Nokea
Solve for x: 3(x - 5) = 2(x + 3)
- A. x = 3
- B. x = 6
- C. x = 9
- D. x = 12
Correct Answer: A
Rationale: To solve the equation 3(x - 5) = 2(x + 3) for x, start by distributing the terms inside the parentheses. This gives you 3x - 15 = 2x + 6. Next, combine like terms by moving all terms with x to one side and the constants to the other side. Subtracting 2x from both sides gives x - 15 = 6. Finally, adding 15 to both sides results in x = 21. Therefore, the correct answer is A: x = 3. Choices B, C, and D are incorrect as they do not result from the correct calculations of the equation.
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In Jim's school, there are 3 girls for every 2 boys. There are 650 students in total. Using this information, how many students are girls?
- A. 260
- B. 130
- C. 65
- D. 390
Correct Answer: A
Rationale: To find the number of girls in Jim's school, we first establish the ratio of girls to boys as 3:2. This ratio implies that out of every 5 students (3 girls + 2 boys), 3 are girls and 2 are boys. Since there are a total of 650 students, we can divide them into 5 equal parts based on the ratio. Each part represents 650 divided by 5, which is 130. Therefore, there are 3 parts of girls in the school, totaling 3 multiplied by 130, which equals 390. Hence, there are 390 girls in Jim's school. Choice A, 260, is incorrect as it does not consider the correct ratio and calculation. Choice B, 130, is incorrect as it only represents one part of the total students, not the number of girls. Choice C, 65, is incorrect as it ignores the total number of students and the ratio provided.
What score must Dwayne get on his next math test to maintain an overall average of at least 90?
- A. 89
- B. 98
- C. 95
- D. 100
Correct Answer: B
Rationale: To maintain an overall average of at least 90, Dwayne must aim for a score of 90 on every test. If his current average is below 90, he needs to make up for it by scoring higher on upcoming tests. Choosing 98 ensures that his overall average remains at or above 90. Choice A (89) is below the desired average of 90, so it would not be sufficient. Choices C (95) and D (100) are higher than necessary to maintain an average of at least 90.
If Sarah reads at an average rate of 21 pages in four nights, how long will it take her to read 140 pages?
- A. 6 nights
- B. 26 nights
- C. 8 nights
- D. 27 nights
Correct Answer: D
Rationale: If Sarah reads 21 pages in four nights, she reads at a rate of 21 / 4 = 5.25 pages per night. To read 140 pages, she would need 140 / 5.25 = 26.67 nights. Since she cannot read a fraction of a night, it would take her 27 nights to read 140 pages, making option D the correct answer. Option A is incorrect as it does not accurately reflect the calculation. Option B is incorrect as it does not consider the fractional part of the calculation, resulting in an inaccurate answer. Option C is incorrect as it does not align with the correct calculation based on Sarah's reading rate.
Bernard can make $80 per day. If he needs to make $300 and only works full days, how many days will this take?
- A. 2
- B. 3
- C. 4
- D. 5
Correct Answer: C
Rationale: To find out how many days Bernard needs to work to make $300, we divide the total amount he needs by how much he makes per day: $300 / $80 = 3.75 days. Since Bernard can only work full days, he would need to work for 4 days to make $300. Therefore, the correct answer is 4 days. Choice A (2 days) is incorrect because it does not match the calculation based on his daily earnings. Choice B (3 days) is incorrect as the calculated result is not a whole number, so Bernard needs to work for more than 3 days. Choice D (5 days) is incorrect as it exceeds the calculated number of days needed to make $300.
Which measure for the center of a small sample set would be most affected by outliers?
- A. Mean
- B. Median
- C. Mode
- D. None of the above
Correct Answer: A
Rationale: The mean is calculated by summing all values in a dataset and then dividing by the total number of values. Outliers, which are data points significantly different from the other values, can greatly impact the mean because they affect the sum. The mean is sensitive to extreme values, making it the measure for the center of a small sample set most affected by outliers. The median, on the other hand, is not influenced by outliers as it represents the middle value when the data points are ordered. The mode is the value that appears most frequently in the dataset and is not directly influenced by outliers. Therefore, the correct answer is the mean, as it is highly influenced by outliers in a small sample set.