Q1. Al revisar los puntajes promedio de cuatro cursos en dos años, ¿es correcta la afirmación de que hubo un aumento en el puntaje respecto al año anterior?

Background

Topic: Data Interpretation and Averages

This question tests your ability to interpret data from a table, compare averages, and evaluate the validity of a claim based on numerical evidence.

Key Terms and Formulas

• Average (mean): The sum of all values divided by the number of values.

• Total average: When groups are of equal size, the overall average is the mean of the group averages.

Step-by-Step Guidance

1. List the average scores for each course in both years from the table.

2. Calculate the total average for each year by adding the four course averages and dividing by 4.

3. Compare the total averages for the two years to determine if there was an increase or decrease.

4. Consider whether the claim is about the majority of courses or the overall average, and check which is supported by the data.

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Q2. Si una inversión en dólares gana 3% y la tasa de cambio dólar-peso se mantiene constante, ¿las ganancias en pesos también serán del 3%?

Background

Topic: Percentages and Currency Exchange

This question tests your understanding of how percentage gains translate across currencies when the exchange rate is constant.

Key Terms and Formulas

• Percentage increase: If an amount increases by x%, the new amount is the original multiplied by (1 + x/100).

• Constant exchange rate: The value in pesos is always 4,000 times the value in dollars.

Step-by-Step Guidance

1. Let the initial investment in dollars be .

2. After a 3% gain, the investment becomes dollars.

3. Convert both the initial and final amounts to pesos using the constant exchange rate.

4. Calculate the percentage increase in pesos and compare it to the percentage increase in dollars.

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Q3. ¿La elección de las franjas 1, 3 y 4 garantiza que todos los estudiantes asistan al museo al menor precio posible?

Background

Topic: Optimization and Cost Minimization

This question tests your ability to analyze constraints (maximum capacities) and optimize total cost for a group.

Key Terms and Formulas

• Optimization: Choosing options that minimize total cost while meeting all requirements.

• Total cost: Sum of (number of students in each group) × (price per student for that group).

Step-by-Step Guidance

1. List the capacities and prices for each time slot (franja).

2. Check if the sum of the maximum students in franjas 1, 3, and 4 is at least 140.

3. Calculate the total cost for using franjas 1, 3, and 4 at full capacity.

4. Consider if using franja 2 instead of franja 3 could result in a lower total cost, and check if all students can still attend.

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Q4. Si la empresa paga $4.200.000 por capacitar a los trabajadores de la dependencia “Insumos” en el módulo I, ¿cuántos empleados tiene esta dependencia?

Background

Topic: Proportional Reasoning and Unit Cost

This question tests your ability to use unit rates and total cost to find the number of participants.

Key Terms and Formulas

• Total cost: Number of employees × hours per module × cost per hour.

• Equation:

Step-by-Step Guidance

1. Identify the intensity (hours) and value per hour for module I from the table.

2. Set up the equation:

3. Solve for (number of employees) by isolating $n$ in the equation.

4. Check if the result falls within the ranges given in the answer choices.

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Q5. Si 50 trabajadores toman el módulo II, ¿cuánto debe pagar cada uno por la capacitación?

Background

Topic: Division of Total Cost Among Participants

This question tests your ability to calculate the per-person cost when a total cost is shared equally.

Key Terms and Formulas

• Total cost for module II:

• Per-person cost:

Step-by-Step Guidance

1. Find the hours and value per hour for module II from the table.

2. Calculate the total cost:

3. Divide the total cost by 50 to find the amount each worker pays.

4. Compare your result to the answer choices.

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Q6. Si la empresa paga $900.000 por capacitar a 40 funcionarios de “Importaciones”, ¿qué módulo tomaron?

Background

Topic: Reverse Calculation Using Unit Rates

This question tests your ability to match a total cost to a module based on the number of participants, hours, and hourly rate.

Key Terms and Formulas

• Total cost:

Step-by-Step Guidance

1. For each module, calculate the total cost for 40 employees using the given hours and hourly rate.

2. Compare each calculated total to to see which matches.

3. Identify the module whose calculation gives the correct total.

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