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Question 1
The total of the prices of two pans is $25.94, and the price of the more expensive pan is $5.96 greater than the price of the less expensive pan. What is the price of the more expensive pan?
Your Answer: Option(s)
Correct Answer: Option(s) D
Rationale
The price of the more expensive pan is $15.95.
To find the price of the more expensive pan, we can set up a system of equations based on the information provided. If we let the price of the less expensive pan be x, then the price of the more expensive pan would be x + $5.96. The total price of both pans is $25.94, leading to the equation: x + (x + 5.96) = 25.94. Solving this gives us the price of the more expensive pan as $15.95.
A) $9.99
If the more expensive pan were priced at $9.99, then the less expensive pan would need to be priced at $4.03 ($9.99 - $5.96). This results in a total of $14.02, which does not match the given total of $25.94.
B) $12.97
Choosing $12.97 as the price for the more expensive pan would imply the less expensive pan costs $6.01 ($12.97 - $5.96). This totals to $18.98, which again does not equal the required total of $25.94.
C) $14.05
If the more expensive pan is $14.05, then the less expensive pan would cost $8.09 ($14.05 - $5.96). Together, they would total $22.14, which is still short of the required total of $25.94.
D) $15.95
Setting the price of the more expensive pan at $15.95 allows for a less expensive pan price of $9.99 ($15.95 - $5.96). This gives a total of $25.94, perfectly matching the total given in the question.
E) $16.98
If the more expensive pan were $16.98, the less expensive pan would have to cost $10.02 ($16.98 - $5.96). This results in a total of $27.00, which exceeds the stated total of $25.94.
Conclusion
The price of the more expensive pan is accurately determined to be $15.95. This value is consistent with the conditions provided in the question, where the total of both pans sums to $25.94, and the price difference aligns precisely with the given parameters. The other options do not satisfy these conditions, confirming that $15.95 is the only valid solution.
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Question 2
Last week at a certain grocery store, 60 employees each worked 30 hours either at a cash register or stocking shelves. Of these employees, 1/5 worked at a cash register 20 hours, ¼ worked at a cash register 12 hours, 1/3 worked at a cash register 15 hours, and the remaining employees worked at a cash register 24 hours last week. What was the average (arithmetic mean) of the numbers of hours that these employees worked stocking shelves last week?
Your Answer: Option(s)
Correct Answer: Option(s) A
Rationale
The average number of hours that these employees worked stocking shelves last week is 12.8.
To determine the average hours worked stocking shelves, we first need to establish the total hours worked by all 60 employees and then subtract the hours spent at cash registers to find the hours spent stocking shelves.
A) 12.8
This choice accurately reflects the average hours worked stocking shelves, calculated by assessing the total hours dedicated to cash registers and then finding the remaining hours that employees spent in stocking shelves. After detailed calculations, it is confirmed that the average is indeed 12.8 hours.
B) 14
Choosing 14 suggests a miscalculation in determining the total hours worked at cash registers. The arithmetic mean should reflect the remaining hours after calculating the proper distribution of hours worked in both roles, which does not align with this figure based on the data provided.
C) 15.8
This option also indicates an incorrect computation of total hours worked at cash registers, leading to an overestimate of the average hours spent stocking shelves. The average should account for the specific distribution of hours worked at cash registers, which does not support this value.
D) 16.4
The selection of 16.4 represents a significant overestimation of the average hours. This figure fails to accurately correspond to the total hours worked at cash registers and does not consider the proper subtraction to find the hours spent stocking shelves.
E) 18
Choosing 18 suggests a substantial misunderstanding of the distribution of work hours. This value implies that the employees spent far more time stocking shelves than what the calculations reveal, thus not aligning with the hour allocations provided in the scenario.
Conclusion
In summary, the average number of hours worked by the employees stocking shelves is 12.8, derived from careful calculations of total hours worked at cash registers. This value demonstrates the importance of accurate arithmetic operations in determining averages from segmented work hours, ensuring clarity in workforce management analytics.
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Question 3
A certain factory normally produces 500 units per hour for a 7(1/2)-hour workday. In a month with 22 workdays, no units are produced in the first 7 days because of a job action. By how many units must production increase on each of the remaining workdays of the month in order to meet normal production levels for the month?
Your Answer: Option(s)
Correct Answer: Option(s) C
Rationale
Production must increase by 1,750 units on each remaining workday.
To meet normal production levels after a week of no production, the factory needs to calculate the increased output required per day for the remaining workdays in the month. Given the total production goal and the days lost, this translates to an increase of 1,750 units per day.
A) 500
This option represents the normal production rate per hour but does not account for the total production needed to make up for the lost units. A mere increase of 500 units per day would not suffice to reach the target production level after losing an entire week.
B) 688
An increase of 688 units is insufficient because it does not consider the total production goal of 3,750 units needed to compensate for the lost production after the job action. This figure does not reflect the necessary adjustments to meet the monthly target.
C) 1,750
This is the correct answer because the factory needs to produce an additional 1,750 units for each of the remaining workdays. With 15 workdays left after the 7-day job action, this increase allows the factory to meet the normal monthly production target of 11,250 units.
D) 3,750
This figure represents the total units that were not produced during the first week rather than the daily increase required. It does not provide a per-day increase that can be sustained across the remaining workdays to fulfill the production goal.
E) 5,500
An increase of 5,500 units per day is excessively high and unrealistic. This number exceeds the total monthly production requirement and suggests a misunderstanding of the production goals and time frame involved in compensating for the lost workdays.
Conclusion
To recover from the production loss due to the job action, the factory must increase its output by 1,750 units per day over the remaining 15 workdays. This adjustment ensures that it meets the monthly production goal of 11,250 units, highlighting the importance of accurate calculations in manufacturing operations.
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Question 4
Each week Ingrid earns a fixed salary and a sales commission that is a fixed percentage of her sales for that week. Ingrid has no other sources of income. Last week Ingrid's total earnings were $500 and her sales were $2,000. This week Ingrid's total earnings were $700 and her sales were $6,000. What is the percentage rate for Ingrid's sales commissions?
Your Answer: Option(s)
Correct Answer: Option(s) C
Rationale
Ingrid's sales commission percentage rate is 5%.
Ingrid's earnings consist of a fixed salary plus a commission based on her sales. By analyzing her total earnings and sales for the two weeks, we can determine that her commission rate is 5%.
A) 0.05%
This option suggests an extremely low commission rate which would not account for Ingrid's total earnings given her sales figures. With sales of $2,000 and a commission of only 0.05%, her total earnings would not reach $500, indicating that this option is incorrect.
B) 4%
If Ingrid's commission rate were 4%, her commission from sales of $2,000 would yield only $80, resulting in total earnings of far less than $500 when combined with her fixed salary. Similarly, with sales of $6,000, the earnings would not reach $700, making this option invalid.
C) 5%
This is the correct answer. At a commission rate of 5%, Ingrid earns $100 from $2,000 in sales (5% of 2000) in the first week. If her fixed salary is $400, her total earnings equal $500. In the second week, she earns $300 from $6,000 in sales (5% of 6000), totaling $700 when added to the same salary of $400, confirming the commission rate.
D) 20%
A commission rate of 20% would result in excessive earnings based on her sales figures. For instance, at 20%, her commission for $2,000 in sales would be $400, leading to total earnings of $800, which exceeds the reported $500.
E) 30%
This option suggests an even higher commission rate, which would lead to total earnings that far surpass what Ingrid reported. At 30%, her commission for $2,000 in sales would be $600, resulting in total earnings of $1,000, which is not possible according to the question.
Conclusion
Ingrid's commission rate of 5% accurately reflects her earnings based on the provided sales data. The calculations for both weeks confirm that this percentage allows her fixed salary and commission to align with her reported total earnings. Incorrect options fail to meet the earnings criteria established in the question, reinforcing the conclusion that 5% is the only viable commission rate.
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Question 5
In a certain list of numbers, the first number is 2, the second number is 3, and each succeeding number is the sum of all the numbers that precede it in the list. If hand k denote the 20th and 24th numbers in the list, respectively, what is the value of k/h?
Your Answer: Option(s)
Correct Answer: Option(s) D
Rationale
k/h equals 16.
In the given sequence, each number is derived from the sum of all preceding numbers, leading to exponential growth. By calculating the 20th and 24th terms, we find their ratio to equal 16.
A) 5
The ratio k/h equating to 5 would imply that the 20th number is significantly smaller than the 24th number; however, the growth of the sequence results in much larger values, making this choice inconsistent with the calculated values.
B) 8
Selecting 8 as the ratio would mean that the 24th number is eight times the 20th number. Given the exponential growth of the sequence, this ratio does not hold true, as the values escalate much more rapidly.
C) 10
A ratio of 10 suggests that the 24th number is ten times the 20th. However, the actual numbers in the sequence grow at a rate that does not support such a ratio, as the terms increase dramatically due to their recursive nature.
D) 16
This choice indicates that the 24th number is 16 times larger than the 20th number. Upon calculating the specific terms in the sequence, this ratio is confirmed, making it the correct solution.
E) 20
If k/h were equal to 20, it would imply an even larger discrepancy between the 20th and 24th numbers than what is present. The rapid growth of the sequence rules out this option as well.
Conclusion
The sequence grows exponentially due to its recursive definition, leading to the conclusion that the ratio of the 20th and 24th numbers is 16. This ratio reflects the significant increase in value as more terms are added, ultimately demonstrating the unique nature of this sequence.
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