HBRI - Hogan Business Reasoning Inventory Quantitative Reasoning: Word Problems Questions and Answers — Questions and Answers
Question 1: A sales team of 5 members was projected to bring in $250,000 in revenue for the quarter. At the end of the quarter, the actual revenue was $310,000. However, two of the original team members had left mid-quarter and were not replaced. What was the percentage increase in revenue per salesperson compared to the original projection?
- 50
- 60
- 75 (Correct answer)
- 80
Correct answer: 75
First, calculate the initial number of invoices per employee: 500 invoices / 10 employees = 50 invoices/employee. Next, calculate the total increased output: 500 invoices * 1.20 = 600 invoices. After the reduction in staff, the new number of employees is 10 - 2 = 8. Finally, calculate the new rate per employee: 600 invoices / 8 employees = 75 invoices/employee.
Question 2: A company's marketing budget is allocated as follows: 40% for digital advertising, 30% for events, 20% for print media, and 10% for public relations. If the total budget is $500,000, and the company decides to decrease the print media budget by 25% and reallocate those funds to digital advertising, what will be the new budget for digital advertising?
- $200,000
- $225,000 (Correct answer)
- $250,000
- $275,000
Correct answer: $225,000
First, calculate the initial budget for print media: 20% of $500,000 is $100,000. Next, calculate the amount of the decrease: 25% of $100,000 is $25,000. This $25,000 is reallocated to digital advertising. The initial digital advertising budget was 40% of $500,000, which is $200,000. The new digital advertising budget is $200,000 + $25,000 = $225,000.
Question 3: A manufacturing plant produces 150 units per hour. The plant operates in two 8-hour shifts per day. If the cost to produce one unit is $12, and the company wants to achieve a daily production cost savings of $3,600, how many units per hour must the plant produce to meet this goal, assuming all other factors remain constant?
- 320
- 352
- 384 (Correct answer)
- 400
Correct answer: 384
First, find the production rate per hour for each machine. Machine 1: 80 widgets / 4 hours = 20 widgets/hour. Machine 2: 120 widgets / 5 hours = 24 widgets/hour. Now, calculate the total production for an 8-hour shift for each machine. Machine 1: 20 widgets/hour * 8 hours = 160 widgets. Machine 2: 24 widgets/hour * 8 hours = 192 widgets. Finally, add their outputs together: 160 + 192 = 352 widgets.
Question 4: A project manager estimates a project will take 4 programmers 120 hours each to complete. The total budgeted cost for their time is $48,000. Due to a deadline change, the project must be completed in a timeframe that only allows for 96 hours of work per programmer. Which of the following must happen to complete the project on time without increasing the total budgeted cost?
- Hire one additional programmer at a lower hourly rate.
- Increase the hourly rate for the existing programmers.
- Reduce the project scope by 20%.
- Hire one additional programmer at the same hourly rate. (Correct answer)
Correct answer: Hire one additional programmer at the same hourly rate.
First, calculate the total hours required: 4 programmers * 120 hours/programmer = 480 total hours. Next, find the hourly rate: $48,000 / 480 hours = $100/hour. With the new deadline, each of the 4 programmers can only work 96 hours, for a total of 4 * 96 = 384 hours. This leaves a deficit of 480 - 384 = 96 hours. To complete the project, an additional 96 hours of work are needed. Hiring one additional programmer to work the new maximum of 96 hours at the same rate ($100/hour) would fulfill the required hours and maintain the budget (5 programmers * 96 hours * $100/hour = $48,000).
Question 5: A retail store purchases jackets for $45 each and sells them for $75. During a sale, the remaining 50 jackets are discounted by 20%. What is the total profit earned on these 50 jackets if they all sell at the discounted price?
- $750 (Correct answer)
- $900
- $1,500
- $3,000
Correct answer: $750
First, calculate the discounted selling price. The original price is $75. A 20% discount is $75 * 0.20 = $15. The discounted price is $75 - $15 = $60. Next, calculate the profit per jacket at the discounted price: $60 (sale price) - $45 (cost) = $15 profit per jacket. Finally, calculate the total profit for the 50 jackets sold: 50 jackets * $15/jacket = $750.
Question 6: A subscription service has 12,000 users. 65% of users are on the 'Basic' plan and the rest are on the 'Premium' plan. The company wants to upsell users so that at least 40% of the total user base is on the 'Premium' plan. What is the minimum number of 'Basic' users that must be converted to 'Premium'?
- 4,200
- 1,200
- 600 (Correct answer)
- 4,800
Correct answer: 600
First, determine the current number of 'Premium' users. If 65% are 'Basic', then 100% - 65% = 35% are 'Premium'. The number of 'Premium' users is 12,000 * 0.35 = 4,200. Next, calculate the target number of 'Premium' users: 40% of 12,000 is 12,000 * 0.40 = 4,800. The number of users that need to be converted is the difference between the target and the current number: 4,800 - 4,200 = 600 users.
HBRI - Hogan Business Reasoning Inventory Quantitative Reasoning: Word Problems Questions and Answers
A sales team of 5 members was projected to bring in $250,000 in revenue for the quarter.
At the end of the quarter, the actual revenue was $310,000.
However, two of the original team members had left mid-quarter and were not replaced.
What was the percentage increase in revenue per salesperson compared to the original projection?