. 3 only
- C. 1 and 7 only
- D. 2, 3, and 7
Correct Answer: D
Rationale: Rationale:
1. 7 is divisible by 1 because every number is divisible by 1.
2. 7 is divisible by 7 because any number is divisible by itself.
3. 7 is not divisible by 2 because 7 is an odd number and not divisible by 2.
4. 7 is not divisible by 3 because the sum of the digits of 7 (7) is not divisible by 3.
Therefore, 7 is divisible by 1, 7, and itself (7), making the correct answer D) 2, 3, and 7.
What is 39 · 8 · 7/6?
- A. 56/39
- B. 39/8
- C. 4 & 7/8
- D. 5 & 8/14
Correct Answer: A
Rationale: To solve the division problem, we need to remember the rule 'Dividing by a fraction is the same as multiplying by its reciprocal.' Therefore, 39 · 8 · 7/6 is equivalent to 39 · 8 6/7. Simplifying this gives (39 6) · (8 7) = 234 · 56 = 56/39. Therefore, the correct answer is A. Choices B, C, and D are incorrect as they do not correctly simplify the given division problem.
Change 1/6 to a percent.
- A. 16.67%
- B. 15%
- C. 14%
- D. 17%
Correct Answer: A
Rationale: To convert 1/6 to a percentage, you multiply 1/6 by 100. This gives you 16.67%. Choice A is correct. Choice B, 15%, is incorrect as it is the rounded value of 1/6 as a percentage. Choice C, 14%, and Choice D, 17%, are also incorrect as they do not represent the accurate conversion of 1/6 to a percentage.