Resource Allocation and Queue Prioritization Practice Questions for XAT: 33+ Solved Questions with Step-by-Step Solutions

Solve 33+ Resource Allocation and Queue Prioritization practice questions for XAT with answers and detailed solutions. Free sample questions below.

Housing Allocation as Resource Distribution

Core principle:

When supply is limited and demand is high, allocation systems must establish rules for distribution.

Key characteristics:

Scarcity drives the need for allocation rules
Multiple stakeholders compete for limited units
Systems must balance efficiency with equity
Queues form naturally when demand exceeds supply

Queue Formation in Housing Systems

Queues emerge when housing demand exceeds available supply at any given time.

FIFO

Allocation based on application date

Priority-based

Allocation based on need or status

Hybrid

Combines time and priority elements

Queue metrics:

Wait time: Duration from application to allocation
Queue length: Number of applicants waiting
Turnover rate: How quickly units become available

Resource Allocation and Queue Prioritization: Solved Questions with Step-by-Step Explanations (5 Problems)

Question 1 · Decision Making (DM) MCQ

Context: A housing committee uses a priority scoring system for 4 applicants: A (Base 80), B (Base 70), C (Base 60), D (Base 50).

There are two types of exceptions:

Type X: +20 points. Eligible if Base Score < 70.
Type Y: +30 points. Eligible if Base Score < 60.

Rules:

Exceptions are allocated in order of Base Score (highest first).
There is exactly 1 slot for Type X and 1 slot for Type Y.
An applicant can claim only one exception.
Tie-breaker: If final scores are equal, the applicant who claimed the exception with the higher point value gets priority. If the exception values are the same, the one with the higher base score wins.

Applicant B realizes that by intentionally reducing their base score to 69 (e.g., by resigning and rejoining), they would become eligible for Type Y instead of Type X.

If B successfully games the system by reducing their base score to 69, what will be the final allocation order (from highest priority to lowest)?

A.
C, B, A, D
B.
B, A, C, D
C.
B, C, A, D
D.
A, B, C, D

Correct Answer:

Step-by-Step Solution

Key idea: This is a system gaming question recognisable by the eligibility thresholds and the incentive to manipulate base scores.

Step 1: Determine the new base scores. A=80, B=69 (gamed), C=60, D=50.

Step 2: Allocate exceptions in order of base score.

A (80): Not eligible for X (<70) or Y (<60). Score = 80.
B (69): Eligible for X (<70) and Y (<60). Since exceptions are allocated highest base first, B picks first. B will pick Y (+30) because it's higher. Score = 69 + 30 = 99.
C (60): Eligible for X and Y. Y is taken by B. C gets X (+20). Score = 60 + 20 = 80.
D (50): Both taken. Score = 50.

Step 3: Rank the final scores.

B: 99
A: 80
C: 80
D: 50

Step 4: Resolve the tie between A and C. Both have 80. A has no exception (value 0). C has Type X (value 20). C wins the tie-break.

Final Order: B, C, A, D.

Wait, let me re-evaluate the tie-breaker rule. "the applicant who claimed the exception with the higher point value gets priority". A claimed NO exception. C claimed X (+20). So C wins.

Order: B, C, A, D.

Let me check the options. Option C is "B, C, A, D".

Wait, in my thought process I said Option B is "B, A, C, D". Let me fix the solution to match the correct option.

If B=99, C=80, A=80. C wins tie over A. So B, C, A, D.

Let me adjust the options in the YAML to make "B, C, A, D" the correct answer.

Answer: C

Question 2 · Decision Making (DM) MCQ

Context: A company has a strict First-In-First-Out (FIFO) housing queue. Employee E is 50th in the queue. The CEO wants to move E to the top to reward exceptional performance. The Union strongly opposes this, citing the FIFO policy.

The HR head proposes a compromise: "E must voluntarily negotiate with the 49 employees ahead in the queue to reach a consensus on a non-monetary swap or compensation. HR will only formalize the exception if a unanimous consensus is reached."

Assertion (A): This consensus-based approach is the most appropriate Decision Making action because it balances the CEO's desire to reward E with the Union's demand for fairness, without violating the core FIFO policy.

Reason (R): By making the exception contingent on voluntary consensus, the system preserves FIFO as the default rule, ensures no financial precedent is set, and distributes the cost of the exception among the willing stakeholders.

Options:

A) Both A and R are true and R is the correct explanation of A.

B) Both A and R are true but R is not the correct explanation of A.

C) A is true but R is false.

D) A is false but R is true.

A.
Both A and R are true and R is the correct explanation of A.
B.
Both A and R are true but R is not the correct explanation of A.
C.
A is true but R is false.
D.
A is false but R is true.

Correct Answer:

Step-by-Step Solution

Key idea: This is a stakeholder management question recognisable by the conflict between a top-down directive (CEO) and a structural rule (Union/FIFO).

Step 1: Evaluate Assertion (A). The consensus approach satisfies the CEO (E can still move up if consensus is reached), satisfies the Union (FIFO is not arbitrarily broken, and no one is forced to move), and maintains fairness (stakeholders have agency). Thus, A is true.

Step 2: Evaluate Reason (R). The reason correctly identifies the mechanism: voluntary consensus shifts the burden from the system to the individuals. It preserves FIFO as the default, avoids setting a monetary precedent (which could lead to future demands), and ensures that those displaced are compensated in a way they find acceptable. Thus, R is true.

Step 3: Check the link. R directly explains WHY A is the most appropriate action. The mechanism described in R is exactly what makes the approach in A successful and policy-compliant.

Answer: A

Question 3 · Decision Making (DM) MCQ

When designing housing allocation systems, what two principles must be balanced?

A.
Efficiency and equity
B.
Speed and cost
C.
Hierarchy and seniority
D.
Demand and supply

Correct Answer:

Step-by-Step Solution

Key idea: This is a recall question about system design principles.

Step 1: Recall from smart notes.

From hap_006 "Balancing Equity and Efficiency": "Systems must balance efficiency with equity"

From hap_001: "Systems must balance efficiency with equity" is listed as a key characteristic.

Step 2: Understand the concepts.

Efficiency: Allocating resources quickly, minimizing waste, maximizing utilization
Equity: Fair distribution, treating similar cases similarly, addressing needs

Step 3: Evaluate options.

Option A directly matches the smart notes - efficiency and equity
Options B, C, D are related concepts but not the primary balance in allocation system design

Answer: A

Question 4 · Decision Making (DM) MCQ

A housing authority defines system balance as:

$Balance = Efficiency \times Equity$

where:

$Efficiency = \frac{units allocated}{total wait time in months}$
$Equity = 1 - \frac{standard deviation of final scores}{mean of final scores}$

Current system: 10 units allocated, total wait time = 50 months, mean final score = 100, standard deviation = 20.

A proposed "fast-track" exception changes the system to: 10 units allocated, total wait time = 45 months, mean final score = 100, standard deviation = 40.

Does the proposed change improve the system balance, and what is the new Equity value?

A.
Yes, new Equity = 0.6
B.
No, new Equity = 0.6
C.
Yes, new Equity = 0.8
D.
No, new Equity = 0.4

Correct Answer:

Step-by-Step Solution

Key idea: this is a comparison question — compute Balance before and after, and check whether it increases.

Step 1: compute current Efficiency and Equity.

Efficiency = 10 / 50 = 0.2

Equity = 1 - (20 / 100) = 1 - 0.2 = 0.8

Balance = 0.2 × 0.8 = 0.16

Step 2: compute new Efficiency and Equity.

Efficiency = 10 / 45 ≈ 0.222

Equity = 1 - (40 / 100) = 1 - 0.4 = 0.6

Balance = 0.222 × 0.6 ≈ 0.133

Step 3: compare.

New Balance (0.133) < Old Balance (0.16), so the change does NOT improve balance.

New Equity = 0.6.

Common trap: assuming any efficiency gain improves balance, or miscalculating Equity (e.g., using variance instead of std dev, or forgetting the "1 -" in the formula).

Answer: B

Question 5 · Decision Making (DM) MSQ

A housing policy states the following rules for exceptions:

An applicant is eligible for a medical exception (queue jump) if they have a chronic illness.
If the applicant's income exceeds $50, 000, t h e m e d i c a l e x ce pt i o ni s d o w n g r a d e d t o a$ 2,000 financial subsidy instead of a queue jump.
Any applicant who receives a financial subsidy is barred from applying for a secondary "large family" exception (which requires $\geq 4$ children).

Consider the following four applicants:

A: Chronic illness, income $45,000, 4 children.
B: Chronic illness, income $60,000, 2 children.
C: No chronic illness, income $40,000, 5 children.
D: Chronic illness, income $55,000, 4 children.

Which of the following statements are TRUE? (Select all that apply)

A.
A receives a queue jump and can also claim the large family exception.
B.
B receives a financial subsidy and is barred from the large family exception.
C.
C is ineligible for any exceptions because their income is below $50,000.
D.
D receives a queue jump due to the large family exception.
E.
If A's income was $55,000, they would receive a financial subsidy and be barred from the large family exception.

Correct Answer:

["A","B","E"]

Step-by-Step Solution

Key idea: this is an observation question involving conditional eligibility — you must trace each applicant through the sequential rules to determine their final exception status.

Step 1: analyze the rules.

Rule 1: Chronic illness $\to$ medical exception (queue jump).
Rule 2: Income > $50 k$ \rightarrow $m e d i c a l e x ce pt i o n d o w n g r a d e d t o$ 2k subsidy.
Rule 3: Subsidy received $\to$ barred from large family exception ( $\geq 4$ children).

Step 2: evaluate Applicant A.

Chronic illness $\to$ eligible for medical exception.
Income $45 k$ \leq50k $\to$ keeps queue jump (no subsidy).
No subsidy $\to$ eligible for large family exception (has 4 children).
Statement A is TRUE.

Step 3: evaluate Applicant B.

Chronic illness $\to$ eligible for medical exception.
Income $60 k >$ 50k $\to$ downgraded to $2k subsidy.
Subsidy received $\to$ barred from large family exception.
Statement B is TRUE.

Step 4: evaluate Applicant C.

No chronic illness $\to$ no medical exception.
Income $40 k$ \leq50k $\to$ irrelevant for medical rule.
5 children $\geq$ 4 $\to$ eligible for large family exception.
Statement C is FALSE.

Step 5: evaluate Applicant D.

Chronic illness $\to$ eligible for medical exception.
Income $55 k >$ 50k $\to$ downgraded to $2k subsidy.
Subsidy received $\to$ barred from large family exception.
Statement D is FALSE.

Step 6: evaluate the hypothetical for A.

If A's income was $55 k >$ 50k $\to$ downgraded to subsidy.
Subsidy received $\to$ barred from large family exception.
Statement E is TRUE.

Common trap: assuming that a low income automatically disqualifies someone from all exceptions, ignoring the large family exception.

Answer: A, B, E

A question from this chapter

Question 1

Context: A housing committee uses a priority scoring system for 4 applicants: A (Base 80), B (Base 70), C (Base 60), D (Base 50). There are two types of exceptions: Type X: +20 points. Eligible if Base Score < 70. Type Y: +30 points. Eligible if Base Score < 60. Rules: Exceptions are allocated in order of Base Score (highest first). There is exactly 1 slot for Type X and 1 slot for Type Y. An applicant can claim only one exception. Tie-breaker: If final scores are equal, the applicant who claimed the exception with the higher point value gets priority. If the exception values are the same, the one with the higher base score wins. Applicant B realizes that by intentionally reducing their base score to 69 (e.g., by resigning and rejoining), they would become eligible for Type Y instead of Type X. If B successfully games the system by reducing their base score to 69, what will be the final allocation order (from highest priority to lowest)?

Question 2

Context: A company has a strict First-In-First-Out (FIFO) housing queue. Employee E is 50th in the queue. The CEO wants to move E to the top to reward exceptional performance. The Union strongly opposes this, citing the FIFO policy. The HR head proposes a compromise: "E must voluntarily negotiate with the 49 employees ahead in the queue to reach a consensus on a non-monetary swap or compensation. HR will only formalize the exception if a unanimous consensus is reached." Assertion (A): This consensus-based approach is the most appropriate Decision Making action because it balances the CEO's desire to reward E with the Union's demand for fairness, without violating the core FIFO policy. Reason (R): By making the exception contingent on voluntary consensus, the system preserves FIFO as the default rule, ensures no financial precedent is set, and distributes the cost of the exception among the willing stakeholders. Options: A) Both A and R are true and R is the correct explanation of A. B) Both A and R are true but R is not the correct explanation of A. C) A is true but R is false. D) A is false but R is true.

Question 3

When designing housing allocation systems, what two principles must be balanced?

Question 4

A housing authority defines system balance as: Balance = Efficiency \times Equity where: Efficiency = \frac{units allocated}{total wait time in months} Equity = 1 - \frac{standard deviation of final scores}{mean of final scores} Current system: 10 units allocated, total wait time = 50 months, mean final score = 100, standard deviation = 20. A proposed "fast-track" exception changes the system to: 10 units allocated, total wait time = 45 months, mean final score = 100, standard deviation = 40. Does the proposed change improve the system balance, and what is the new Equity value?

Question 5

A housing policy states the following rules for exceptions: An applicant is eligible for a medical exception (queue jump) if they have a chronic illness. If the applicant's income exceeds 50, 000, t h e m e d i c a l e x ce pt i o ni s d o w n g r a d e d t o a 2,000 financial subsidy instead of a queue jump. Any applicant who receives a financial subsidy is barred from applying for a secondary "large family" exception (which requires \geq 4 children). Consider the following four applicants: A: Chronic illness, income $45,000, 4 children. B: Chronic illness, income $60,000, 2 children. C: No chronic illness, income $40,000, 5 children. D: Chronic illness, income $55,000, 4 children. Which of the following statements are TRUE? (Select all that apply)

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Resource Allocation and Queue Prioritization Practice Questions for XAT: 33+ Solved Questions with Step-by-Step Solutions

Housing Allocation as Resource Distribution

Housing Allocation as Resource Distribution

Key characteristics:

Queue Formation in Housing Systems

Queue Formation in Housing Systems

Queue metrics:

Resource Allocation and Queue Prioritization: Solved Questions with Step-by-Step Explanations (5 Problems)

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

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