After spending 80% of her $60, Lana is left with how much money when she invests the remaining amount and earns an 80% profit?
Your Answer: Option(s)
Correct Answer: Option(s) A
Rationale
Lana is left with $21.60.
After spending 80% of her $60, Lana is left with $12. When she invests this remaining amount and earns an 80% profit, she makes an additional $9.60 ($12*0.8), which when added to the remaining $12, gives a total of $21.60.
A) $21.60
This is the correct answer. Lana spends 80% of her $60, leaving her with $12. When she invests this remaining amount and earns an 80% profit, she makes an additional $9.60 ($12*0.8). So, her total money after the investment is $12 + $9.60 = $21.60.
B) $9.60
This option only considers the profit that Lana earns from her investment and does not include the initial investment amount that she had left after spending 80% of her $60.
C) $86.40
This amount is incorrect as it exceeds Lana's initial amount of $60. After spending 80% of her $60, Lana is left with $12. When she invests this remaining amount and earns an 80% profit, she makes an additional $9.60, not $86.40.
D) $60.00
This option inaccurately suggests that Lana neither spent any of her money nor made any profit from her investment, which contradicts the information provided in the question.
Conclusion
Lana initially had $60. After spending 80% of this, she was left with $12. She then invested this amount and made an 80% profit, which resulted in an additional $9.60. Therefore, the total amount she had after investing and making a profit was $21.60.
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Question 2
Four friends are sharing a pizza. One friend eats half of the pizza. The other three friends equally divide the rest among themselves. What portion of the pizza did each of the other three friends receive?
Your Answer: Option(s)
Correct Answer: Option(s) D
Rationale
Each of the other three friends received 1/6 of the pizza.
After one friend ate half of the pizza, the remaining half was equally divided among the other three friends. Therefore, each of these three friends received one-third of the remaining half, which equates to 1/6 of the entire pizza.
A) 1/6
This option is incorrect. The fraction of 1/6 represents the correct share of the pizza that each of the three friends received after the first friend ate half of it.
B) 1/4
This option is incorrect. If the pizza was divided equally among all four friends, then each friend would receive 1/4 of the pizza. However, in this scenario, one friend ate half of the pizza, leaving the remaining half to be divided equally among the other three friends.
C) 1/3
This option is incorrect. If the pizza was divided equally among the three friends after the first friend ate half of it, then each of the three friends would receive 1/3 of the remaining half pizza, not 1/3 of the entire pizza.
D) 1/6
Each of the three friends received 1/6 of the pizza. After the first friend ate half of the pizza, the remaining half was divided equally among the other three friends. Each friend therefore received 1/3 of the remaining half, which equates to 1/6 of the entire pizza.
Conclusion
The question describes a scenario where one friend ate half of a pizza, and the remaining half was divided equally among three other friends. Therefore, each of these three friends received 1/3 of the remaining half, which is equivalent to 1/6 of the entire pizza. The other options of 1/4 and 1/3 do not correctly represent the share of the pizza that each of the remaining three friends received.
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Question 3
When the weights of newborn babies are graphed, the distribution of weights is symmetric with the majority of weights centered around a single peak. Which of the following describes the shape of this distribution?
Your Answer: Option(s)
Correct Answer: Option(s) D
Rationale
The distribution of the weights of newborn babies is bell-shaped.
This means that the data is symmetrically distributed around the mean, median, and mode, which are all equal in a bell-shaped distribution. The majority of the values are concentrated around the center, with fewer values occurring as we move farther away from the center in either direction.
A) Skewed right
In a right-skewed distribution, most of the data points fall to the left of the graph, with a long tail extending to the right. This means that a small number of very large values pull the mean to the right of the median. However, the newborn weights are symmetrically distributed, not skewed to the right.
B) Bimodal
A bimodal distribution has two peaks, indicating two different modes, or most common values, in the data set. The distribution of newborn weights is described as having a majority of weights centered around a single peak, not two, so it cannot be bimodal.
C) Uniform
A uniform distribution has roughly the same frequency of occurrence for all values in the data set, meaning that the graph would appear as a flat line. This does not describe the distribution of newborn weights, which is centered around a single peak.
D) Bell-shaped
A bell-shaped distribution, also known as a normal or Gaussian distribution, is symmetric and has a peak at the mean, median, and mode. This accurately describes the distribution of newborn weights, which is symmetric and centered around a single peak.
Conclusion
The weights of newborn babies follow a bell-shaped distribution, meaning that the weights are symmetrically distributed around a central peak. This distribution has a distinct shape with the majority of weights clustered around the mean, median, and mode, and fewer weights as you move away from the center in either direction. The other options - right-skewed, bimodal, and uniform - do not accurately describe this pattern of distribution.
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Question 4
How should the frequency for each day of the week that students get up after 8 a.m. be best displayed from a class survey?
Your Answer: Option(s)
Correct Answer: Option(s) A
Rationale
A bar graph would be the best way to display the frequency for each day of the week that students get up after 8 a.m. from a class survey.
A bar graph is ideal for comparing discrete categories or groups, such as days of the week. In this case, each day would be represented by a separate bar, and the height of the bar would indicate the frequency of students getting up after 8 a.m. on that particular day.
A) Bar graph
This is the correct choice because bar graphs are particularly useful for comparing quantities across different categories. In this context, the categories would be the days of the week, and the quantity to compare would be the number of students waking up after 8 a.m. each day.
B) Scatter plot
A scatter plot is not suitable for this kind of data. Scatter plots are typically used to display and compare numerical variables along two axes, which are useful for seeing relationships or correlations between two different variables. In the given question, there's only one variable (number of students waking up after 8 a.m.) across categorical data (days of the week), which doesn't fit with the scatter plot's typical use.
C) Histogram
A histogram is also not the best choice for this data. Histograms are used to display the distribution of continuous data, where data points are arranged into predetermined intervals or bins. The data set in the question is discrete (specific days of the week), not continuous, so a histogram would not be appropriate.
D) Pie chart
A pie chart isn't the best choice either. Pie charts are used to show proportions of a whole. In this scenario, we're not looking at proportions of a whole, but the frequency of an event (students waking up after 8 a.m.) across different categories (days of the week).
Conclusion
In representing categorical data, such as the days of the week, along with the frequency of an event, a bar graph is the most suitable choice. It distinctly illustrates each category with the frequency of the event occurring. Scatter plots, histograms, and pie charts are less effective for this set of data due to their respective uses for different kinds of data distribution and comparison.
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Question 5
How many milliliters are in 0.5 liters?
Your Answer: Option(s)
Correct Answer: Option(s) C
Rationale
There are 500 milliliters in 0.5 liters.
The conversion factor between liters and milliliters is 1 liter equals 1000 milliliters. Therefore, to convert 0.5 liters to milliliters, multiply 0.5 by 1000, which results in 500 milliliters.
A) 5,000
This answer would be correct if the conversion was for 5 liters instead of 0.5 liters. 5 liters equals 5000 milliliters, not 0.5 liters.
B) 5
This answer would be correct if the conversion was for 0.005 liters instead of 0.5 liters. 0.005 liters equals 5 milliliters, not 0.5 liters.
C) 500
This is the correct answer. 0.5 liters equals 500 milliliters. This is calculated by multiplying 0.5 liters by the conversion factor of 1000 milliliters per liter.
D) 50
This answer would be correct if the conversion was for 0.05 liters instead of 0.5 liters. 0.05 liters equals 50 milliliters, not 0.5 liters.
Conclusion
To convert liters to milliliters, we multiply the number of liters by 1000. Therefore, 0.5 liters equals 500 milliliters, not 5,000, 5, or 50 milliliters. Understanding the correct conversion factor is essential to accurately convert between different units of measurement.
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