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Question 4381Question →

In a straight row of cadets facing North, Vikram is positioned $13^{\text{th}}$ from the left end and Rahul is positioned $31^{\text{st}}$ from the right end. If they interchange their positions, Vikram becomes $39^{\text{th}}$ from the left end. Another cadet, Sanjay, is standing exactly in the middle of Vikram and Rahul's new positions. What is Sanjay's position from the right end?

44^{\text{th}}

26^{\text{th}}

43^{\text{rd}}

45^{\text{th}}

Show answer & explanation

Answer: $44^{\text{th}}$

Answer

Sanjay's position is

44^{\text{th}}

from the right end.

The correct answer accurately determines the total number of cadets as

69

by combining the left and right ranks of the intersection seat. It identifies Sanjay's position as

26^{\text{th}}

from the left by averaging

13

and

39

, and finally correctly converts this to the

44^{\text{th}}

position from the right using the formula

N - L + 1

Step-by-Step Solution

Calculate the total number of cadets in the row.

Total =

39 + 31 - 1 = 69

cadets.

After the swap, Vikram is

39^{\text{th}}

from the left. This physical seat is the same as Rahul's original seat, which was

31^{\text{st}}

from the right. The formula for total is

L + R - 1

Determine the new positions of Vikram and Rahul from the left end.

Vikram's new position =

39^{\text{th}}

from the left. Rahul's new position =

13^{\text{th}}

from the left.

Since they swapped, Rahul occupies Vikram's original seat, which is

13^{\text{th}}

from the left.

Calculate Sanjay's position from the left end.

Sanjay's position =

(13 + 39) \div 2 = 26^{\text{th}}

from the left.

Sanjay is exactly in the middle of

13

and

39

, so we average the two positions.

Convert Sanjay's position from the left end to the right end.

Sanjay's position from the right =

69 - 26 + 1 = 44^{\text{th}}

The formula to find the rank from the opposite end is

\text{Total} - \text{Current Rank} + 1

Key Concept

Position Interchange and Midpoint Calculations

Question 4382Question →

Read the given statements carefully and determine which of the conclusions logically follows.

Statement 1: Under the 'Digital Panchayat' policy, rural broadband funding is disbursed only to village councils that have fully digitized their financial records for the preceding three years.
Statement 2: The Haripur village council recently received rural broadband funding under this policy.

Conclusions:
I. The Haripur village council has fully digitized its financial records for the preceding three years.
II. The primary objective of the 'Digital Panchayat' policy is to promote financial transparency in village administration.

Which of the following options is correct?

Only Conclusion I follows

Only Conclusion II follows

Both Conclusions I and II follow

Neither Conclusion I nor II follows

Show answer & explanation

Answer: Only Conclusion I follows

Answer

Only Conclusion I follows

Conclusion I is a direct logical deduction because Statement 1 establishes digitizing financial records as an absolute prerequisite ('only to') for funding. Since Statement 2 confirms Haripur received funding, they must have fulfilled this prerequisite. Conclusion II introduces unstated information about the policy's primary objective, which cannot be logically derived from the text.

Step-by-Step Solution

Analyze the logical structure of Statement 1.

The phrase 'disbursed only to' creates a necessary condition. It implies that receiving funding guarantees the village council has fully digitized its records.

Identifying necessary and sufficient conditions is required to evaluate logical deductions accurately.

Evaluate Conclusion I against the statements.

Statement 2 confirms Haripur received the funding. Based on the rule in Statement 1, Haripur must have met the necessary condition. Therefore, Conclusion I is logically valid.

Applying the specific case from Statement 2 to the general rule in Statement 1 verifies the conclusion.

Evaluate Conclusion II against the statements.

Conclusion II introduces the 'primary objective' of the policy. The given statements only outline a funding prerequisite, not the intent or ultimate goals of the policy. Therefore, Conclusion II does not follow.

Valid conclusions must be derived strictly from the provided text, without bringing in external real-world assumptions.

Key Concept

Logical Deduction from Conditional Statements

Question 4383Question →

During a cybersecurity drill, passwords are obfuscated using a specific two-step alphabetic logic. If the system transforms the access word TABLE into HAZPW, what will the access word CHAIR be transformed into under the same logic?

YTASJ

XSZRI

DIBJS

WRYQH

Show answer & explanation

Answer: YTASJ

Answer

The correct transformation for the word CHAIR is YTASJ.

The encryption logic applies a reverse alphabetical index to each letter (where A=Z, B=Y, etc.) and then shifts that result forward by one letter (+1). Applying this to CHAIR gives the intermediate letters XSZRI, which then shift +1 to become YTASJ.

Step-by-Step Solution

Analyze the transformation from TABLE to HAZPW to identify the first logical step.

The reverse alphabetical equivalents for T-A-B-L-E are G-Z-Y-O-V.

Finding the foundational pattern requires testing common cryptographic shifts, starting with opposite letters.

Determine the second logical step by comparing the intermediate reversed letters to the final code.

Shifting G-Z-Y-O-V forward by one letter (+1) in the alphabet results in H-A-Z-P-W.

This confirms the two-step logic: reverse the letter, then shift +1.

Apply the first step (reverse alphabet) to the target word CHAIR.

The reverse alphabetical equivalents for C-H-A-I-R are X-S-Z-R-I.

To begin encrypting the new access word according to the established rule.

Apply the second step (+1 shift) to the intermediate result.

Shifting X-S-Z-R-I forward by one letter (+1) results in Y-T-A-S-J.

To complete the obfuscation logic and determine the final coded sequence.

Key Concept

Reverse Alphabetical Indexing and Positional Shifting

Question 4384Question →

As the Regional Health Director, you must allocate a limited stockpile of exactly 1,000 rapid diagnostic kits during the early stages of a newly detected viral outbreak.

The current requested demands are:
1. Central Hospital ICU: 200 kits (for severe symptomatic patients and frontline medical staff)
2. Outbreak Epicenter Quarantine Zone: 500 kits (for high-risk contact tracing)
3. International Airport: 600 kits (for blanket screening of all arriving passengers)
4. General City Pharmacies: 400 kits (for voluntary public purchase)

Based on standard emergency medical triage and administrative priority protocols, which of the following resource allocation decisions should be implemented? (Select all that apply)

Select all that apply

Allocate 200 kits to the Central Hospital ICU immediately to protect critical healthcare capacity and frontline staff.

Allocate 500 kits to the epicenter quarantine zone to actively contain known local transmission chains through targeted contact tracing.

Distribute exactly 250 kits to each of the four sectors to guarantee equal resource distribution and prevent public grievances.

Requisition 400 kits from private city pharmacies without invoking emergency acquisition statutes to supply the airport.

Deploy all 1,000 kits exclusively to the airport for blanket screening to prevent new international cases from entering.

Show answer & explanation

Answer: Allocate 200 kits to the Central Hospital ICU immediately to protect critical healthcare capacity and frontline staff.; Allocate 500 kits to the epicenter quarantine zone to actively contain known local transmission chains through targeted contact tracing.

Answer

The correct priorities are to allocate 200 kits to the Central Hospital ICU and 500 kits to the epicenter quarantine zone.

In public health administration, priority ranking requires securing critical infrastructure (the ICU) first, followed by containing the active spread at its source (the epicenter). Fulfilling these two demands requires 700 kits, which is well within the 1,000-kit constraint and correctly applies triage principles.

Step-by-Step Solution

Analyze the total available resources against the total demand.

Available resources: 1,000 kits. Total demand: 1,700 kits. There is a deficit of 700 kits.

Identifying the shortage confirms that strict administrative triage and priority ranking are necessary.

Rank the competing demands based on urgency, severity, and public health impact.

Rank 1: ICU (life-saving & infrastructure protection). Rank 2: Epicenter (active containment). Rank 3: Airport (surveillance). Rank 4: Pharmacies (voluntary access).

Standard triage protocols prioritize direct critical care and source containment over surveillance and general public access.

Allocate resources sequentially down the priority list until depleted.

The ICU receives its full 200 kits. The Epicenter receives its full 500 kits. This consumes 700 kits, leaving 300 kits available for the next priority (the airport).

To ensure the most critical and time-sensitive needs are fully met before addressing lower-priority demands.

Evaluate the feasibility and legality of the proposed actions.

Allocating to the ICU and epicenter uses 700 kits, which is mathematically feasible within the 1,000 limit. Arbitrary property seizure and purely mathematically equal distributions violate legal frameworks and triage efficiency.

To ensure the final selected actions strictly adhere to both logistical limits and administrative rules.

Key Concept

Crisis Triage and Objective Priority Ranking

Question 4385Question →

According to the definitive rules of a stellar taxonomy system, every pulsar is categorized as a neutron star, and certain neutron stars are simultaneously classified as magnetars.

From these conditions alone, it is logically valid to deduce that at least some pulsars must be magnetars.

True

False

Show answer & explanation

Answer: False

Answer

The statement is false because the deduction is logically invalid due to an undistributed middle term.

The deduction is logically invalid. In syllogistic logic, the middle term linking two concepts must be distributed in at least one premise. Since 'neutron star' is not distributed in either premise, we cannot definitively link pulsars and magnetars.

Step-by-Step Solution

Translate the given conditions into standard categorical propositions.

Premise 1: All Pulsars are Neutron Stars (All P are N). Premise 2: Some Neutron Stars are Magnetars (Some N are M). Conclusion: Some Pulsars are Magnetars (Some P are M).

Standardizing the propositions makes it easier to apply the formal rules of syllogistic logic.

Identify the middle term that connects the two premises.

The middle term is 'Neutron Stars' (N).

The middle term is crucial because its distribution determines whether a link can be formed between the major and minor terms.

Evaluate the distribution of the middle term in both premises.

In 'All P are N', 'N' is the predicate of a universal affirmative proposition, so it is undistributed. In 'Some N are M', 'N' is the subject of a particular affirmative proposition, so it is also undistributed.

A valid syllogism requires the middle term to be distributed (referring to the entire class) in at least one premise.

Determine the validity of the deduction based on the distribution.

Because the middle term is never distributed, the deduction is invalid.

Without a distributed middle term, it is entirely possible for 'Pulsars' and 'Magnetars' to occupy completely separate portions of the 'Neutron Stars' category.

Key Concept

Categorical Syllogisms and the Fallacy of the Undistributed Middle

Question 4386Question →

An archivist intends to perfectly reuse a daily calendar planner originally printed for the year $2096$ . In order for every single date in the planner to fall on the exact same day of the week for the entire year, what is the earliest subsequent year for which this planner can be used again?

2124

2108

2102

2136

Show answer & explanation

Answer: $2108$

Answer

The earliest subsequent year with an identical calendar is

2108

A perfectly repeating calendar must satisfy two strict conditions: the starting weekday must be identical (meaning the accumulated odd days between them must be a multiple of

7

), and both years must share the same leap status. The year

2096

is a leap year. Because

2100

is not a leap year (it is not divisible by

400

), the standard

28

-year repetition cycle is interrupted. We must count the odd days manually. Between

2096

and

2107

, there are

12

years in total:

2

leap years (

2096, 2104

) and

10

normal years. The sum of odd days is

(2 \times 2) + (10 \times 1) = 14

. Since

14

is exactly divisible by

7

, the year

2108

starts on the same day as

2096

. Because

2108

is also a leap year, every date including February 29 perfectly aligns.

Step-by-Step Solution

Determine the leap year status of the original year.

The year

2096

is divisible by

4

, so it is a leap year with

366

days.

A leap year calendar can only perfectly repeat in another leap year. Otherwise, dates from March 1 onwards will shift out of alignment.

Identify the century boundary behavior for the upcoming century.

The upcoming century year is

2100

. Since

2100

is not perfectly divisible by

400

, it is a normal year (not a leap year).

Crossing a non-leap century breaks the standard

28

-year repetition cycle for leap years, necessitating a manual calculation of odd days.

Calculate cumulative odd days year-by-year starting from

2096

Normal years contribute

1

odd day (

365 \pmod 7 = 1

); leap years contribute

2

odd days (

366 \pmod 7 = 2

). The sum must reach a multiple of

7

exactly at the start of a leap year.

A cumulative odd day sum that is a multiple of

7

ensures the starting day of the week exactly matches the original year.

Trace the odd days until both the weekday and leap year conditions are met.

From

2096

2107

(a span of

12

years), there are

10

normal years and

2

leap years (

2096

and

2104

). Total odd days =

(10 \times 1) + (2 \times 2) = 14

. The sum

14

is a multiple of

7

Because the odd days perfectly balance out to

0 \pmod 7

, the next year (

2108

) starts on the identical weekday. Since

2108

is also a leap year, its entire calendar matches

2096

Key Concept

Calendar Repetition Rules and Non-400 Century Boundaries

Question 4387Question →

An arithmetic expression is given as $20 \times 26 - 40$ . Which of the following represents the positive remainder when the final computed value of this expression is divided by $7$ ?

Show answer & explanation

Answer: 4

Answer

The correct positive remainder is 4.

By following the order of operations, the expression evaluates to 480. When 480 is divided by 7, the quotient is 68, leaving a positive remainder of 4 (

68 \times 7 = 476

, and

480 - 476 = 4

). The same result is efficiently reached using modular arithmetic:

(6 \times 5) - 5 = 25

, and

25 \equiv 4 \pmod 7

Step-by-Step Solution

Calculate the exact numerical value of the expression.

20 \times 26 - 40 = 520 - 40 = 480

Applying standard order of operations (BODMAS), multiplication is performed before subtraction.

Divide the computed value by 7 to find the remainder.

480 \div 7 = 68

with a remainder of

4

The remainder is the integer left over after dividing the total by the divisor.

Verify using modular arithmetic (optional).

20 \equiv -1 \pmod 7

26 \equiv 5 \pmod 7

, and

40 \equiv 5 \pmod 7

. Thus,

(-1 \times 5) - 5 = -10

. Modulo 7,

-10 \equiv -3 \equiv 4

Modular arithmetic provides a faster secondary method to confirm the remainder without computing large numbers.

Key Concept

Divisibility Rules and Remainder Theorem

Question 4388Question →

An autonomous delivery drone is programmed to navigate from a central warehouse to a remote drop-off location. The drone executes the following sequence of movements:

1. It takes off and flies $10\text{ km}$ due North.
2. It turns $90^\circ$ to its right and flies $20\text{ km}$ .
3. It then rotates $135^\circ$ anti-clockwise and flies $10\sqrt{2}\text{ km}$ .
4. Finally, it turns $135^\circ$ clockwise and flies $5\text{ km}$ to reach the destination.

What is the shortest direct distance between the warehouse and the drop-off destination?

15\text{ km}

20\text{ km}

35\text{ km}

25\text{ km}

Show answer & explanation

Answer: $25\text{ km}$

Answer

The shortest direct distance between the warehouse and the drop-off destination is

25\text{ km}

The correct answer is found by tracking the drone's position on a 2D plane. By applying the vector components of each movement, the net displacement is

15\text{ km}

East and

20\text{ km}

North. The shortest direct distance is the hypotenuse of these components:

\sqrt{15^2 + 20^2} = 25\text{ km}

Step-by-Step Solution

Determine the drone's position after the first two movements.

Starting at origin

(0,0)

, the drone flies

10\text{ km}

North to

(0, 10)

. Turning

90^\circ

right faces it East; flying

20\text{ km}

brings it to

(20, 10)

Tracking coordinates on a plane allows for precise calculation of vector displacements.

Calculate the coordinates after the

135^\circ

anti-clockwise rotation.

Facing East, a

135^\circ

anti-clockwise turn points the drone North-West. A distance of

10\sqrt{2}\text{ km}

NW means moving

10\text{ km}

West and

10\text{ km}

North. The new position is

(20-10, 10+10) = (10, 20)

The North-West vector components of

10\sqrt{2}

are split equally into

(-10, +10)

on a standard coordinate grid.

Calculate the final position after the

135^\circ

clockwise rotation.

Facing North-West, a

135^\circ

clockwise turn points the drone East. Flying

5\text{ km}

East adds

+5

to the x-coordinate. The final position is

(10+5, 20) = (15, 20)

Establishing the final drop-off location coordinates relative to the warehouse to allow for distance calculation.

Compute the shortest direct distance using the final coordinates.

Using the Pythagorean theorem: Distance

= \sqrt{15^2 + 20^2} = \sqrt{225 + 400} = \sqrt{625} = 25\text{ km}

The shortest direct distance corresponds to the hypotenuse of the right-angled triangle formed by the net horizontal and vertical displacements.

Key Concept

Vector displacement, angular rotation tracking, and Pythagorean theorem application.

Question 4389Question →

The State Board of Industrial Development (SBID) allocates industrial plots in the "Tech-Park Zone".

Criteria for allocation of an industrial plot, as of August 14, 2026, are as follows.
An applicant company must:
1. Have a registered corporate office in the state for at least the last 5 years.
2. Have an annual turnover of not less than ₹50 Crores in the last financial year (2025-2026).
3. Guarantee direct employment generation for at least 150 local residents.
4. Have an approved eco-friendly waste management plan certified by the State Pollution Control Board (SPCB).
5. Deposit an initial earnest money of ₹10 Lakhs.

Exceptions:
However, if an applicant company satisfies all the above criteria EXCEPT:
(A) at (2) above, but is a recognized "Green-Tech Startup" registered under the Central Startup Scheme, the case is referred to the Secretary of SBID.
(B) at (3) above, but guarantees to invest more than ₹20 Crores in automated robotic manufacturing, the case is referred to the Tech-Park Director.
(C) at (4) above, but has deposited an additional environmental security fund of ₹5 Lakhs, the case is referred to the Environmental Compliance Committee (ECC).

"Zenith Eco-Systems" was registered and established its corporate office in the state in May 2019. The company's annual turnover in the 2025-2026 financial year was ₹75 Crores. It has an SPCB-certified waste management plan and has successfully deposited the ₹10 Lakhs earnest money. The company guarantees direct employment for 120 local residents, and to offset this, has submitted a binding guarantee to invest ₹25 Crores exclusively in automated robotic manufacturing.

Based on the information above, what administrative decision should be taken regarding this application?

The case should be referred to the Tech-Park Director.

The application should be rejected.

The industrial plot should be allocated directly.

The case should be referred to the Secretary of SBID.

Show answer & explanation

Answer: The case should be referred to the Tech-Park Director.

Answer

The case should be referred to the Tech-Park Director.

The company satisfies all primary criteria except for criterion 3 (employment generation), as it only provides 120 jobs instead of the required 150. However, because the company guarantees an investment of ₹25 Crores exclusively in automated robotic manufacturing, it satisfies the condition of the second exception. According to this exception rule, such cases must be referred to the Tech-Park Director.

Step-by-Step Solution

Evaluate Criterion 1 (Corporate office for 5 years)

Satisfied

The company was registered in May 2019, which is over 7 years ago as of August 2026.

Evaluate Criterion 2 (Turnover ≥ ₹50 Crores)

Satisfied

The company's turnover in the 2025-2026 financial year was ₹75 Crores.

Evaluate Criterion 3 (Employment ≥ 150)

Failed

The company only guarantees direct employment for 120 local residents.

Evaluate Criterion 4 (SPCB-certified plan) and Criterion 5 (₹10 Lakh deposit)

Satisfied

The company possesses the required SPCB certificate and has successfully deposited the earnest money.

Check for applicable exceptions for the failed criterion

The second exception applies

The company fails only criterion 3 and meets the specific exception condition by guaranteeing a ₹25 Crores investment in automated robotic manufacturing. Therefore, the prescribed action is a referral to the Tech-Park Director.

Key Concept

Applying multiple conditional rules and exception protocols in administrative scenarios to reach a procedural decision.

Question 4390Question →

Eight friends—A, B, C, D, E, F, G, and H—are seated around a square table. Four of them sit at the four corners of the table and face the center, while the other four sit in the middle of each of the four sides and face outward (away from the center).

The following information is known about their seating arrangement:
• A sits third to the left of C, who does not sit at any of the corners.
• E sits second to the right of A.
• Only two people sit between E and B.
• D sits to the immediate left of H, who faces the center.
• H is not an immediate neighbour of A.
• F is not an immediate neighbour of C.

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

G sits to the immediate left of B.

H sits third to the right of F.

A sits second to the right of E.

E sits exactly opposite to G.

Show answer & explanation

Answer: E sits exactly opposite to G.

Answer

The true statement is that E sits exactly opposite to G.

Based on the fully deduced arrangement (clockwise starting from top-middle): C (Out), H (In), D (Out), E (In), F (Out), A (In), B (Out), G (In). Checking the correct statement: E is at the bottom-right corner and G is at the top-left corner, making them diagonally opposite to each other.

Step-by-Step Solution

Determine the basic orientation and place C and A.

C is at a middle position (facing outward). A is placed 3 positions counter-clockwise from C (since left of outward is counter-clockwise). This places A at a corner facing the center.

The first clue provides a fixed starting relationship. 'C does not sit at a corner' confirms C is in the middle of a side.

Determine the positions of E and B based on A's position.

Since A faces the center, right is counter-clockwise. E is placed 2 positions counter-clockwise from A (at the next corner). B is placed 3 positions away from E, which lands exactly opposite C on the middle of a side.

The clues 'E sits second to the right of A' and 'Only two people sit between E and B' dictate these exact relative placements.

Identify the positions of H and D.

H must face the center, meaning H is at a corner. The only corners left are adjacent to C. Since H cannot be next to A, H takes the corner on C's right. Because H faces inward, its immediate left is the adjacent middle seat, which is given to D.

Combining 'H faces the center', 'D is immediate left of H', and 'H is not adjacent to A' leaves only one valid corner-middle pair for H and D.

Place the remaining friends F and G.

Only one middle seat and one corner seat remain. Since F cannot be next to C, F takes the remaining middle seat. G takes the remaining corner seat.

Process of elimination based on the constraint 'F is not an immediate neighbour of C' perfectly resolves the final two seats.

Key Concept

Mixed-orientation spatial reasoning and relative directional assignment in closed shapes.

Question 4391Question →

An Election Returning Officer is conducting a mandatory briefing for polling staff a day before the elections. The officer clearly outlines a strict zero-tolerance policy for procedural deviations, speaking with a measured cadence and even volume. Several staff members, overwhelmed and stressed by the high-stakes responsibility, later report that the officer was verbally abusive. They also attribute their failure to grasp the protocols to the poor acoustics of the auditorium. Applying the core elements of the communication process, which of the following is the most accurate evaluation of this breakdown?

The staff's high stress levels functioned as psychological noise, causing them to falsely decode the officer's assertive boundary-setting as aggressive behavior.

The cognitive stress experienced by the polling staff should be classified as an environmental noise barrier because it occurred within the physical setting of the auditorium.

The officer's strict zero-tolerance mandate is a clear example of aggressive communication because it imposes rigid rules on the receivers without their input.

The measured cadence and even volume maintained by the officer represent kinesic communication channels that the staff failed to properly interpret.

Show answer & explanation

Answer: The staff's high stress levels functioned as psychological noise, causing them to falsely decode the officer's assertive boundary-setting as aggressive behavior.

Answer

The statement identifying the staff's stress as psychological noise that distorted their decoding of the officer's assertive behavior is correct.

The scenario perfectly illustrates how a receiver's internal state (psychological noise) can alter the decoding phase of communication. The officer's behavior was highly assertive—setting clear, firm professional boundaries without hostility—but the staff's heightened stress levels caused them to perceive the interaction as an aggressive attack.

Step-by-Step Solution

Analyze the sender's communication style and message.

The officer set strict procedural rules using a measured cadence and even volume.

To determine if the message was inherently aggressive or simply assertive, and to identify the non-verbal channels used.

Identify the receivers' psychological state and its impact on the message.

The staff were stressed and overwhelmed, which distorted their perception and caused them to feel abused.

To classify the type of communication barrier present (psychological vs. environmental).

Evaluate the options against standard communication theory definitions.

The interaction demonstrates psychological noise disrupting the decoding of an assertive message, eliminating options that misclassify stress as environmental, firmness as aggression, or voice features as kinesics.

To select the only statement that correctly maps the scenario to established elements of the communication process.

Key Concept

Elements of Communication: Psychological Barriers and Assertive Communication

Question 4392Question →

During a family reunion, a guest asks Victor, a married man, about the identity of a young man standing across the room. Victor replies, 'The father of that young man's sister is the husband of my wife's mother.' What is the relationship of the young man to Victor?

Show answer & explanation

Answer: brother-in-law; Brother-in-law; brother in law; Brother in law; Brother In Law

Answer

Brother-in-law

Breaking down Victor's statement: 'my wife's mother' is his mother-in-law, and her 'husband' is his father-in-law. On the other side, 'the father of that young man's sister' is simply the young man's father. Therefore, the young man's father is Victor's father-in-law. This means the young man is the brother of Victor's wife, making him Victor's brother-in-law.

Step-by-Step Solution

Analyze the second part of Victor's statement: 'the husband of my wife's mother'.

Victor's wife's mother is his mother-in-law. Her husband is Victor's father-in-law.

Breaking down complex relational chains starting from the speaker's perspective makes it easier to find the anchor person.

Analyze the first part of Victor's statement: 'The father of that young man's sister'.

The sister of the young man shares the same father as the young man. Therefore, this refers to the young man's own father.

Simplifying the subject of the sentence directly links the relative to the young man.

Equate the two simplified components.

The young man's father is Victor's father-in-law.

The sentence states that the person from Step 2 'is' the person from Step 1.

Determine the final relationship based on the equation.

Since the young man's father is Victor's father-in-law, the young man must be the brother of Victor's wife. Therefore, the young man is Victor's brother-in-law.

Connecting the young man's immediate family to Victor's immediate family provides the specific relational term.

Key Concept

Blood Relations (Pointing Narrative)

Question 4393Question →

A cybersecurity agency audited $250$ government web portals and found vulnerabilities across three categories: Data Breach ( $D$ ), Injection Attacks ( $I$ ), and Authentication Flaws ( $A$ ). The audit report stated:
- $110$ portals were vulnerable to Data Breach
- $130$ portals were vulnerable to Injection Attacks
- $100$ portals were vulnerable to Authentication Flaws
- $45$ portals had both $D$ and $I$ vulnerabilities
- $55$ portals had both $I$ and $A$ vulnerabilities
- $40$ portals had both $D$ and $A$ vulnerabilities
- $20$ portals had all three types of vulnerabilities

Based on this data, how many portals had exactly one type of vulnerability?

120

60

220

80

Show answer & explanation

Answer: $120$

Answer

There are

120

portals with exactly one type of vulnerability.

To find the number of portals with exactly one vulnerability, we isolate the non-overlapping portion of each set. For set

D

, this is

110 - 45 - 40 + 20 = 45

. For set

I

, it is

130 - 45 - 55 + 20 = 50

. For set

A

, it is

100 - 40 - 55 + 20 = 25

. Adding these exclusive regions gives

45 + 50 + 25 = 120

Step-by-Step Solution

Calculate the number of portals vulnerable ONLY to Data Breach (

D

|D_{only}| = |D| - |D \cap I| - |D \cap A| + |D \cap I \cap A| = 110 - 45 - 40 + 20 = 45

Subtracting the pairwise intersections removes the portals with multiple vulnerabilities, but it subtracts the triple intersection twice, so it must be added back once.

Calculate the number of portals vulnerable ONLY to Injection Attacks (

I

|I_{only}| = |I| - |D \cap I| - |I \cap A| + |D \cap I \cap A| = 130 - 45 - 55 + 20 = 50

Applying the same region isolation principle to set

I

Calculate the number of portals vulnerable ONLY to Authentication Flaws (

A

|A_{only}| = |A| - |D \cap A| - |I \cap A| + |D \cap I \cap A| = 100 - 40 - 55 + 20 = 25

Applying the same region isolation principle to set

A

Sum the three isolated regions to find the total number of portals with exactly one vulnerability.

45 + 50 + 25 = 120

These regions represent portals that have one and only one type of vulnerability.

Key Concept

Applying set theory and the inclusion-exclusion principle to isolate specific regions within a three-set Venn diagram.

Question 4394Question →

Six diplomats representing Brazil, Canada, Denmark, Egypt, France, and Ghana are seated in a single straight row facing North during an international summit. Based on the following conditions, arrange the diplomats in the correct order from the extreme left (Position 1) to the extreme right (Position 6) of the row:

- The diplomat from Brazil sits at the extreme left of the row.
- The diplomat from Canada sits exactly between the diplomats from Brazil and Denmark.
- The diplomat from Ghana sits at the extreme right of the row.
- The diplomat from France sits immediately to the left of the diplomat from Ghana.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from left to right is: Brazil, Canada, Denmark, Egypt, France, and Ghana.

By following the direct placement clues sequentially, we can fill the 6 seats without any ambiguity. Brazil takes the far left (1) and Ghana takes the far right (6). Canada and Denmark follow Brazil in that order to satisfy the 'between' condition, filling seats 2 and 3. France goes just before Ghana into seat 5. The only remaining empty seat is seat 4, which is filled by Egypt.

Step-by-Step Solution

Place the diplomats at the extreme ends of the row.

Brazil is at Position 1 and Ghana is at Position 6.

The first and third clues explicitly state the positions for Brazil and Ghana.

Determine the positions of Canada and Denmark.

Canada is at Position 2 and Denmark is at Position 3.

The second clue states Canada is exactly between Brazil and Denmark. Since Brazil is at Position 1, Canada must be at Position 2 and Denmark at Position 3.

Determine the position of France.

France is at Position 5.

The fourth clue states France is immediately to the left of Ghana. Since Ghana is at Position 6, France must be at Position 5.

Assign the final remaining seat.

Egypt is at Position 4.

Positions 1, 2, 3, 5, and 6 are filled. The only diplomat left is Egypt, so they must sit in the only remaining seat, which is Position 4.

Key Concept

Linear seating arrangement with fixed positions and relative placement clues.

Estimated Time:1m 0s

Question 4395Question →

A metropolitan transport network assigns an identification string to each station name using a consistent alphabetic transformation logic. Under this system, the station named NORTH is encoded as OQUXM, and the station named SOUTH is encoded as TQXXM.

What will be the encoded identification string for the station named CENTRAL?

Show answer & explanation

Answer: DGQXWGS; dgqxwgs

Answer

DGQXWGS

The coding logic applies an increasing forward shift to the English alphabet based on the letter's position in the word (1st letter +1, 2nd letter +2, 3rd letter +3, etc.). Applying this sequence to CENTRAL (C+1, E+2, N+3, T+4, R+5, A+6, L+7) yields DGQXWGS.

Step-by-Step Solution

Analyze the transformation pattern from the first example, NORTH to OQUXM.

N(+1) = O; O(+2) = Q; R(+3) = U; T(+4) = X; H(+5) = M.

To identify the underlying coding rule, which involves an increasing positional shift.

Verify the identified pattern using the second example, SOUTH to TQXXM.

S(+1) = T; O(+2) = Q; U(+3) = X; T(+4) = X; H(+5) = M.

To confirm that the logic applies consistently across different inputs.

Calculate the shifted letters for the target word CENTRAL by applying the verified pattern.

C(+1)=D, E(+2)=G, N(+3)=Q, T(+4)=X, R(+5)=W, A(+6)=G, L(+7)=S.

To determine the final encoded string according to the established algorithm.

Key Concept

Positional Alphabet Shifting

Question 4396Question →

A language institute conducted a survey among $400$ civil service aspirants to assess their proficiency in three foreign languages: French, German, and Spanish. The survey revealed the following data:
- $180$ aspirants are proficient in French.
- $150$ aspirants are proficient in German.
- $160$ aspirants are proficient in Spanish.
- $40$ aspirants are proficient in exactly French and German, but not Spanish.
- $30$ aspirants are proficient in exactly German and Spanish, but not French.
- $50$ aspirants are proficient in exactly French and Spanish, but not German.
- $70$ aspirants are not proficient in any of these three languages.

What is the number of aspirants who are proficient in all three languages?

Show answer & explanation

Answer: 20

Answer

By determining the union of the three sets (

400 - 70 = 330

) and applying the inclusion-exclusion principle while correctly distinguishing between 'exactly two' and the full intersection of two sets, we find that

20

aspirants are proficient in all three languages.

Step-by-Step Solution

Determine the number of aspirants proficient in at least one of the three languages.

n(F \cup G \cup S) = 400 - 70 = 330

The total population consists of those who speak at least one language and those who speak none.

Set up an equation using the Principle of Inclusion-Exclusion for three sets. Let

x

be the number of aspirants proficient in all three languages.

n(F \cap G) = 40 + x

n(G \cap S) = 30 + x

, and

n(F \cap S) = 50 + x

The total intersection of any two sets includes those in exactly those two sets plus those in all three sets.

Substitute all values into the union formula.

330 = 180 + 150 + 160 - (40 + x) - (30 + x) - (50 + x) + x

The formula

n(F \cup G \cup S) = n(F) + n(G) + n(S) - n(F \cap G) - n(G \cap S) - n(F \cap S) + n(F \cap G \cap S)

accounts for all overlapping regions.

Simplify the equation and solve for

x

330 = 490 - 120 - 2x \implies 330 = 370 - 2x \implies 2x = 40 \implies x = 20

Basic algebraic simplification yields the final value for the intersection of all three sets.

Key Concept

Principle of Inclusion-Exclusion for Three Sets

Alternative Method

Instead of using the union formula, use a region-based approach in a Venn diagram. Let the central 'all three' region be

x

. Calculate the 'only one' regions in terms of

x

: Only French =

180 - (40 + 50 + x) = 90 - x

. Only German =

150 - (40 + 30 + x) = 80 - x

. Only Spanish =

160 - (50 + 30 + x) = 80 - x

. The sum of all disjoint regions inside the union is

(90 - x) + (80 - x) + (80 - x) + 40 + 30 + 50 + x = 370 - 2x

. Since the union is

400 - 70 = 330

, we have

370 - 2x = 330

, which gives

x = 20

Estimated Time:2m 0s

Question 4397Question →

Six executives (K, L, M, N, O, and P) are seated around an equilateral triangular table. Three of them sit at the three corners, facing the center of the table. The other three sit exactly at the midpoints of the three sides, facing outward (away from the center).

Based on the following conditions, select all statements that are true regarding their final seating positions:

1. M sits at the midpoint of one of the sides.
2. N sits third to the right of M.
3. P sits second to the left of N.
4. O sits to the immediate right of P.
5. K is not an immediate neighbor of M.

Select all that apply

O sits exactly between N and P.

K sits second to the left of O.

L sits to the immediate left of M.

N sits second to the right of L.

Show answer & explanation

Answer: O sits exactly between N and P.; K sits second to the left of O.

Answer

The correct statements are that O sits exactly between N and P, and K sits second to the left of O.

Based on the verified seating chart, N is at the top corner and P is at the bottom-right corner, leaving the right midpoint exactly between them for O. Furthermore, O is at the right midpoint facing outward; moving two spaces to O's left (counter-clockwise) leads to K at the left midpoint.

Step-by-Step Solution

Determine the left/right orientations based on facing direction.

For corner seats (facing IN), Left is Clockwise and Right is Counter-Clockwise. For midpoint seats (facing OUT), Left is Counter-Clockwise and Right is Clockwise.

Establishing relative direction mapping is essential before placing any individuals in mixed-facing geometry.

Place M and locate N.

Assume M sits at the bottom midpoint (facing out). Since M's right is clockwise, moving three positions clockwise places N at the top corner (facing in).

Condition 1 and 2 give a direct relationship between a midpoint and a corner.

Locate P based on N's position.

N is at a corner facing in, so N's left is clockwise. Moving two positions clockwise from the top corner places P at the bottom-right corner (facing in).

Condition 3 connects N to P deterministically.

Locate O relative to P.

P faces in, so P's right is counter-clockwise. Moving one position counter-clockwise from P places O at the right midpoint (facing out).

Condition 4 uses P's position to place O.

Place K and L using the negative condition.

The remaining seats are the left midpoint and the bottom-left corner. M is at the bottom midpoint. K cannot be M's neighbor, so K must take the left midpoint (facing out). L takes the remaining bottom-left corner (facing in).

Condition 5 eliminates the only other open spot for K, completing the seating chart.

Key Concept

Positional Mapping in Mixed-Orientation Polygons

Question 4398Question →

Evaluate whether the following conclusion logically follows from the given statement.

Statement: To enhance urban air quality by 2026, the Municipal Corporation has mandated that all commercial delivery fleets operating within the city limits must transition to 100% electric vehicles (EVs). Delivery agencies failing to meet this mandate will have their commercial operating licenses suspended.

Conclusion: A commercial delivery agency that successfully transitions 100% of its fleet to electric vehicles will definitely have its commercial operating license renewed without suspension.

True

False

Show answer & explanation

Answer: False

Answer

The conclusion does not logically follow (False).

The original statement explicitly dictates the consequence of failing the mandate (license suspension). However, it does not state that transitioning to EVs is the only requirement for keeping a license. The conclusion falsely assumes that complying with this single mandate guarantees the license will not be suspended, entirely ignoring other potential regulatory requirements that a business must follow.

Step-by-Step Solution

Analyze the conditional relationship established in the original statement.

The statement defines a strict penalty condition: IF an agency does not transition to 100% EVs, THEN its license will be suspended.

Mapping the exact cause-and-effect relationship prevents the introduction of outside assumptions.

Evaluate the proposed conclusion against the established conditions.

The conclusion claims that IF an agency transitions to 100% EVs, THEN its license will definitely not be suspended.

This step tests for the formal logical fallacy known as denying the antecedent (or the fallacy of the inverse).

Determine formal logical validity based only on the provided text.

Complying with the EV mandate successfully avoids one specific cause of suspension, but it does not eliminate all other possible causes of suspension that are not mentioned in the text.

A valid inference cannot guarantee a positive outcome based solely on the avoidance of one specific negative condition.

Key Concept

Logical Deduction and Identifying the Fallacy of the Inverse

Estimated Time:1m 0s

Question 4399Question →

During various administrative and public service interactions, officials display different forms of non-verbal communication. Match the specific behavioral scenarios observed in these settings with their correct kinesic category.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The traffic superintendent's gesture matches Emblem; the surveyor's hand movement matches Illustrator; the probationary officer's actions match Adaptor; and the judge's expressions match Affect Display.

Each administrative scenario perfectly demonstrates one of the four primary categories of kinesics. The 'thumbs up' is an Emblem because it replaces words. The tracing of an arc is an Illustrator because it draws what is being said. Fidgeting with a tie is an Adaptor because it manages nervous energy. Frowning is an Affect Display because it shows emotion.

Step-by-Step Solution

Analyze the traffic superintendent's 'thumbs up' gesture.

Identify that the gesture directly substitutes a specific verbal message without needing accompanying speech.

Emblems are a category of kinesics defined by having a direct dictionary translation within a culture.

Evaluate the district surveyor's hand movements.

Identify that the movement visually reinforces the spoken words about the flood's physical size.

Illustrators are body movements that accompany and physically demonstrate or emphasize the corresponding speech.

Assess the probationary officer's behavior of adjusting their tie and rubbing their neck.

Identify these as unconscious, self-directed movements triggered by a high-stress situation.

Adaptors are habitual movements used to manage physical or emotional tension and regulate arousal.

Examine the civil court judge's facial expression and posture.

Identify the frowning and resting head as a direct manifestation of frustration or contemplation.

Affect displays are facial expressions and body language that reveal an individual's internal emotional state.

Key Concept

Categories of Kinesics (Emblems, Illustrators, Adaptors, Affect Displays)

Question 4400Question →

A genealogist is tracing the lineage of a particular family and uncovers the following records:
• Morgan is the only sibling of Robin.
• Robin is legally married to Taylor.
• Taylor is the biological mother of Jamie.
�� Casey is the son of Morgan.

Based exclusively on these genealogical records, which of the following conclusions is definitively true?

Casey and Jamie are first cousins.

Morgan is the paternal uncle of Jamie.

Jamie is the nephew of Morgan.

Taylor is the sister of Morgan.

Show answer & explanation

Answer: Casey and Jamie are first cousins.

Answer

Casey and Jamie are first cousins.

Based on the records, Robin is the father of Jamie (being the spouse of Jamie's mother, Taylor). Morgan is the sibling of Robin. Since Casey is the child of Morgan, and Jamie is the child of Robin, Casey and Jamie are the children of siblings. This definitively makes them first cousins. Their exact genders do not change this cousin relationship.

Step-by-Step Solution

Determine Robin's relationship to Jamie.

Robin is the father of Jamie.

The records state Taylor is Jamie's mother and Robin is married to Taylor.

Determine the relationship between Morgan and Robin.

Morgan and Robin are siblings.

This is explicitly stated in the first genealogical record.

Establish the relationship between the two children, Casey and Jamie.

Casey and Jamie are first cousins.

Casey is the child of Morgan. Jamie is the child of Robin. Because their parents (Morgan and Robin) are siblings, the children are first cousins.

Key Concept

Logical deduction of generational relationships while avoiding gender assumptions based on proper names.

Estimated Time:1m 30s

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