Logical Reasoning and Analytical Ability Practice Questions — State PSC Exam — Page 2

Question 21Question →

Consider the following statements regarding modern smart-city infrastructure:
1. All autonomous vehicles are sensor-equipped machines.
2. No sensor-equipped machines are completely unpredictable systems.
3. Some completely unpredictable systems are weather phenomena.

Which of the following candidate conclusions logically follow from the given statements? Select all that apply.

Select all that apply

No autonomous vehicles are completely unpredictable systems.

Some weather phenomena are not sensor-equipped machines.

All sensor-equipped machines are autonomous vehicles.

Some autonomous vehicles are weather phenomena.

Show answer & explanation

Answer: No autonomous vehicles are completely unpredictable systems.; Some weather phenomena are not sensor-equipped machines.

Answer

The logically valid conclusions are: 'No autonomous vehicles are completely unpredictable systems' and 'Some weather phenomena are not sensor-equipped machines'.

The first valid conclusion correctly deduces that if the set of autonomous vehicles is entirely contained within the set of sensor-equipped machines, and the set of sensor-equipped machines is completely separate from the set of unpredictable systems, then autonomous vehicles must also be completely separate from unpredictable systems. The second valid conclusion correctly notes that since a portion of weather phenomena overlaps with unpredictable systems, and unpredictable systems are completely separate from sensor-equipped machines, that overlapping portion of weather phenomena cannot be sensor-equipped machines.

Step-by-Step Solution

1

Analyze the relationship between autonomous vehicles, sensor-equipped machines, and unpredictable systems.

Since every autonomous vehicle is a sensor-equipped machine, and no sensor-equipped machine is an unpredictable system, it follows that no autonomous vehicle can be an unpredictable system.

Applying the logical deduction rule for universal affirmative and universal negative premises.

2

Analyze the relationship between weather phenomena, unpredictable systems, and sensor-equipped machines.

We know some unpredictable systems are weather phenomena. Since unpredictable systems cannot be sensor-equipped machines, the specific weather phenomena that are unpredictable systems also cannot be sensor-equipped machines.

Applying the logical deduction rule for particular affirmative and universal negative premises.

3

Evaluate the remaining candidate conclusions for logical validity.

The conclusion stating that all sensor-equipped machines are autonomous vehicles is an invalid conversion. The conclusion linking autonomous vehicles to weather phenomena is invalid because no direct relationship is established between them in the premises.

Conclusions must be definitively proven by the given statements without external assumptions.

Key Concept

Evaluating categorical propositions and identifying valid logical deductions using standard syllogism rules.

Question 22Question →

Seven scientists—Dr. Aris, Dr. Bell, Dr. Chen, Dr. Diaz, Dr. Evans, Dr. Ford, and Dr. Grant—are seated at equal distances around a circular table. Some are facing the center, while others are facing outward.

1. Dr. Ford faces the center. Dr. Chen sits second to the left of Dr. Ford.
2. Dr. Grant sits third to the right of Dr. Chen. Dr. Grant faces outward.
3. Dr. Aris sits to the immediate left of Dr. Grant.
4. Dr. Evans sits second to the right of Dr. Aris, and faces the same direction as Dr. Ford.
5. Dr. Bell is not an immediate neighbor of Dr. Chen.
6. Dr. Diaz and Dr. Bell face opposite directions.
7. Both immediate neighbors of Dr. Chen face the center.

Based on the seating arrangement, which of the following statements is definitely true?

Exactly two scientists sit between Dr. Ford and Dr. Evans when counted clockwise from Dr. Ford.

Dr. Ford sits second to the left of Dr. Chen.

Dr. Diaz sits third to the right of Dr. Grant.

Dr. Bell faces the center and sits to the immediate left of Dr. Evans.

Show answer & explanation

Answer: Exactly two scientists sit between Dr. Ford and Dr. Evans when counted clockwise from Dr. Ford.

Answer

Exactly two scientists sit between Dr. Ford and Dr. Evans when counted clockwise from Dr. Ford.

When the complete seating arrangement is deduced, Dr. Ford is at position 1 and Dr. Evans is at position 4. Counting clockwise from Dr. Ford (positions 1 to 4), there are exactly two seats (positions 2 and 3), which are occupied by Dr. Diaz and Dr. Chen.

Step-by-Step Solution

1

Fix Dr. Ford's position and place Dr. Chen.

Dr. Ford is at position 1 (facing center). Since left is clockwise for center-facing, Dr. Chen is at position 3.

Establishing a relative starting point is necessary for circular arrangements.

2

Determine Dr. Chen's facing direction to place Dr. Grant.

If Dr. Chen faced outward, Dr. Grant would be at position 6, forcing Dr. Aris to position 5, and Dr. Evans to position 7. This leaves positions 2 and 4 for Dr. Bell and Dr. Diaz. However, Dr. Bell cannot be adjacent to Dr. Chen, so Dr. Bell would have no valid seat. Thus, Dr. Chen MUST face the center. Therefore, Dr. Grant sits at position 7 (facing outward).

Testing hypotheses for facing directions ensures we avoid logical dead-ends later in the puzzle.

3

Place Dr. Aris and Dr. Evans.

Dr. Grant faces outward, so left is anti-clockwise. Dr. Aris sits at position 6. To place Dr. Evans second to the right of Dr. Aris into an empty seat, Dr. Aris must face the center (placing Dr. Evans at position 4). Dr. Evans also faces the center (same as Dr. Ford).

Directionality of Dr. Grant directly determines Dr. Aris's location, which chains into Dr. Evans's location.

4

Place the remaining scientists and determine final facing directions.

Positions 2 and 5 are empty. Dr. Bell cannot be adjacent to Dr. Chen (position 3), so Dr. Bell takes position 5, leaving position 2 for Dr. Diaz. Dr. Chen's neighbors (Dr. Diaz and Dr. Evans) both face the center. Since Dr. Diaz faces the center, Dr. Bell must face outward (opposite to Dr. Diaz).

Fulfilling the negative constraint (not an immediate neighbor) resolves the final positions, and the neighboring condition resolves the remaining directions.

Key Concept

Circular seating arrangements with mixed facing directions

Question 23Question →

In a certain coded language, family relationships are represented as follows:

$P \star Q$ means $P$ is the father of $Q$ .
$P \diamond Q$ means $P$ is the mother of $Q$ .
$P \triangle Q$ means $P$ is the brother of $Q$ .
$P \nabla Q$ means $P$ is the sister of $Q$ .

Based on the expression $Kiran \star Anjali \nabla Samir \triangle Rohan$ , what is the relationship of Rohan to Kiran?

Son

Daughter

Grandson

Cannot be determined

Show answer & explanation

Answer: Cannot be determined

Answer

The relationship cannot be determined because Rohan's gender is not explicitly stated in the expression.

The expression establishes that Anjali, Samir, and Rohan are all siblings, placing them in the generation immediately below Kiran. Because Kiran is Anjali's father, Kiran is the father of all three. However, the expression ends with '

Samir \triangle Rohan

', which only tells us that Samir is a brother to Rohan. It provides zero information about Rohan's gender. Because strict logical reasoning rules dictate that gender cannot be assumed from a proper name, Rohan could be either the son or the daughter of Kiran. Therefore, the exact relationship cannot be definitively determined.

Step-by-Step Solution

1

Decode the first relationship:

Kiran \star Anjali

.

Kiran is the father of Anjali.

The

\star

symbol designates the first person as the father of the second person.

2

Decode the second relationship:

Anjali \nabla Samir

.

Anjali is the sister of Samir.

The

\nabla

symbol designates the first person as the sister. Combined with Step 1, this means Samir is also a child of Kiran.

3

Decode the third relationship:

Samir \triangle Rohan

.

Samir is the brother of Rohan.

The

\triangle

symbol designates the first person as the brother. This means Rohan is a sibling to both Anjali and Samir, and therefore is a child of Kiran.

4

Determine Rohan's gender to finalize the relationship to Kiran.

Rohan's gender remains completely unknown.

The final operator only defines Samir's gender (as a brother). Strict logical reasoning rules prohibit assuming gender from the name 'Rohan'. Thus, Rohan could be either a son or a daughter.

Key Concept

Coded Blood Relations and Logical Gender Constraints

Question 24Question →

Match each movement sequence in Column I with its correct final position or facing direction in Column II.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Sequence 1 matches with 6 m East of the starting point; Sequence 2 matches with 12 m North of the starting point; Sequence 3 matches with Facing South-West direction; Sequence 4 matches with 10√2 m South-West of the starting point.

Each movement sequence correctly matches its geometric displacement vector or facing direction by tracking cardinal axes and angular rotations step-by-step.

Step-by-Step Solution

1

Analyze Sequence 1

Displacement:

+8\text{ m}

(North),

+6\text{ m}

(East),

-8\text{ m}

(South). Net displacement =

(6, 0)

, which is

6\text{ m}

East of start.

Opposite North and South movements cancel each other out.

2

Analyze Sequence 2

Displacement:

+5\text{ m}

(East),

+12\text{ m}

(North),

-5\text{ m}

(West). Net displacement =

(0, 12)

, which is

12\text{ m}

North of start.

Opposite East and West movements cancel each other out.

3

Analyze Sequence 3

Initial direction = South (

180^\circ

). Anti-clockwise turn of

135^\circ

gives North-East (

45^\circ

). Clockwise turn of

180^\circ

gives South-West (

225^\circ

).

A

180^\circ

rotation reverses the current facing direction.

4

Analyze Sequence 4

At sunrise, sun is in East, shadow is West. Walking

10\text{ m}

West and

10\text{ m}

South gives displacement

(-10, -10)

. Distance =

\sqrt{10^2 + 10^2} = 10\sqrt{2}\text{ m}

towards South-West.

Using the Pythagorean theorem for perpendicular displacements along cardinal axes.

Key Concept

Direction and Distance Test

Question 25Question →

The State Disaster Management Agency (SDMA) has established guidelines for classifying districts under the "Drought Relief Emergency Fund" (DREF). As of August 2026, a district is designated as "Category A" (Immediate Allocation) if it meets the following primary criteria:

1. Has a recorded rainfall deficit of at least 40% over the most recent monsoon season.
2. Has agricultural land comprising more than 60% of its total geographical area.
3. Has a functional water-reservoir capacity dropping below 25%.
4. Has not received any state emergency relief funds in the last 2 years (since August 2024).

Exceptions to the primary criteria:
* If a district satisfies all criteria EXCEPT (2), but is officially notified as a "Tribal Majority District", the case is referred to the SDMA Chief Director.
* If a district satisfies all criteria EXCEPT (3), but its primary sown crop is "Water-Intensive", it is classified as "Category B" (Partial Allocation).

Case File:
Navan District recorded a rainfall deficit of 45% during the last monsoon. Its current functional water-reservoir capacity stands at 18%. The district last received state emergency relief funds in January 2023. Agricultural land makes up 52% of the district's total area. Navan is officially notified as a Tribal Majority District.

Based on the criteria provided, which of the following administrative decisions must be taken for Navan District?

The case of the district should be referred to the SDMA Chief Director.

The district should be classified as "Category A" for Immediate Allocation.

The district should be classified as "Category B" for Partial Allocation.

The request should be immediately rejected and the district marked ineligible for future aid due to low agricultural coverage.

Show answer & explanation

Answer: The case of the district should be referred to the SDMA Chief Director.

Answer

The case of the district should be referred to the SDMA Chief Director.

The correct answer accurately evaluates the district data against the given criteria. Navan District passes rules 1, 3, and 4 but fails rule 2 (52% agricultural land instead of >60%). According to the first exception clause, a district failing only rule 2 that is also a Tribal Majority District must be referred to the SDMA Chief Director.

Step-by-Step Solution

1

Evaluate Criterion 1 (Rainfall deficit >= 40%).

Pass

Navan District recorded a rainfall deficit of 45%, which is greater than the required 40% minimum.

2

Evaluate Criterion 2 (Agricultural land > 60%).

Fail

Navan District's agricultural land comprises 52%, which does not meet the strict requirement of being more than 60%.

3

Evaluate Criterion 3 (Reservoir capacity < 25%).

Pass

Navan District's reservoir capacity is at 18%, which is below the 25% threshold.

4

Evaluate Criterion 4 (No relief funds since August 2024).

Pass

The district last received funds in January 2023, which is more than 2 years prior to August 2026.

5

Check exception conditions for the failed criterion.

Refer to SDMA Chief Director

Navan District satisfies all criteria except (2). It is officially notified as a Tribal Majority District, fulfilling the specific exception requirement that directs the case to the SDMA Chief Director.

Key Concept

Applying complex, multi-layered administrative criteria and identifying the correct nested exception pathway based on case facts.

Question 26Question →

Read the following administrative circular carefully.

Statement: The State Transport Authority (STA) has issued a directive mandating that all inter-city commercial buses must be retrofitted with GPS tracking devices and driver-fatigue monitoring cameras within the next three months, failing which their route permits will be permanently revoked.

Which of the following assumptions are implicit in the given statement? (Select all that apply)

Select all that apply

A substantial number of inter-city commercial buses currently lack GPS tracking and driver-fatigue monitoring systems.

The threat of permanently revoking a route permit is a consequence severe enough to compel bus operators to comply with the mandate.

The implementation of the mandate will result in a significant decrease in the frequency of road accidents involving inter-city commercial buses.

The financial cost of purchasing and installing the required safety devices is affordable for all commercial bus operators.

Show answer & explanation

Answer: A substantial number of inter-city commercial buses currently lack GPS tracking and driver-fatigue monitoring systems.; The threat of permanently revoking a route permit is a consequence severe enough to compel bus operators to comply with the mandate.

Answer

The implicit assumptions are that a substantial number of buses currently lack these devices, and that revoking route permits is a severe enough consequence to ensure compliance.

The correct options are valid assumptions because a corrective mandate logically necessitates that the problem currently exists (buses lack the devices), and the chosen enforcement mechanism logically requires the belief that the penalty will work (permit revocation compels compliance).

Step-by-Step Solution

1

Analyze the core action and the enforcer in the statement.

The STA is mandating safety equipment retrofitting within three months under the threat of permanent permit revocation.

Understanding the policy and its enforcement mechanism is essential to uncover the unstated premises.

2

Evaluate the first candidate assumption regarding current bus equipment.

The mandate implies that a gap exists. If all buses were already equipped, the mandate would be redundant. Thus, it is assumed many buses lack these devices.

A policy aimed at changing a condition inherently assumes that the desired condition does not already universally exist.

3

Evaluate the second candidate assumption regarding the penalty.

The STA uses permit revocation to enforce the rule, assuming this penalty is impactful enough to force operators to incur the cost of retrofitting.

Administrative mandates rely on the premise that their attached penalties are effective deterrents.

4

Evaluate the remaining candidate assumptions for logical validity.

Decreased accidents is a future intended outcome (inference), not an assumption. Affordability is an external practical consideration, not logically required by the mandate.

It is critical to distinguish between foundational premises (assumptions), expected outcomes (inferences), and real-world practicalities (external bias).

Key Concept

Distinguishing implicit premises (assumptions) from expected outcomes (inferences) and external factual biases in administrative statements.

Question 27Question →

Five genre films—Comedy, Drama, Horror, Romance, and Sci-Fi—are scheduled to be screened one after another from Monday to Friday, with exactly one film shown per day.

Arrange the films in their correct chronological sequence from Monday to Friday based on the following conditions:
1. Exactly two films are screened between the Comedy film and the Sci-Fi film.
2. The Romance film is screened immediately before the Sci-Fi film.
3. The Drama film is screened on a day after the Comedy film, but not on Friday.
4. The Horror film is screened on a day before the Romance film.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct chronological sequence from Monday to Friday is: Horror, Comedy, Drama, Romance, and Sci-Fi.

The given conditions logically lock the films into a single valid sequence. The 'Comedy-gap-gap-Sci-Fi' structure paired with Romance immediately preceding Sci-Fi forces a strict 4-day block. Placing this block starting on Monday fails the Horror-before-Romance condition, meaning the block must start on Tuesday. This leaves exactly one valid chronological slot for each remaining film.

Step-by-Step Solution

1

Determine the relative block of Comedy, Romance, and Sci-Fi.

Condition 2 puts Romance immediately before Sci-Fi, giving the sequence: [Romance, Sci-Fi]. Condition 1 states there are two films between Comedy and Sci-Fi. Because Romance is right before Sci-Fi, Comedy must come before the gap, yielding the frame: [Comedy, _, Romance, Sci-Fi].

Establishing rigid blocks minimizes the number of possible placements across the five days.

2

Test the [Comedy, _, Romance, Sci-Fi] block against the five-day schedule.

This 4-day block can either start on Monday (spanning Mon-Thu) or start on Tuesday (spanning Tue-Fri).

The block requires four consecutive days, limiting it to only two possible anchor points in a five-day week.

3

Evaluate the Monday start frame.

If we use [Comedy, _, Romance, Sci-Fi, _], Drama and Horror must be placed on Tuesday and Friday. Condition 3 says Drama is after Comedy but NOT on Friday. Thus, Drama must be on Tuesday, leaving Horror for Friday. However, Condition 4 requires Horror to be before Romance. Since Friday is after Thursday, this frame is invalid.

Testing specific edge conditions eliminates invalid scheduling permutations.

4

Evaluate the Tuesday start frame.

Using the frame [_, Comedy, _, Romance, Sci-Fi] leaves Monday and Wednesday for Drama and Horror. Drama must be after Comedy (Tuesday), so Drama is Wednesday. This leaves Horror for Monday. Horror on Monday is before Romance on Thursday, satisfying Condition 4. The sequence is completely and logically filled.

Applying the final logical constraints confirms the unique deterministic arrangement.

Key Concept

Linear Sequencing and Conditional Placement

Estimated Time:2m 0s

Question 28Question →

Statement: An internal financial audit has revealed that a prominent state-funded university has systematically inflated its student enrollment figures over the past five years to illegally secure massive surplus infrastructural grants from the Higher Education Ministry.

Courses of Action:
I. The Higher Education Ministry should immediately suspend the university's academic charter and invalidate the ongoing academic sessions until the misappropriated funds are fully recovered by the state exchequer.
II. The government should immediately freeze all further discretionary funding to the institution, institute a high-level investigative committee to identify the culpable administrators, and appoint a temporary oversight board to ensure uninterrupted classes for genuine students.

Which of the following logically follows?

Only course of action I follows

Only course of action II follows

Either course of action I or II follows

Neither course of action I nor II follows

Both courses of action I and II follow

Show answer & explanation

Answer: Only course of action II follows

Answer

Only course of action II logically follows, as it addresses the financial fraud while protecting the academic interests of innocent students.

The correct answer identifies that only the second proposed action is logically sound. In public administration, a valid course of action must solve the immediate problem without creating a disproportionately larger crisis. Course of action II achieves this by stopping the financial fraud and investigating the culprits while explicitly protecting the academic careers of genuine students. Course of action I is invalid because invalidating all academic sessions is an extreme, collateral-damage-heavy response that unfairly punishes innocent students for the administration's crimes.

Step-by-Step Solution

1

Analyze the problem presented in the statement.

The core problem is financial fraud committed by the university administration through inflated enrollment figures to secure surplus government grants.

Identifying the perpetrators (administrators) and the potential victims (students, taxpayers) is necessary to evaluate the appropriateness of any proposed action.

2

Evaluate Course of Action I against administrative principles.

Course of action I proposes suspending the academic charter and invalidating ongoing sessions. This action penalizes innocent students for the crimes of the administration.

A valid course of action must be proportionate and must not inflict massive collateral damage on innocent stakeholders.

3

Evaluate Course of Action II against administrative principles.

Course of action II proposes freezing funds to stop the crime, investigating the guilty administrators, and appointing a board to keep classes running for real students.

This is a balanced, ethical, and highly feasible policy that resolves the crisis without harming the public.

4

Synthesize the evaluations to select the correct option.

Since only the second action is a valid, proportionate response, 'Only course of action II follows' is the correct conclusion.

Finalizing the logical deduction based on the validity of each individual course of action.

Key Concept

Proportionate Administrative Action and Stakeholder Protection

Estimated Time:1m 15s

Question 29Question →

Problem: A routine performance review of a state-run healthcare initiative discovered that 15% of the allocated quarterly funds were misdirected due to data entry mistakes made by temporary staff during the digitization of patient records.
Proposed Course of Action: The health department should immediately deduct the misdirected funds directly from the salaries of the temporary staff to recover the financial loss.

Determine if the following statement is true or false: The proposed course of action is logically sound and represents a practical administrative remedy.

True

False

Show answer & explanation

Answer: False

Answer

False

The proposed course of action is invalid because deducting misdirected scheme funds from the salaries of temporary staff for unintentional clerical errors is an extreme and disproportionate measure. Furthermore, it fails to address the root cause, which is a lack of systemic data verification.

Step-by-Step Solution

1

Analyze the problem stem to identify the core issue and its cause.

The problem is a systemic financial misdirection caused by unintentional data entry errors made by temporary personnel, rather than intentional fraud.

Identifying the nature of the root cause is crucial for determining the appropriate administrative response.

2

Evaluate the proposed course of action for proportionality and feasibility.

Deducting government scheme funds from the salaries of temporary staff is highly disproportionate to a clerical mistake and is likely legally unfeasible.

A valid administrative course of action must be fair, legally viable, and not introduce disproportionate harm.

3

Determine if the proposed action addresses the systemic root cause of the problem.

The proposed action focuses purely on punitive financial recovery and fails to implement data validation protocols or training to prevent future mistakes.

Effective courses of action must implement sustainable corrections to prevent the problem from recurring.

Key Concept

Evaluating the proportionality, legality, and root-cause effectiveness of an administrative course of action.

Question 30Question →

Four corporate managers—K, L, M, and N—are assigned to four different regional offices: North, South, East, and West. Additionally, each manager specializes in exactly one distinct sector: Finance, HR, Marketing, and Operations. Read the following operational conditions carefully:

1. The manager assigned to the North office specializes in Finance.
2. L specializes in Marketing but is neither assigned to the East nor the West office.
3. N is assigned to the West office but does not specialize in Operations.
4. K is not assigned to the East office.

Based on these conditions, match each manager with their correct specialization sector.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Manager K matches with Finance, Manager L matches with Marketing, Manager M matches with Operations, and Manager N matches with HR.

By cross-referencing office locations with specializations, we logically deduce the grid: K (North, Finance), L (South, Marketing), M (East, Operations), and N (West, HR).

Step-by-Step Solution

1

Determine L's office assignment.

L is assigned to the South office.

L specializes in Marketing, so L cannot be in the North office (which is reserved for Finance). Given L is also not in the East or West offices, the only remaining option is the South office.

2

Determine K and M's office assignments.

K is assigned to the North office and M is assigned to the East office.

N is assigned to the West office, leaving North and East open. Since condition 4 states K is not in the East, K must take the North office. M is left with the East office.

3

Determine K's specialization.

K specializes in Finance.

K is in the North office, and condition 1 states the North office manager specializes in Finance.

4

Determine N and M's specializations.

N specializes in HR and M specializes in Operations.

The remaining specializations are HR and Operations. Condition 3 states N (West office) does not specialize in Operations. Therefore, N must specialize in HR, leaving Operations for M.

Key Concept

Analytical Matrix Deductions

Estimated Time:2m 0s

Question 31Question →

The State Education Board has recently issued the following mandate to all affiliated institutions:

'Starting from the upcoming academic session, every primary school is required to allocate the first 30 minutes of the daily schedule strictly for physical mindfulness routines. This measure is introduced with the objective of enhancing overall student concentration and classroom discipline.'

Based on this mandate, which of the underlying assumptions are implicit? (Select all that apply)

Select all that apply

Physical mindfulness routines yield a positive effect on student concentration and classroom discipline.

Primary school students possess the required capability to participate in mindfulness routines for 30 consecutive minutes.

The fundamental reason for current disciplinary issues in classrooms is the omission of early morning physical activities.

Institutions that currently do not mandate any physical education face the highest rates of student concentration deficits.

Show answer & explanation

Answer: Physical mindfulness routines yield a positive effect on student concentration and classroom discipline.; Primary school students possess the required capability to participate in mindfulness routines for 30 consecutive minutes.

Answer

The implicit assumptions are that physical mindfulness routines positively impact concentration and discipline, and that primary school students have the capacity to sustain these routines for 30 minutes.

An assumption is an unstated premise that must be true for a statement's logic to hold. For the mandate to rationally aim at improving concentration and discipline through mindfulness routines, the Board must assume these routines actually produce that positive impact. Furthermore, by mandating a strict 30-minute duration for primary students, the authorities inherently assume that students of this young demographic are physically and mentally capable of sustaining the activity for that length of time. Without both premises, the initiative would be illogical and unfeasible.

Step-by-Step Solution

1

Analyze the action and the stated objective in the mandate.

Action: Mandating 30 minutes of physical mindfulness. Objective: Enhancing concentration and discipline.

Identifying the core components of the statement is necessary to extract what must be true for the statement to be logical.

2

Evaluate the cause-and-effect assumption required for the policy.

The Board must assume the action will lead to the objective. Therefore, it is assumed that mindfulness routines positively affect concentration and discipline.

If this were not assumed, introducing the measure to achieve the stated goal would be irrational.

3

Evaluate the feasibility assumption required for the policy.

The Board must assume that the specific target audience (primary students) can successfully perform the mandated task for the given duration (30 minutes).

A mandate is logically built on the premise that it can actually be executed by the subjects it governs.

4

Eliminate distractors that state extreme causal relationships or rely on external comparative facts.

Options claiming mindfulness is the 'fundamental reason' for poor discipline or comparing different school types are rejected as they are not logically required for the mandate to stand.

Implicit assumptions must be strictly necessary for the statement, not just plausible inferences or external truths.

Key Concept

Evaluating Implicit Assumptions in Policy Mandates

Estimated Time:1m 30s

Question 32Question →

Statement: A sudden outbreak of a highly contagious, though non-lethal, viral fever has been reported in three densely populated residential colonies of the city. This has led to a massive surge in patient numbers, severely overwhelming the local primary health centers.

Which of the following proposed courses of action logically follow and should be implemented by the administration? (Select all that apply)

Select all that apply

The municipal health department should immediately deploy mobile medical units to the affected colonies to triage patients and distribute symptomatic medications.

The local administration should impose an immediate, absolute lockdown in the affected colonies, prohibiting residents from leaving their homes.

The health department should launch a targeted public awareness campaign detailing preventive hygiene measures and guidelines on when hospital care is actually required.

The chief medical officer should bypass standard safety regulations and procurement rules to rapidly acquire unapproved experimental antiviral drugs.

Show answer & explanation

Answer: The municipal health department should immediately deploy mobile medical units to the affected colonies to triage patients and distribute symptomatic medications.; The health department should launch a targeted public awareness campaign detailing preventive hygiene measures and guidelines on when hospital care is actually required.

Answer

The administration should deploy mobile medical units for triage and launch a public awareness campaign on prevention and hospital visit guidelines.

The correct actions represent a balanced, multi-pronged approach. Deploying mobile units provides immediate relief to the overwhelmed health centers by treating minor cases locally, while the awareness campaign offers a long-term preventive measure to lower infection rates and reduce panic-driven hospital visits. Both actions are highly feasible, proportional to a non-lethal outbreak, and directly address the stated problems.

Step-by-Step Solution

1

Analyze the core problem presented in the statement.

The problem has two main components: a contagious but non-lethal disease outbreak, and the resulting severe overcrowding of local primary health centers.

Identifying the specific parameters of the crisis is necessary to determine proportional and relevant administrative responses.

2

Evaluate the practical and administrative feasibility of each proposed solution against the problem.

Deploying mobile units and launching educational campaigns practically manage the patient load and prevent spread. Strict lockdowns and bypassing medical safety regulations are either too extreme or violate statutory rules.

Valid courses of action must solve the problem without introducing disproportionate harm or violating established administrative protocols.

Key Concept

Evaluating Administrative Proportionality and Feasibility in Crisis Management

Question 33Question →

Match each movement sequence described in List-I with its corresponding final position relative to the starting point in List-II.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Sequence 1 matches

5\text{ km}

North-East, Sequence 2 matches

5\text{ km}

South-East, Sequence 3 matches

5\text{ km}

South-West, and Sequence 4 matches

5\text{ km}

North-West.

Each movement sequence consists of two perpendicular steps of lengths

3\text{ km}

and

4\text{ km}

. By the Pythagorean theorem, the net displacement magnitude is

5\text{ km}

in all cases. The directional quadrant depends on the facing direction prior to the right turn: North+Right points North-East, East+Right points South-East, South+Right points South-West, and West+Right points North-West.

Step-by-Step Solution

1

Determine orientation and turns for each movement path.

Facing North and turning right leads East. Facing East and turning right leads South. Facing South and turning right leads West. Facing West and turning right leads North.

A

90^\circ

clockwise rotation corresponds to a right turn.

2

Calculate the magnitude of shortest distance for each path using the Pythagorean theorem.

In all four cases, the perpendicular components are

3\text{ km}

and

4\text{ km}

. The shortest distance is

\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = 5\text{ km}

.

The straight-line displacement forms a right-angled triangle.

3

Determine the resultant direction quadrant for each sequence.

(North, East)

\rightarrow

North-East; (East, South)

\rightarrow

South-East; (South, West)

\rightarrow

South-West; (West, North)

\rightarrow

North-West.

Combining two orthogonal direction vectors places the final point in the respective sub-cardinal quadrant.

Key Concept

Direction sense analysis, orthogonal turns, and Pythagorean distance calculation

Question 34Question →

Five administrative project files—File Alpha, File Beta, File Gamma, File Delta, and File Epsilon—were reviewed and cleared sequentially by a scrutiny committee. Based on the following clearance conditions, arrange the five files in the correct chronological order from the first file cleared to the last file cleared:

1. File Beta was cleared immediately after File Alpha.
2. File Delta was cleared after File Epsilon but before File Gamma.
3. File Alpha was cleared at some point after File Gamma.

What is the correct sequence of clearance from first to last?

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Answer

The correct sequence of clearance from first to last is File Epsilon, File Delta, File Gamma, File Alpha, and File Beta.

File Epsilon is cleared first because File Delta follows File Epsilon, File Gamma follows File Delta, File Alpha follows File Gamma, and File Beta directly follows File Alpha. This forms the deterministic order: File Epsilon, File Delta, File Gamma, File Alpha, File Beta.

Step-by-Step Solution

1

Analyze relative position constraints for File Epsilon, File Delta, and File Gamma.

From condition 2, File Delta was cleared after File Epsilon but before File Gamma, establishing the partial order: File Epsilon → File Delta → File Gamma.

Delta must sit strictly between Epsilon and Gamma.

2

Analyze relative position constraints for File Gamma, File Alpha, and File Beta.

From condition 3, File Alpha was cleared after File Gamma (File Gamma → File Alpha). From condition 1, File Beta was cleared immediately after File Alpha (File Alpha → File Beta). Combining these yields: File Gamma → File Alpha → File Beta.

Alpha follows Gamma, and Beta directly locks in behind Alpha.

3

Merge all partial orders to form the unique complete sequence.

Combining (File Epsilon → File Delta → File Gamma) with (File Gamma → File Alpha → File Beta) gives the unique sequence: File Epsilon → File Delta → File Gamma → File Alpha → File Beta.

This satisfies every relative clearance condition without contradiction.

Key Concept

Linear Sequential Ordering and Constraint Satisfaction

Question 35Question →

A delivery courier starts from a central warehouse and travels $5\text{ km}$ due North. The courier then turns right and travels $12\text{ km}$ due East, and finally turns right again and travels $5\text{ km}$ due South. What is the shortest distance and direction of the courier relative to the starting warehouse?

12\text{ km}

to the East

12\text{ km}

to the West

22\text{ km}

to the East

5\text{ km}

to the South

Show answer & explanation

Answer: $12\text{ km}$ to the East

Answer

12\text{ km}

to the East

Taking the starting warehouse as the origin

(0,0)

, moving

5\text{ km}

North reaches point

(0, 5)

. Turning right (facing East) and walking

12\text{ km}

reaches point

(12, 5)

. Turning right again (facing South while at

(12,5)

) and traveling

5\text{ km}

brings the courier to

(12, 0)

. The straight-line distance from

(0,0)

to

(12,0)

is

12\text{ km}

in the positive x-direction, which corresponds to

12\text{ km}

to the East.

Step-by-Step Solution

1

Analyze vertical (North-South) displacement

The courier moves

5\text{ km}

North and later

5\text{ km}

South. Net vertical displacement =

5\text{ km} - 5\text{ km} = 0\text{ km}

.

Equal distances traveled in opposite directions along the vertical axis cancel out completely.

2

Analyze horizontal (East-West) displacement

The courier moves

12\text{ km}

East. Net horizontal displacement =

12\text{ km}

East.

There are no opposing Westward turns to reduce the Eastward travel.

3

Determine final straight-line position

The courier is located

12\text{ km}

due East of the starting warehouse.

Combining zero vertical shift and

12\text{ km}

Eastward shift gives a final vector of

12\text{ km}

East.

Key Concept

Vector Cancellation and Net Displacement

Question 36Question →

Five senior policy analysts—Anish, Babita, Chirag, Divya, and Esha—are scheduled to deliver research presentations sequentially from 1st to 5th slot. The schedule must satisfy the following conditions:
1. Babita presents immediately before Esha, but at some point after Anish.
2. Chirag does not give the 1st presentation, and there are exactly two presentations scheduled between Chirag and Divya.
3. Divya delivers her presentation before Babita.
4. Esha is not assigned to the final (5th) presentation slot.

Arrange the five analysts in the correct sequence of their presentations from 1st to 5th.

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Answer

The correct chronological sequence from 1st to 5th presentation slot is Anish, Divya, Babita, Esha, and Chirag.

The unique sequence Anish (1st) → Divya (2nd) → Babita (3rd) → Esha (4th) → Chirag (5th) satisfies every constraint: (Babita, Esha) form an adjacent block in slots 3 and 4, Babita comes after Anish, Divya (2nd) precedes Babita (3rd), Esha is not 5th, and exactly two analysts (Babita and Esha) present between Divya and Chirag.

Step-by-Step Solution

1

Analyze the block constraint for Babita and Esha.

Babita and Esha form a consecutive pair (Babita, Esha). Since Esha cannot be in slot 5, this pair must occupy slots (1,2), (2,3), or (3,4).

Babita presents immediately before Esha, and Esha is excluded from the 5th slot.

2

Evaluate possible slot pairs for (Babita, Esha) using condition 1 and condition 3.

Babita cannot be in slot 1 because she must present after Anish. If Babita were in slot 2, Esha would be in slot 3, forcing Anish to slot 1; however, that leaves slots 4 and 5 for Chirag and Divya, which violates the requirement of having two presentations between them. Thus, Babita must be in slot 3 and Esha in slot 4.

Placing Babita in slot 3 is the only placement consistent with all positional separation requirements.

3

Determine the slots for Divya and Chirag.

The remaining vacant slots are 1, 2, and 5. The only pair among these with exactly two slots between them is slot 2 and slot 5. Since Divya must present before Babita (slot 3), Divya is in slot 2 and Chirag is in slot 5.

Exactly two presentations (slots 3 and 4) must separate Divya and Chirag, and Divya comes before Babita.

4

Assign the remaining slot to Anish.

Slot 1 is the only remaining unfilled slot, so Anish is placed in slot 1.

This satisfies the condition that Babita presents at some point after Anish.

Key Concept

Linear Ordering and Constraint Satisfaction

Question 37Question →

Match each person's multi-turn displacement sequence in List I with their corresponding final position relative to their starting point in List II.

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Answer

Person P matches with

5\text{ km}

East and

3\text{ km}

North; Person Q matches with

4\text{ km}

East and

5\text{ km}

South; Person R matches with

5\text{ km}

West and

8\text{ km}

North; Person S matches with

5\text{ km}

West and

2\text{ km}

North.

Each trajectory is resolved correctly by tracking facing direction changes and vector sum components. Person P resolves to

(+5, +3)

, Person Q resolves to

(+4, -5)

, Person R resolves to

(-5, +8)

, and Person S resolves to

(-5, +2)

.

Step-by-Step Solution

1

Set up a Cartesian coordinate system with starting points at

(0,0)

, where North is

+y

, South is

-y

, East is

+x

, and West is

-x

.

Displacements along cardinal directions align directly with coordinate axes.

Converting directional movements to Cartesian vectors simplifies multi-turn trajectory calculations.

2

Decompose angular diagonal movements into horizontal and vertical components using

d\sqrt{2}

vector resolution.

A distance of

d\sqrt{2}\text{ km}

in sub-cardinal directions resolves to

|\Delta x| = d

and

|\Delta y| = d

.

In 45-degree sub-cardinal directions (NE, NW, SE, SW),

\cos(45^\circ) = \sin(45^\circ) = 1/\sqrt{2}

.

3

Calculate final coordinates for each person by summing intermediate vector components.

P reaches

(5,3)

; Q reaches

(4,-5)

; R reaches

(-5,8)

; S reaches

(-5,2)

.

Sequential vector addition yields the accurate net displacement relative to the origin.

Key Concept

Vector resolution of multi-turn cardinal and sub-cardinal displacements

Estimated Time:2m 30s

Question 38Question →

Match each administrative policy or natural event in List I with its most direct logical outcome or primary effect in List II.

Click a left item, then click its matching right item

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Answer

The correct pairings are: Monetary policy tightening with borrowing reduction; Rainfall deficit with crop yield decline; Congestion tax with public transit surge; and Solar subsidies with renewable adoption.

Each correct match pairs an independent variable (the cause or policy) with its most direct, logical dependent variable (the effect or outcome). The relationships rely on standard principles of economics, public behavior, and environmental science without requiring unstated assumptions.

Step-by-Step Solution

1

Analyze the first event regarding the central bank increasing interest rates.

Identify that higher interest rates make loans more expensive.

This directly links to the effect of rising commercial borrowing costs and slowing corporate expansion.

2

Examine the second event regarding a severe monsoon rainfall deficit.

Recognize this as an agricultural stress factor.

A lack of water directly impacts crop growth, logically leading to decreased yields and increased market prices.

3

Evaluate the third event about a municipal congestion tax.

Determine that this acts as a financial deterrent for driving private vehicles in the downtown area.

Commuters will seek cheaper alternatives, directly resulting in a surge in public transit ridership.

4

Assess the fourth event concerning subsidies for solar panels.

Conclude that financial subsidies reduce the out-of-pocket cost for end-users.

Lower costs directly stimulate market demand, resulting in a dramatic increase in residential renewable energy adoption.

Key Concept

Identifying direct causal relationships by connecting macroeconomic, environmental, and administrative events with their immediate logical outcomes.

Question 39Question →

Four police officers on patrol follow different multi-step tactical movement routes involving angular rotations and shadow orientations. Match each officer's movement sequence (List-I) with their net displacement vector relative to their starting point (List-II).

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Answer

Officer A matches

7\text{ m}

directly East; Officer B matches

20\text{ m}

North-West; Officer C matches

14\sqrt{2}\text{ m}

South-East; Officer D matches

15\text{ m}

South-East.

Each officer's sequence correctly resolves into orthogonal components when accounting for shadow direction (sunrise shadow = West, sunset shadow = East) and angular turn directions (clockwise vs anti-clockwise). Officer A reaches

(7, 0)

, Officer B reaches

(-12, 16)

with distance

20\text{ m}

, Officer C reaches

(14, -14)

with distance

14\sqrt{2}\text{ m}

, and Officer D reaches

(12, -9)

with distance

15\text{ m}

.

Step-by-Step Solution

1

Set up a standard Cartesian coordinate system where East is

+x

, West is

-x

, North is

+y

, and South is

-y

. Establish shadow directions: sunrise shadow points West; sunset shadow points East.

Sunrise shadow facing = West; Sunset shadow facing = East.

Sun rises in the East (shadows cast West) and sets in the West (shadows cast East).

2

Resolve Officer A's displacement steps into orthogonal components: Step 1 (12 m East) =

(+12, 0)

; Step 2 (

135^\circ

CW from East = SW,

10\sqrt{2}\text{ m}

) =

(-10, -10)

; Step 3 (

90^\circ

Anti-CW from SW = SE,

5\sqrt{2}\text{ m}

) =

(+5, -5)

; Step 4 (

135^\circ

Anti-CW from SE = North,

15\text{ m}

) =

(0, +15)

. Sum components.

\sum x = 12 - 10 + 5 + 0 = 7\text{ m}

,

\sum y = 0 - 10 - 5 + 15 = 0\text{ m}

. Displacement =

7\text{ m}

East.

Direct vector addition yields net position

(7, 0)

.

3

Resolve Officer B's displacement steps starting facing West: Step 1 (20 m West) =

(-20, 0)

; Step 2 (

45^\circ

Anti-CW from West = SW,

10\sqrt{2}\text{ m}

) =

(-10, -10)

; Step 3 (

135^\circ

CW from SW = North,

26\text{ m}

) =

(0, +26)

; Step 4 (

90^\circ

CW from North = East,

18\text{ m}

) =

(+18, 0)

. Sum components.

\sum x = -20 - 10 + 18 = -12\text{ m}

,

\sum y = -10 + 26 = +16\text{ m}

. Net magnitude

\sqrt{(-12)^2 + 16^2} = 20\text{ m}

North-West.

Pythagorean magnitude

\sqrt{144 + 256} = 20\text{ m}

in NW quadrant.

4

Resolve Officer C's displacement steps: Step 1 (12 m North) =

(0, +12)

; Step 2 (24 m East) =

(+24, 0)

; Step 3 (

135^\circ

CW from East = SW,

10\sqrt{2}\text{ m}

) =

(-10, -10)

; Step 4 (

45^\circ

Anti-CW from SW = South,

16\text{ m}

) =

(0, -16)

. Sum components.

\sum x = 24 - 10 = 14\text{ m}

,

\sum y = 12 - 10 - 16 = -14\text{ m}

. Magnitude

\sqrt{14^2 + (-14)^2} = 14\sqrt{2}\text{ m}

South-East.

Equal magnitude orthogonal components in

+x

and

-y

yield a

45^\circ

SE vector.

5

Resolve Officer D's displacement steps starting facing East: Step 1 (9 m East) =

(+9, 0)

; Step 2 (

45^\circ

CW from East = SE,

8\sqrt{2}\text{ m}

) =

(+8, -8)

; Step 3 (

90^\circ

CW from SE = SW,

5\sqrt{2}\text{ m}

) =

(-5, -5)

; Step 4 (

135^\circ

CW from SW = North,

4\text{ m}

) =

(0, +4)

. Sum components.

\sum x = 9 + 8 - 5 = 12\text{ m}

,

\sum y = -8 - 5 + 4 = -9\text{ m}

. Magnitude

\sqrt{12^2 + (-9)^2} = 15\text{ m}

South-East.

Pythagorean triplet

(9, 12, 15)

in SE quadrant.

Key Concept

Vector resolution of multi-step angular displacements and shadow-based directional orientation.

Estimated Time:3m 0s

Question 40Question →

Five senior officers—Ananya, Bhavesh, Chitra, Dev, and Ehsaan—are ranked from Rank 1 (highest seniority) to Rank 5 (lowest seniority). Each officer heads a distinct department among Home, Finance, Urban Development, Health, and Education.

Based on the following administrative records, determine the unique order of the five officers from Rank 1 (highest) to Rank 5 (lowest):
1. The officer heading Education is ranked immediately above the officer heading Finance, who in turn is ranked immediately above Chitra.
2. Ananya is ranked higher than the officer heading Health, who is ranked higher than Ehsaan.
3. Bhavesh is ranked lower than the officer heading Urban Development, but higher than Dev.
4. Bhavesh does not head the Education or Home department.
5. Dev does not head the Health or Finance department, and Ehsaan is not the officer heading Home.

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Answer

The correct sequence from Rank 1 (highest) to Rank 5 (lowest) is Ananya, Bhavesh, Dev, Ehsaan, and Chitra.

By placing the contiguous three-rank block (Education, Finance, Chitra) at Ranks 3, 4, and 5, we satisfy all constraints: Ananya (Urban Development, Rank 1) > Bhavesh (Health, Rank 2) > Dev (Education, Rank 3) > Ehsaan (Finance, Rank 4) > Chitra (Home, Rank 5).

Step-by-Step Solution

1

Analyze the contiguous block from Clue 1

Education, Finance, and Chitra form a three-rank contiguous block at Ranks

k

,

k+1

, and

k+2

respectively.

Clue 1 states Education is immediately above Finance, which is immediately above Chitra.

2

Deduce Bhavesh's department and rank constraints

Bhavesh heads Health and occupies Rank 2.

From Clue 3, Urban Dev < Bhavesh < Dev. From Clue 2, Ananya < Health < Ehsaan. Bhavesh cannot be Education or Home (Clue 4). If Bhavesh headed Finance, Urban Dev would conflict with Education. Thus Bhavesh must head Health. Since Urban Dev and Ananya are both senior to Bhavesh, and Dev and Ehsaan are junior to Bhavesh, Bhavesh cannot be Rank 1, 4, or 5. Evaluating the block position forces

k=3

(Education at Rank 3, Finance at Rank 4, Chitra at Rank 5), placing Bhavesh at Rank 2.

3

Determine Rank 1 officer and department

Ananya is at Rank 1 and heads Urban Development.

Urban Development is ranked above Bhavesh (Rank 2), so it must be at Rank 1. Ananya is also ranked above Health (Bhavesh at Rank 2), so Ananya must be at Rank 1.

4

Assign remaining officers to Ranks 3, 4, and 5

Dev is at Rank 3 (Education), Ehsaan is at Rank 4 (Finance), and Chitra is at Rank 5 (Home).

Chitra is fixed at Rank 5 (

k+2

). Ranks 3 and 4 belong to Education and Finance. Dev cannot head Finance (Clue 5), so Dev must head Education at Rank 3. Ehsaan takes Finance at Rank 4. By elimination, Chitra heads Home.

Key Concept

Analytical Puzzle Sequence & Multi-Attribute Elimination

Estimated Time:3m 0s

Logical Reasoning and Analytical Ability

Answer

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