All practice questions

A freight logistics company operates delivery trucks on two distinct transit routes: Route Alpha and Route Beta.

- On Route Alpha, trucks travel at a constant speed of $60$ miles per hour and consume fuel at a rate of $8$ gallons per hour.
- On Route Beta, trucks travel at a constant speed of $45$ miles per hour and consume fuel at a rate of $6$ gallons per hour.

Yesterday, a fleet of trucks completed a total combined distance of $900$ miles across both routes in a combined total operating time of $16$ hours.

Based on this information, select the option that correctly identifies both the ratio of the distance traveled on Route Alpha to the distance traveled on Route Beta (Column 1) and the percentage of total fuel consumed that was used on Route Alpha (Column 2).

A pharmaceutical laboratory uses two automated centrifuge units, Unit Alpha and Unit Beta, to process liquid compound solutions into a central storage tank.

- Unit Alpha processes a solution containing $15\%$ active compound at a constant rate of $40$ liters per hour.
- Unit Beta processes a solution containing $35\%$ active compound at a constant rate of $60$ liters per hour.

If both units operate simultaneously for $5$ hours, what is the percentage of active compound in the total combined solution collected in the tank?

A museum conservation board classifies historical artifacts into three management streams based on two parameters: Material Sensitivity (High or Moderate) and Structural Fragility Index (a numerical score from $1$ to $100$). The classification rules are defined as follows:

- Track Y (Long-Term Preservation): Assigned if an artifact has High Material Sensitivity AND a Structural Fragility Index score of at least $70$.
- Track X (Immediate Stabilization): Assigned if an artifact meets EXACTLY ONE of the two conditions (either High Material Sensitivity OR a Structural Fragility Index score of at least $70$, but not both).
- Routine Storage: Assigned if an artifact meets NEITHER condition (Moderate Material Sensitivity AND a Structural Fragility Index score below $70$).

Match each of the following three artifacts to its correct management stream.

A central logistics facility classifies incoming freight shipments into four priority processing queues—Queue 1 (Highest Priority), Queue 2, Queue 3, and Queue 4 (Lowest Priority)—based on two parameters: Hazard Level (High, Medium, Low) and Perishability Index (1 to 5, where 5 indicates maximum perishability).

The classification rules are as follows:
- Queue 1: Any shipment with a High Hazard Level, OR a Perishability Index of 4 or 5.
- Queue 2: Any shipment NOT in Queue 1 that has a Medium Hazard Level AND a Perishability Index of 3.
- Queue 3: Any shipment NOT in Queue 1 or 2 that has a Low Hazard Level with a Perishability Index of 3, OR a Medium Hazard Level with a Perishability Index less than 3.
- Queue 4: Any shipment NOT in Queue 1, 2, or 3 that has a Low Hazard Level with a Perishability Index of 1 or 2.

Four shipments are evaluated:
- Shipment Alpha: Low Hazard Level, Perishability Index of 5
- Shipment Beta: Medium Hazard Level, Perishability Index of 3
- Shipment Gamma: Medium Hazard Level, Perishability Index of 2
- Shipment Delta: Low Hazard Level, Perishability Index of 1

Based on the classification rules, in what sequence should these four shipments be arranged from highest priority queue (Queue 1) to lowest priority queue (Queue 4)?

A regional logistics operator manages cargo transit on a river corridor using two types of vessels: Express Barges ($E$) and Heavy-Haul Barges ($H$). Weekly operational constraints are defined as follows:

- Fuel Allowance: Each Express Barge consumes $8$ metric tons of fuel per trip, and each Heavy-Haul Barge consumes $12$ metric tons. Total weekly fuel consumption cannot exceed $144$ metric tons.
- Crew Availability: Each Express Barge requires $3$ crew shifts, and each Heavy-Haul Barge requires $2$ crew shifts. Total available crew shifts per week cannot exceed $30$.
- Service Minimum: The operator must deploy at least $2$ Heavy-Haul Barges ($H \ge 2$) per week to maintain baseline commercial obligations.
- Profit Structure: Each Express Barge generates a net profit of $\$5,000$, and each Heavy-Haul Barge generates a net profit of $\$6,000$.

Match each operational metric on the left with its correct optimal value under the profit-maximizing schedule of integer barge deployments.

A venture capital firm classifies its portfolio companies into four strategic management categories based on two quarterly performance metrics: Burn Multiple ($B$) and Customer Retention Rate ($R$).

Classification Criteria:
- Category 1 (Prime Growth): $B \le 1.5$ and $R \ge 85\%$
- Category 2 (Capital Efficient): $B \le 1.5$ and $R < 85\%$
- Category 3 (Expansion Focused): $B > 1.5$ and $R \ge 85\%$
- Category 4 (High Risk): $B > 1.5$ and $R < 85\%$

Match each portfolio company to its corresponding strategic management category.

A cloud analytics company configures daily data processing operations using two types of virtual server instances: Compute-Optimized ($C$) and Memory-Optimized ($M$). The operational parameters and constraints are as follows:

- Each $C$ instance processes 50 batch jobs per hour and incurs an operating cost of $15 per hour. - Each$ M $instance processes 30 batch jobs per hour and incurs an operating cost of$ 10 per hour.
- The system must process at least 360 batch jobs per hour in total.
- The total hourly operating budget for server instances cannot exceed $115. - Due to active database caching policies, at least 3$ M $instances must be active at all times ($ M \ge 3 $). -$ C $and$ M$ must both be non-negative integers.

Which of the following combinations of Compute ($C$) and Memory ($M$) server instances maximizes the total hourly job throughput while satisfying all operational constraints?

A metropolitan transit authority categorizes electric buses into three maintenance tiers based on two performance metrics: Cumulative Mileage (in thousands of kilometers) and Battery State of Health (SoH) (as a percentage).

The classification policy dictates:
- Tier I (Standard Operation): Cumulative Mileage $\le 200$ thousand km AND Battery SoH $\ge 85\%$.
- Tier II (Battery Refurbishment): Cumulative Mileage $\le 300$ thousand km with Battery SoH between $70\%$ and $84\%$ (inclusive); OR Cumulative Mileage between $201$ and $300$ thousand km (inclusive) with Battery SoH $\ge 85\%$.
- Tier III (Fleet Retirement): Cumulative Mileage $> 300$ thousand km OR Battery SoH $< 70\%$ regardless of mileage.

Two buses in the fleet present the following data:
- Bus X: Cumulative Mileage = $160$ thousand km; Battery SoH = $90\%$
- Bus Y: Cumulative Mileage = $180$ thousand km; Battery SoH = $82\%$

Based on the classification policy, which of the following correctly pairs Bus X and Bus Y with their respective maintenance tiers?

A municipal transit agency is installing two types of electric vehicle (EV) charging stations at a new central station: Level 2 Chargers ($L$) and Level 3 Fast Chargers ($D$). Each Level 2 charger costs $\$4,000$ to install and draws $10\text{ kW}$ of grid power. Each Level 3 charger costs $\$15,000$ to install and draws $50\text{ kW}$ of grid power. The agency has a total installation budget of $\$100,000$ and a maximum available grid power allocation of $320\text{ kW}$. To meet minimum service grant requirements, the hub must install at least 5 Level 2 chargers ($L \ge 5$) and at least 3 Level 3 chargers ($D \ge 3$). Each Level 2 charger can serve up to 8 sessions per day, and each Level 3 charger can serve up to 30 sessions per day. Match each operational optimization metric on the left with its corresponding correct value on the right that maximizes the total daily charging sessions served by the hub.

A boutique catering kitchen prepares custom corporate event packages containing two types of dessert selections: Specialty Layer Cakes ($L$) and Miniature Cupcake Sets ($M$). Each Specialty Layer Cake requires $3$ hours of decorating labor and $4$ kg of specialized flour. Each Miniature Cupcake Set requires $1$ hour of decorating labor and $2$ kg of specialized flour. For an upcoming event order, the kitchen has a maximum resource availability of $30$ total hours of decorating labor and $44$ kg of specialized flour. To meet client specifications, the kitchen must produce at least $4$ Specialty Layer Cakes. If each Specialty Layer Cake yields a profit of $\$50$ and each Miniature Cupcake Set yields a profit of $\$20$, which of the following pairs of $(L, M)$ represents the combination of Specialty Layer Cakes and Miniature Cupcake Sets that maximizes total profit while satisfying all resource constraints?

A printing company produces two types of customized marketing materials: Standard brochures ($S$) and Premium brochures ($P$). Each Standard brochure requires $2$ minutes of printing time and $1$ minute of binding time. Each Premium brochure requires $3$ minutes of printing time and $3$ minutes of binding time. The production facility has a maximum daily capacity of $240$ minutes for printing and $180$ minutes for binding. Due to a recurring client agreement, the facility must produce at least $20$ Standard brochures per day. The profit is $\$4$ per Standard brochure and $\$9$ per Premium brochure. Match each optimization variable or outcome on the left with its correct value on the right that maximizes daily total profit while satisfying all operational constraints.

A high-tech manufacturing firm produces custom drone components: Micro-Sensors ($S$) and Control Units ($U$). Each Micro-Sensor requires 2 hours of precision calibration and 1 GB of firmware memory allocation. Each Control Unit requires 5 hours of precision calibration and 4 GB of firmware memory allocation. For an upcoming production batch, the facility has a maximum of 40 hours of calibration time available and a maximum total memory allocation limit of 30 GB. If the firm earns a profit of $100 per Micro-Sensor and$ 350 per Control Unit, which of the following combinations of Micro-Sensors ($S$) and Control Units ($U$) maximizes total batch profit while satisfying all operational bounds?

A regional emergency health network deploys two types of mobile medical units for event coverage: Rapid Response Units ($R$) and Heavy Support Units ($H$).

The deployment is governed by the following staffing and operational constraints:
- Each Rapid Response Unit ($R$) requires $1$ paramedic and $2$ EMTs.
- Each Heavy Support Unit ($H$) requires $3$ paramedics and $1$ EMT.
- On any given shift, a maximum of $21$ paramedics and $22$ EMTs are available.
- Operational policy mandates deploying at least $3$ Rapid Response Units ($R \ge 3$) and at least $2$ Heavy Support Units ($H \ge 2$).

Each Rapid Response Unit can treat $10$ patients per hour, and each Heavy Support Unit can treat $15$ patients per hour.

Match each operational metric on the left to its corresponding optimal value on the right that maximizes total patient treatment capacity per hour.

A renewable energy company designs micro-grid installations containing two types of modular components: Battery Storage Units ($B$) and Solar Inverter Modules ($I$). The installation configuration is subject to the following system constraints:

1. Budget Bound: Each Battery Storage Unit costs \$4,000 and each Inverter Module costs \$2,000. The total installation budget cannot exceed \$32,000, giving the constraint$ 2B + I \le 16 $. 2. **Peak Power Requirement**: To meet grid stability requirements, the combined system rating must satisfy$ 3B + 4I \ge 30 $. 3. **Physical Space Limit**: Due to floor load capacity, a maximum of 6 Battery Storage Units can be installed ($ B \le 6$).