The Department of Education and Training announced on the afternoon of 3/6 that it had finalized the scoring guidelines for problem 5 of the math exam, worth 0,5 points.
The problem is as follows:
A company plans to rent a warehouse and deploy a number of workers to complete an order of 1000 products. Warehouse rental costs are calculated daily at 3 million VND per day. Each worker produces 5 products per day, and the company plans to reward each worker 1 million VND upon completion of the order. The company aims to minimize the total cost of warehouse rental and worker bonuses upon order completion. How many workers should the company deploy, and for how many days should it rent the warehouse?
The Department stated that this is an optimization problem related to real-life situations, concerning order fulfillment, with assumptions about completion, daily warehouse rental costs, and worker bonuses after order completion.
According to the scoring guidelines, students will receive 0,25 points if they complete all four steps:
- Define x as the number of workers to be deployed (x is a positive natural number).
- Define y as the number of days the warehouse is rented (y is a positive natural number).
- According to the problem, 5xy >= 1000.
- The total cost is S = x + 3y (million VND).
Subsequently, students will earn the remaining 0,25 points if they establish the expression S = x + 3y >= x + 600/x = [(x - 24)(x - 25)]/x + 49 >= 49, and then find x = 25 (workers) and y = 8 (days).
If students set the condition 5xy = 1000, they will lose 0,25 points for the above step, but will still receive 0,25 points for the subsequent step if done correctly, as agreed by the 38 math exam scoring team leaders.
In recent days, many teachers and experts have expressed differing opinions regarding whether the condition should be 5xy = 1000 or 5xy >= 1000. Many argue that since the problem requires completing 1000 products, using the '=' sign is appropriate.
However, some teachers hold a contrasting view. This group of educators argues that setting 5xy = 1000 from the outset overlooks cases such as x = 30, y = 7. In this scenario, 5xy = 1050, and the company still completes the 1000-product order, so such cases cannot be immediately excluded.
Problem 5 'coincidentally' works with the equality sign because the equation 5xy = 1000 has positive integer solutions. However, if the problem were changed to 1009 products, students could not 'force' 5xy = 1009, as the equation would not have positive integer solutions. Therefore, if the solution immediately sets 5xy = 1000 without explaining why equality is considered, the reasoning is not rigorous.
 |
10th-grade students taking the exam in Hanoi in 2026. Photo: Hoang Giang
Hanoi's public 10th-grade entrance exam took place on 30-31/5 with a record 124,000 candidates. With an enrollment target of approximately 82,660, the admission rate was 66% of those who took the exam.
The 10th-grade exam scoring process occurred from 31/5 to 10/6. Results are expected to be announced between 19-22/6.
Thanh Hang
