Tüm alıştırma soruları

4581 soru

Tüm türler4,581 Çoktan seçmeli2,372 Çoklu seçim712 Doğru / Yanlış174 Sayısal188 Eşleştirme670 Sıralama415 Boşluk doldurma20 Kısa cevap30

Soru 421Soru →

An industrial cutting machine is programmed to divide a rectangular metallic sheet measuring $\frac{24}{5}$ meters in length and $\frac{16}{3}$ meters in width into identical square plates. If the square plates must be of the maximum possible size without leaving any wasted material, what is the area of each resulting square plate?

\frac{64}{225} \text{ m}^2

2304 \text{ m}^2

64 \text{ m}^2

\frac{256}{25} \text{ m}^2

Cevabı ve açıklamayı göster

Cevap: $\frac{64}{225} \text{ m}^2$

Cevap

The area of each resulting square plate is \frac{64}{225} \text{ m}^2.

To cut the rectangle into identical squares of maximum size without waste, the side length of the square must be the Highest Common Factor (HCF) of the rectangle's dimensions. Using the fraction formula, the HCF of

\frac{24}{5}

and

\frac{16}{3}

\frac{\text{HCF}(24, 16)}{\text{LCM}(5, 3)} = \frac{8}{15}

meters. The area of the square is the side length squared, which is

(\frac{8}{15})^2 = \frac{64}{225} \text{ m}^2

Adım Adım Çözüm

Determine the required mathematical operation for finding the maximum square size.

The side length of the square must be the Highest Common Factor (HCF) of the length (24/5) and width (16/3).

To divide a rectangle into identical squares without waste, the square's side must perfectly divide both dimensions. The 'maximum size' implies finding the greatest common divisor.

Apply the rule for finding the HCF of fractions.

HCF(a/b, c/d) = HCF(a, c) / LCM(b, d). Thus, HCF(24/5, 16/3) = HCF(24, 16) / LCM(5, 3).

The standard formula for the HCF of fractions requires taking the HCF of the numerators divided by the LCM of the denominators.

Calculate the specific HCF and LCM values.

HCF(24, 16) = 8 and LCM(5, 3) = 15. The side length of the square is \frac{8}{15} meters.

8 is the largest integer dividing both 24 and 16. 15 is the smallest integer divisible by both 5 and 3.

Calculate the area of the square.

Area = (\frac{8}{15})^2 = \frac{64}{225} \text{ m}^2.

The question specifically asks for the area of the plate, which is the square of its side length.

Anahtar Kavram

HCF of Fractions and Geometric Application

Soru 422Soru →

During the execution of a critical state infrastructure project, civil servants frequently encounter complex ethical challenges. Match the following specific administrative dilemmas faced by officials with the core governance principle that must primarily dictate their resolution.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The correct matching aligns the communication barrier with administrative equity, the safety testing bypass with statutory mandates, the spouse's firm with conflict of interest recusal, and the facilitation fee with financial integrity.

Each dilemma fundamentally challenges a distinct pillar of public administration. The language barrier marginalizes a vulnerable group, demanding equity. The pressure to skip safety tests threatens public welfare and the rule of law. The spouse's involvement is a direct conflict of interest requiring formal recusal. The offered fee is a bribe, testing financial integrity.

Adım Adım Çözüm

Analyze the District Collector's dilemma regarding the indigenous community.

Identified as an issue of information asymmetry and marginalization.

When citizens cannot access their rights due to language barriers, the governing principle must be Administrative Equity and Proactive Transparency.

Analyze the Chief Engineer's dilemma regarding political pressure and soil testing.

Identified as a conflict between political expediency and public safety.

Administrative ethics dictate that Statutory Safety Mandates and Rule of Law must always supersede political or electoral timelines.

Analyze the Tender Evaluation Officer's dilemma regarding the spouse's firm.

Identified as a textbook conflict of interest.

Even if the bid is technically sound, the familial connection requires Institutional Probity through Conflict of Interest Recusal to prevent perceived or actual bias.

Analyze the Land Settlement Officer's dilemma regarding the 'facilitation fee'.

Identified as an attempted bribery and subversion of standard queues.

Such offers must be rejected under the principle of Absolute Financial Integrity and Impartial Public Service.

Anahtar Kavram

Situational Ethics and Administrative Dilemmas

Soru 423Soru →

In a straight row of cadets facing North for a morning assembly, Cadet Marcus is standing $15^{\text{th}}$ from the left end and Cadet Victor is standing $28^{\text{th}}$ from the right end. If they interchange their positions, Cadet Marcus becomes $35^{\text{th}}$ from the left end. What is Cadet Victor's new position from the right end?

47^{\text{th}}

48^{\text{th}}

49^{\text{th}}

62^{\text{nd}}

Cevabı ve açıklamayı göster

Cevap: $48^{\text{th}}$

Cevap

48^{\text{th}}

The correct answer accurately calculates the total number of cadets as

62

and correctly applies the formula to find the rank from the opposite end (

62 - 15 + 1 = 48

Adım Adım Çözüm

Calculate the total number of cadets in the row.

Total =

62

cadets.

After the interchange, Marcus occupies Victor's original position. This physical spot is

35^{\text{th}}

from the left and

28^{\text{th}}

from the right. The total number of cadets is

L + R - 1 = 35 + 28 - 1 = 62

Determine Victor's new position from the left.

Victor is now

15^{\text{th}}

from the left.

During the interchange, Victor takes Marcus's original spot, which was given as

15^{\text{th}}

from the left.

Calculate Victor's new position from the right end.

Victor is

48^{\text{th}}

from the right.

Using the position conversion formula (Total - Position from left + 1), Victor's position from the right is

62 - 15 + 1 = 48

Anahtar Kavram

Position Interchange and Total Calculation in Linear Arrangements

Alternatif Yöntem

Since Marcus's position shifted by

20

places (

35 - 15 = 20

) during the interchange, Victor's position must also shift by the exact same number of places relative to his starting end. Therefore, Victor's new position from the right end is simply

28 + 20 = 48^{\text{th}}

Tahmini Süre:1m 0s

Soru 424Soru →

Four navigation buoys in a harbor flash at regular intervals of $3 \frac{1}{3}$ minutes, $4 \frac{1}{6}$ minutes, $5 \frac{5}{9}$ minutes, and $7 \frac{1}{2}$ minutes, respectively. If all four buoys flash simultaneously at exactly 12:00 noon, how many additional times will they all flash together again within the next $12$ hours?

Cevabı ve açıklamayı göster

Cevap: 4

Cevap

The correct answer is derived by finding the Least Common Multiple of the fractional intervals to determine the duration between simultaneous flashes (150 minutes). Then, by converting the 12-hour period into 720 minutes, dividing 720 by 150 yields 4.8, indicating the buoys will flash together 4 additional times within that exact timeframe.

Adım Adım Çözüm

Convert the mixed numbers into improper fractions.

The intervals are

\frac{10}{3}

\frac{25}{6}

\frac{50}{9}

, and

\frac{15}{2}

minutes.

Mathematical operations involving LCM and HCF of fractions require them to be in proper or improper fractional forms, rather than mixed numbers.

Determine the mathematical formula required for simultaneous events.

We must calculate the Least Common Multiple (LCM) of the intervals using the formula:

\text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}}

Simultaneous cyclic events synchronize at the lowest common multiple of their individual intervals.

Calculate the LCM of the numerators.

The numerators are

10, 25, 50

, and

15

. Their LCM is

150

150

is the smallest integer divisible by all four numerators (

150 = 10 \times 15 = 25 \times 6 = 50 \times 3 = 15 \times 10

Calculate the HCF of the denominators.

The denominators are

3, 6, 9

, and

2

. Their HCF is

1

The numbers

2

and

3

are coprime (they share no common factors greater than

1

), forcing the overall HCF of the set to be

1

Calculate the exact time interval between simultaneous flashes.

The LCM of the intervals is

\frac{150}{1} = 150

minutes.

Applying the results from steps 3 and 4 directly into the fractional LCM formula.

Determine how many times this 150-minute interval fits into the 12-hour window.

12 \text{ hours} = 720 \text{ minutes}

\lfloor \frac{720}{150} \rfloor = \lfloor 4.8 \rfloor = 4

Dividing the total available time by the simultaneous interval length gives the exact count of additional flashes.

Anahtar Kavram

LCM of fractions in simultaneous cyclic events

Soru 425Soru →

You are the District Magistrate of a drought-affected district. The state government has issued a strict vulnerability-based priority list for dispatching emergency water tankers. An influential local politician demands that you immediately divert three tankers to a neighborhood where his primary supporters reside, which is currently classified as 'low priority' based on objective hydrological data. The politician threatens to mobilize a massive protest blocking the main district highway, which would paralyze the movement of all relief convoys, if his demand is not met. What is the most appropriate administrative action in this situation?

Firmly deny the request citing the objective priority list, officially inform the state control room about the highway threat, and arrange preventive police deployment along the relief convoy routes.

Divert one tanker to the requested neighborhood as a strategic compromise to ensure that the remaining relief convoys can travel safely without facing highway blockades.

Order the immediate preventive detention of the politician to ensure the relief operations can proceed smoothly without any political interference.

Temporarily halt the movement of all relief convoys across the district to ensure the safety of the staff until a formal negotiation is concluded with the politician.

Cevabı ve açıklamayı göster

Cevap: Firmly deny the request citing the objective priority list, officially inform the state control room about the highway threat, and arrange preventive police deployment along the relief convoy routes.

Cevap

Firmly deny the request citing the objective priority list, officially inform the state control room about the highway threat, and arrange preventive police deployment along the relief convoy routes.

The correct answer demonstrates administrative fortitude and adherence to objective, data-driven protocols. By refusing the coercive demand, the administrator upholds fairness. By arranging police deployment and informing the state control room, the administrator addresses the threat of disruption proportionally and legally, ensuring the relief effort continues safely.

Adım Adım Çözüm

Analyze the core ethical and administrative conflict.

The conflict is between adhering to an objective, data-driven public duty (priority list) versus succumbing to political pressure and threats of disruption.

Identifying the competing interests is necessary to determine the legally and ethically sound path.

Evaluate the proposed actions against administrative principles.

Compromising violates protocol. Preventive detention or halting operations are extreme, disproportionate reactions. Enforcing the list with police backup maintains order and protocol.

Administrative decisions must be objective, proportionate, and strictly adhere to the rule of law.

Select the action that upholds public interest while utilizing appropriate institutional mechanisms.

The correct approach is to reject the coercion, document the threat with higher authorities, and secure the logistics using law enforcement.

This balances the delivery of essential services with the maintenance of law and order, without yielding to blackmail.

Anahtar Kavram

Situational Ethics and Administrative Dilemmas

Soru 426Soru →

Consider the composite number $X = p^3 \cdot q^2$ , where $p$ and $q$ are distinct prime numbers. Which of the following statements regarding the factors and properties of $X$ are correct?

Geçerli olan tümünü seçin

The total number of positive factors of

X

is exactly

12

p=2

and

q=3

, the sum of all positive factors of

X

195

The total number of positive factors can be derived by the expression

3 + 1 \times 2 + 1

, which yields exactly

6

factors.

The total number of positive factors of

X

that are multiples of either

p

q

17

, calculated by directly adding the

9

factors divisible by

p

to the

8

factors divisible by

q

Cevabı ve açıklamayı göster

Cevap: The total number of positive factors of $X$ is exactly $12$ .; If $p=2$ and $q=3$ , the sum of all positive factors of $X$ is $195$ .

Cevap

The correct statements are that the total number of positive factors is exactly 12, and if p=2 and q=3, the sum of all positive factors is 195.

The correct options properly apply the theorems of prime factorization. A composite number with prime factorization

p^a \cdot q^b

always has

(a+1)(b+1)

total factors, which confirms the count of

12

. Furthermore, the geometric series expansion for the sum of factors correctly evaluates to

195

when substituting

p=2

and

q=3

Adım Adım Çözüm

Determine the total number of positive factors of X.

The prime powers are 3 and 2. Using the formula (a+1)(b+1), we get (3+1)(2+1) = 4 * 3 = 12.

This establishes the baseline count of factors necessary for evaluating the first statement and the arithmetic logic of the third statement.

Calculate the sum of factors for the specific case where p=2 and q=3.

The sum is (1 + 2 + 4 + 8) * (1 + 3 + 9) = 15 * 13 = 195.

This verifies the explicit calculation claim made in the second statement.

Analyze the arithmetic expression proposed for factor counting: 3 + 1 * 2 + 1.

The expression lacks brackets. By standard order of operations, 3 + (1*2) + 1 = 6, which is mathematically flawed for factor counting.

Identifying the missing parentheses reveals a fundamental BODMAS order of operations violation.

Apply the inclusion-exclusion principle to count factors that are multiples of p or q.

Factors divisible by p: 9. Factors divisible by q: 8. Intersection (divisible by pq): 6. Union = 9 + 8 - 6 = 11.

This verifies whether directly adding the two sets is mathematically sound, proving that the fourth statement double-counts the overlap.

Anahtar Kavram

Prime factorization properties, including total factor counting, sum of factors, and applying set theory (inclusion-exclusion) to factor subsets.

Tahmini Süre:1m 30s

Soru 427Soru →

Evaluate the remainder when the numeric expression $47^{101} + 111^{101} - 25$ is divided by $16$ .

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

By applying the properties of modular arithmetic, we determine that

47 \equiv -1 \pmod{16}

and

111 \equiv -1 \pmod{16}

. Raising these to the 101st power yields

-1

and

-1

. Subtracting 25 gives a total of

-27

. To find the positive remainder, we add the next highest multiple of 16 (which is 32) to -27, yielding a final valid positive remainder of 5.

Adım Adım Çözüm

Find the remainder of the bases when divided by 16.

47 \equiv -1 \pmod{16}

and

111 \equiv -1 \pmod{16}

Using negative remainders (since

47 = 16 \times 3 - 1

and

111 = 16 \times 7 - 1

) significantly simplifies the calculation of large powers.

Substitute the simplified bases into the original expression.

(47)^{101} + (111)^{101} - 25 \equiv (-1)^{101} + (-1)^{101} - 25 \pmod{16}

The properties of modular arithmetic allow replacing bases with their congruent values modulo the divisor.

Evaluate the exponents and the constant term.

(-1) + (-1) - 25 = -27

An odd power of a negative number remains negative, so

(-1)^{101} = -1

Find the equivalent positive remainder for -27 modulo 16.

-27 \equiv 5 \pmod{16}

Adding multiples of 16 (in this case,

16 \times 2 = 32

) to

-27

yields a positive remainder in the valid range of

0

15

. Calculating

-27 + 32 = 5

gives the final remainder.

Anahtar Kavram

Modular arithmetic with large powers using negative remainders

Alternatif Yöntem

Instead of converting the bases to -1, one could convert them to positive 15. The expression becomes

15^{101} + 15^{101} - 25

. However, evaluating this requires recognizing that

15 \equiv -1 \pmod{16}

to easily compute the large exponents, which ultimately merges back into the primary solution path.

Tahmini Süre:1m 30s

Soru 428Soru →

You are the Sub-Divisional Officer (SDO) overseeing land acquisition for a critical government hospital. During the demarcation process, you discover that a portion of the designated land contains a traditional, unmarked burial ground sacred to a local marginalized indigenous community. This site is not officially recorded in the revenue registry. The local Member of Legislative Assembly (MLA) pressures you to bulldoze the site immediately to lay the foundation stone before the election code of conduct comes into effect, arguing that the land legally belongs to the state and the hospital serves the greater public good.

Arrange the following courses of action from the most ethically sound and administratively appropriate to the least appropriate:

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The most appropriate action is to halt clearance and initiate dialogue. This is followed by proceeding with clearance while offering compensation. The third is using police force for immediate clearance. The least appropriate is secretly encouraging an NGO to file a stay order.

The most appropriate action resolves the conflict through transparency, dialogue, and empathy. The subsequent actions degrade in appropriateness: substituting dialogue with monetary compensation, resorting to insensitive state coercion, and finally, committing outright administrative misconduct through covert subversion.

Adım Adım Çözüm

Evaluate the most ethical and transparent approach.

Initiating dialogue and apprising authorities is identified as the best balance of empathy, legality, and transparency.

Administrative decisions involving marginalized communities require participatory justice and emotional intelligence, not just strict adherence to incomplete records.

Assess the remaining options based on adherence to law versus ethical conduct.

Proceeding with clearance while offering compensation is placed second.

It fulfills the legal mandate of building the hospital but lacks the ethical depth of community consultation.

Determine the worst possible administrative actions.

Using police force is placed third, and secretly subverting the department is placed last.

While using force is coercive and insensitive, it is done openly under the color of law. Subverting the department from within is deceitful, violates conduct rules, and destroys institutional integrity.

Anahtar Kavram

Balancing statutory duties, public interest, and constitutional empathy in the face of political pressure and cultural sensitivities.

Soru 429Soru →

Read the following municipal directive carefully and evaluate the candidate assumptions. Which of the following assumptions are logically implicit in the directive? (Select all that apply)

Directive: "To address changing transportation trends, the City Council mandates that all newly constructed commercial complexes with a parking capacity exceeding 50 vehicles must allocate at least 10% of their parking spaces for dedicated electric vehicle (EV) charging stations."

Geçerli olan tümünü seçin

A significant number of individuals visiting these new commercial complexes will be driving electric vehicles.

Builders of new commercial complexes possess or can acquire the necessary technical and financial resources to install electric vehicle charging infrastructure.

Implementing this mandate will lead to a measurable improvement in the city's overall air quality over the next five years.

The global supply of fossil fuels is rapidly decreasing, necessitating an immediate shift to electric transportation.

Cevabı ve açıklamayı göster

Cevap: A significant number of individuals visiting these new commercial complexes will be driving electric vehicles.; Builders of new commercial complexes possess or can acquire the necessary technical and financial resources to install electric vehicle charging infrastructure.

Cevap

The implicit assumptions are that a significant number of visitors will use electric vehicles, and that builders have the capacity to install the required infrastructure.

The correct options represent unstated premises that must be true for the City Council's directive to be logical and executable. There must be an expected user base for the charging stations (the drivers), and the developers must have the practical ability to install them. Without these foundational premises, the mandate would be arbitrary and impossible to enforce.

Adım Adım Çözüm

Analyze the stated directive and its primary motivation.

The directive requires large new commercial complexes to install EV chargers, motivated by 'changing transportation trends'.

Identifying explicit facts is the first step in determining what unstated premises must logically support them.

Test the assumption regarding visitor EV usage.

It is a valid assumption. The mandate would be irrational if the Council did not expect visitors to actually drive electric vehicles to these complexes.

An assumption must act as a necessary logical bridge; without expected users, the infrastructure mandate fails to make sense.

Test the assumption regarding developer capability.

It is a valid assumption. The Council must presume that builders can feasibly execute the installation.

Regulatory requirements implicitly assume that the subjects of the regulation have the means to comply.

Evaluate the remaining options for logical errors.

The statement about improving air quality is discarded as an inference. The statement about fossil fuel depletion is discarded as external knowledge.

Assumptions must be strictly required for the author's statement, differentiating them from likely consequences or outside facts.

Anahtar Kavram

Identifying Implicit Premises vs. Inferences and External Knowledge

Soru 430Soru →

Eight friends—S, T, U, V, W, X, Y, and Z—are sitting in a straight line facing North.

- V sits fourth to the left of W.
- W sits at one of the extreme ends of the line.
- Only two people sit between V and X.
- Y sits third to the right of S.
- S is not an immediate neighbor of V.
- Z sits to the immediate left of T.

Which of the following statements are correct?

Geçerli olan tümünü seçin

U sits exactly between S and V.

Y sits second to the left of T.

T sits to the immediate left of Z.

X sits at the extreme right end of the line.

Cevabı ve açıklamayı göster

Cevap: U sits exactly between S and V.; Y sits second to the left of T.

Cevap

The statements 'U sits exactly between S and V' and 'Y sits second to the left of T' are correct.

Based on the systematic deduction of the constraints, the exact left-to-right order of the eight friends is X, S, U, V, Y, Z, T, W. In this confirmed arrangement, U (position 3) is situated directly between S (position 2) and V (position 4). Additionally, T is at position 7, meaning the second position to its left is position 5, which is exactly where Y sits.

Adım Adım Çözüm

Determine the positions of W and V.

W is at position 8 (extreme right) and V is at position 4.

W is at an extreme end, and V is 4th to the left of W. If W were at the left end (position 1), V couldn't physically be to its left. Thus, W must be at the extreme right (8). Counting 4 spots left places V at 4.

Locate X based on V's position.

X must be at position 1.

Two people sit between V (4) and X. This means X can either be at 1 or 7. We test both possibilities in the next steps.

Evaluate the scenario where X is at position 7.

This scenario leads to a logical contradiction and is eliminated.

If X=7, S (who cannot be adjacent to V at 3 or 5) must be at 1 or 2. If S=1, Y becomes 4, which is already occupied by V. If S=2, Y becomes 5. This leaves spots 1, 3, and 6 empty. However, Z and T require adjacent spots, which are unavailable here. Thus, X cannot be 7.

Finalize positions with X at position 1.

The final arrangement from left to right is: X, S, U, V, Y, Z, T, W.

With X=1, testing valid spots for S yields S=2 (since S cannot be 3 or 5) and Y=5. The remaining empty spots are 3, 6, and 7. Since Z sits to the immediate left of T, they must take the adjacent spots 6 and 7 (Z=6, T=7). U must take the last remaining spot, which is 3.

Anahtar Kavram

Linear Seating Arrangement with North-Facing Orientation

Soru 431Soru →

Consider the number $N = 2^4 \times 3^3 \times 5^2$ . How many positive factors of $N$ are also multiples of $120$ ?

Cevabı ve açıklamayı göster

Cevap: 12

Cevap

For a factor of

N

to be a multiple of

120

, it must contain at least the prime factorization of

120

, which is

2^3 \times 3^1 \times 5^1

. We can factor this out from

N

N = 120 \times (2^1 \times 3^2 \times 5^1)

. The number of such factors is simply the total number of divisors of the remaining portion

(2^1 \times 3^2 \times 5^1)

, which is calculated by adding

1

to each exponent and multiplying them:

(1+1) \times (2+1) \times (1+1) = 12

Adım Adım Çözüm

Determine the prime factorization of 120.

120 = 2^3 \times 3^1 \times 5^1

To find factors of N that are multiples of 120, we must know the minimum prime powers required.

Determine the prime factorization of the quotient N / 120.

\frac{2^4 \times 3^3 \times 5^2}{2^3 \times 3^1 \times 5^1} = 2^{(4-3)} \times 3^{(3-1)} \times 5^{(2-1)} = 2^1 \times 3^2 \times 5^1

Any factor of N that is a multiple of 120 can be expressed as

120 \times k

, where

k

must be a factor of the remaining prime powers of N.

Calculate the total number of positive factors for the quotient

k

(1 + 1) \times (2 + 1) \times (1 + 1) = 2 \times 3 \times 2 = 12

The number of choices for

k

corresponds exactly to the number of factors of N that are multiples of 120.

Anahtar Kavram

Identifying restricted factors and multiples using prime factorization.

Soru 432Soru →

Three different positions of the same die are shown below. The six faces of the die are marked with the Greek letters $\alpha, \beta, \gamma, \delta, \epsilon$ , and $\zeta$ .

- Position 1: Top is $\alpha$ , Front is $\beta$ , Right is $\delta$
- Position 2: Top is $\beta$ , Front is $\gamma$ , Right is $\delta$
- Position 3: Top is $\beta$ , Front is $\alpha$ , Right is $\zeta$

Based on the given positions, which letter is on the face opposite to $\delta$ ?

\alpha

\beta

\gamma

\zeta

Cevabı ve açıklamayı göster

Cevap: $\zeta$

Cevap

The letter on the face opposite to

\delta

\zeta

By analyzing the adjacent faces across the three positions, we can determine all opposite pairs. Gathering all unique adjacent faces for

\beta

, we find it is adjacent to

\alpha, \gamma, \delta

, and

\zeta

. This leaves

\epsilon

as the opposite face to

\beta

. Next, evaluating

\alpha

shows it is adjacent to

\beta, \delta, \zeta

, and

\epsilon

(since

\beta

and

\epsilon

are opposites), leaving

\gamma

as the opposite face to

\alpha

. By the process of elimination, the remaining two faces,

\delta

and

\zeta

, must be opposite to each other.

Adım Adım Çözüm

Identify all visible adjacent faces for

\beta

across the given positions.

In Position 1,

\beta

is adjacent to

\alpha

and

\delta

. In Position 2,

\beta

is adjacent to

\gamma

and

\delta

. In Position 3,

\beta

is adjacent to

\alpha

and

\zeta

. Combining these,

\beta

is adjacent to

\alpha, \gamma, \delta

, and

\zeta

Since a single face of a die can have exactly four adjacent faces, finding all four uniquely determines the fifth face as its opposite.

Determine the face opposite to

\beta

Because

\alpha, \gamma, \delta

, and

\zeta

are adjacent to

\beta

, the only remaining letter,

\epsilon

, must be opposite to

\beta

By the process of elimination among the six faces, the one face not adjacent to a given face must lie on the opposite side.

Determine the faces adjacent and opposite to

\alpha

From Position 1 and 3,

\alpha

is adjacent to

\beta, \delta

, and

\zeta

. Because

\beta

is opposite

\epsilon

\alpha

must also be adjacent to

\epsilon

. This means

\alpha

is adjacent to

\beta, \delta, \epsilon

, and

\zeta

, leaving

\gamma

as the face opposite to

\alpha

Repeating the deduction process systematically for another face eliminates a second pair of opposite faces.

Identify the final opposite pair.

Since we have established that

\beta

is opposite

\epsilon

and

\alpha

is opposite

\gamma

, the remaining two faces,

\delta

and

\zeta

, must be opposite each other.

Once two pairs of opposite faces on a six-sided die are found, the last two remaining faces form the final opposite pair.

Anahtar Kavram

Identifying opposite faces on a 3D die by mapping adjacent faces from multiple rotational views.

Tahmini Süre:1m 30s

Soru 433Soru →

Consider the following statement and the two assumptions that follow it.

Statement:
An advisory issued by the State Water Board states: "Due to the critically low levels in the central reservoir, all residential complexes must install rainwater harvesting units by the end of this year to avoid heavy financial penalties."

Assumptions:
I. The water level in the central reservoir will return to normal capacity immediately after the end of this year.
II. Residential complexes have the practical capability to procure and install the rainwater harvesting units within the stipulated time frame.

Which of the given assumptions is/are logically implicit in the statement?

Only assumption I is implicit

Only assumption II is implicit

Neither assumption I nor II is implicit

Both assumptions I and II are implicit

Cevabı ve açıklamayı göster

Cevap: Only assumption II is implicit

Cevap

Only assumption II is implicit

Assumption II is implicit because any governing body issuing a time-bound directive with a penalty must fundamentally assume that the target audience is capable of completing the task within the given timeframe. Assumption I is not implicit; the board assumes the units will alleviate the crisis, but it does not assume an immediate return to normal capacity by the end of the year, making it an invalid and extreme inference.

Adım Adım Çözüm

Analyze Assumption I against the statement.

Assumption I suggests the reservoir will return to normal capacity immediately after the deadline.

An assumption is an unstated premise necessary for the statement to be logically sound. The board mandates harvesting units to mitigate water shortage, but there is no logical requirement or assumption that this single action will instantly restore the reservoir to full capacity. This is an exaggerated inference.

Analyze Assumption II against the statement.

Assumption II suggests residents have the capability to install the units by the end of the year.

For any administrative body to impose a strict deadline accompanied by heavy penalties, there must be a fundamental assumption that compliance is practically possible. If it were impossible, the mandate would be illogical.

Synthesize the findings to select the correct option.

Only Assumption II satisfies the criteria of being logically implicit.

Since Assumption I fails the implicit premise test and Assumption II passes, the correct conclusion is that solely the second assumption is implicit.

Anahtar Kavram

Identifying valid implicit premises in administrative mandates and distinguishing them from unwarranted inferences.

Soru 434Soru →

Eight colleagues—Fiona, George, Hannah, Ian, Jack, Kelly, Liam, and Mia—are sitting around a square table. Four of them sit at the four corners of the table facing outward (away from the center), while the other four sit in the middle of each of the four sides facing inward (towards the center).

The following information is known about their seating arrangement:
1. Fiona sits at one of the corners.
2. Jack is an immediate neighbor of both Fiona and Kelly.
3. George sits third to the left of Kelly.
4. Hannah sits second to the right of George.
5. Ian is an immediate neighbor of Hannah.
6. Liam sits second to the right of Ian.

Who sits to the immediate left of Mia?

Ian

Kelly

George

Liam

Cevabı ve açıklamayı göster

Cevap: Ian

Cevap

Ian

Based on the logical deduction of all clues, Mia is forced into the Right-Middle seat and faces the center of the table. Because she faces inward, her immediate left is in the clockwise direction along the table's perimeter. The person sitting in that adjacent corner is Ian.

Adım Adım Çözüm

Analyze the facing directions

Corner seats face outward (left is counter-clockwise, right is clockwise). Middle seats face inward (left is clockwise, right is counter-clockwise).

Establishing the correct left and right directions for each seat type is crucial before placing anyone.

Place Fiona, Jack, and Kelly

Assume Fiona is at the Top-Left corner. Since Jack is between Fiona and Kelly, Jack must be at the Top-Middle seat, and Kelly must be at the Top-Right corner.

A corner person's neighbor must be a middle person, locking in this three-person block.

Determine George's position

George is at the Left-Middle seat.

Kelly is at a corner (facing outward). Her left is counter-clockwise. Counting three seats counter-clockwise from Kelly places George at the Left-Middle seat.

Determine Hannah's position

Hannah is at the Bottom-Middle seat.

George is at a middle seat (facing inward). His right is counter-clockwise. Two seats counter-clockwise from George places Hannah at the Bottom-Middle seat.

Place Ian and Liam

Ian is at the Bottom-Right corner, and Liam is at the Bottom-Left corner.

Ian is next to Hannah, so he must be at Bottom-Right or Bottom-Left. If Ian were at Bottom-Left (facing outward), his second right (clockwise) would be Top-Left (Fiona), which is occupied. Thus, Ian must be at Bottom-Right. His second right (clockwise) is Bottom-Left, placing Liam there.

Identify Mia and answer the question

Mia is at the remaining Right-Middle seat. The person to her immediate left is Ian.

Mia faces inward, so her left is clockwise, pointing directly to the Bottom-Right corner where Ian is seated.

Anahtar Kavram

Positional logic with mixed facing directions (inward vs. outward) on a closed polygon.

Soru 435Soru →

An urgent health bulletin released by the district administration states: "To combat the severe outbreak of waterborne infections, all citizens are advised to drink only boiled water for the next three months."

Evaluate the following candidate assumptions based on the given statement:
Assumption I: Boiling water is the only method available to completely eradicate waterborne pathogens.
Assumption II: A substantial number of citizens will read the bulletin and act upon the administration's advice.

Which of the following options correctly identifies the implicit assumption(s)?

Only assumption I is implicit

Only assumption II is implicit

Both assumptions I and II are implicit

Neither assumption I nor II is implicit

Cevabı ve açıklamayı göster

Cevap: Only assumption II is implicit

Cevap

Only assumption II is implicit

The correct answer accurately identifies that only the second assumption is implicit. In standard logical reasoning, whenever a notice, advisory, or appeal is issued, it is fundamentally assumed that it will be read and acted upon by a significant portion of its target audience. The first assumption is invalid because it introduces extreme exclusivity ('only method available') that is not a required premise for issuing the health bulletin.

Adım Adım Çözüm

Analyze the main statement and its core intent.

The statement is a public advisory aimed at preventing waterborne infections by urging citizens to drink boiled water.

Understanding the nature of the statement (an administrative directive/advisory) is necessary to determine what conditions must be true for the statement to be made.

Evaluate Assumption I.

Assumption I claims boiling is the 'only method available'. The statement advises drinking 'only boiled water', but this does not logically necessitate that it is the sole existing scientific method to eradicate pathogens.

Implicit assumptions must not exaggerate or add extreme constraints beyond what is strictly necessary for the original statement to hold true.

Evaluate Assumption II.

Assumption II states that citizens will act upon the advice. This is a universally accepted premise in logical reasoning regarding public notices.

An authority would not issue a public advisory if they assumed the public would entirely ignore it. Therefore, expecting compliance is a necessary underlying premise.

Anahtar Kavram

Evaluating implicit premises in administrative advisories and recognizing extreme qualifiers.

Soru 436Soru →

A District Forest Officer (DFO) observes that a marginalized tribal community, which holds statutory rights to collect minor forest produce, has resorted to illegally felling protected timber trees due to extreme financial distress from a recent crop failure. A prominent environmental NGO threatens a public campaign against the department for ecological negligence. Simultaneously, local elected representatives pressure the DFO to turn a blind eye to the logging to protect their voter base. Which of the following is the most administratively appropriate and ethically sound course of action for the DFO?

Informally allow the community to harvest a restricted quota of timber until the crisis passes, while assuring the NGO that the department is conducting a lengthy investigation.

Immediately deploy armed personnel to arrest all community members involved and permanently revoke their statutory rights to minor forest produce as a strict deterrent.

Enforce the law by halting the illegal felling of timber trees through standard departmental procedures, while officially requesting the district administration to expedite emergency economic relief for the affected community.

Impose an absolute ban on the collection of all resources from the forest, including minor produce, to appease the NGO and quickly eliminate any threat to the ecosystem.

Cevabı ve açıklamayı göster

Cevap: Enforce the law by halting the illegal felling of timber trees through standard departmental procedures, while officially requesting the district administration to expedite emergency economic relief for the affected community.

Cevap

The most appropriate action is to enforce the law by halting the illegal felling through standard procedures, while officially requesting the district administration to provide emergency economic relief.

The correct action demonstrates an optimal balance of administrative firmness and compassion. It upholds the rule of law by stopping the illegal felling, neutralizes political and NGO pressures through objective law enforcement, and addresses the underlying humanitarian crisis by engaging the appropriate district welfare authorities without overstepping departmental bounds.

Adım Adım Çözüm

Identify the core administrative and ethical conflicts.

The DFO faces a clash between the statutory duty to protect timber, the humanitarian crisis of the tribal community, and external pressures from NGOs and politicians.

Understanding all competing interests is required to formulate a balanced, objective response.

Evaluate legal and procedural boundaries.

The DFO cannot legally permit timber felling, nor can the DFO unlawfully revoke established rights to minor produce or ignore political/NGO interference.

Administrative decisions must strictly adhere to the rule of law and statutory protocols.

Formulate a comprehensive, balanced response.

The DFO must stop the illegal activity using standard enforcement to satisfy the legal mandate, while utilizing inter-departmental coordination (district welfare authorities) to address the root cause of economic distress.

This resolves the immediate illegality without resorting to disproportionate cruelty, effectively neutralizing both political and NGO pressures through objective law enforcement.

Anahtar Kavram

Administrative Proportionality, Compassion, and Adherence to Rule of Law

Soru 437Soru →

Six students—K, L, M, N, O, and P—are sitting in a straight line facing North.

1. K sits third to the right of N, and neither of them sits at the extreme ends of the line.
2. O sits to the immediate left of P.
3. P does not sit at an extreme end.
4. M sits to the right of K.

Based on the seating arrangement, match the students (Left) with their correct seating position descriptions (Right).

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Student L sits at the extreme left end; Student N sits immediately between L and O; Student O sits third to the left of M; Student P sits exactly between O and K.

Based on the logical deduction of the constraints, the final left-to-right order is exactly: L, N, O, P, K, M. The matching pairs perfectly describe each student's relative placement in this deduced sequence.

Adım Adım Çözüm

Determine the possible positions for N and K.

N is at position 2 and K is at position 5.

Since K is third to the right of N, the possible position pairs for (N, K) are (1,4), (2,5), and (3,6). The constraints state that neither N nor K sits at the extreme ends (1 and 6). Therefore, they must occupy positions 2 and 5.

Determine the position of M.

M is placed at position 6.

M sits to the right of K. Since K is at position 5, the only available seat to the right is position 6.

Determine the positions of O and P.

O is at position 3 and P is at position 4.

O is to the immediate left of P, requiring two adjacent empty seats. The only adjacent available seats are 3 and 4. Thus, O takes seat 3 and P takes seat 4. This also satisfies the condition that P is not at an extreme end.

Determine the final remaining position for L.

L is placed at position 1.

Seat 1 is the only unoccupied position remaining. The complete seating arrangement from left to right is L, N, O, P, K, M.

Anahtar Kavram

Deducing exact linear seating arrangements by anchoring fixed distance constraints and eliminating invalid positions.

Tahmini Süre:2m 0s

Soru 438Soru →

Read the following urban planning directive carefully and evaluate the candidate assumptions.

Statement:
"To reduce urban heat island effects, the City Planning Commission has mandated that all new commercial buildings with a roof area exceeding 500 square meters must install 'green roofs' featuring vegetative layers starting next year."

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

Geçerli olan tümünü seçin

Suitable vegetation and structural materials for green roofs are currently accessible to commercial builders in the city.

Installing vegetative layers on the roofs of large commercial buildings will have a positive impact on mitigating urban heat.

The city's overall ambient temperatures will decrease immediately and significantly within the first year of the mandate.

Green roofs are structurally more durable and less expensive to maintain than traditional commercial roofing materials.

Cevabı ve açıklamayı göster

Cevap: Suitable vegetation and structural materials for green roofs are currently accessible to commercial builders in the city.; Installing vegetative layers on the roofs of large commercial buildings will have a positive impact on mitigating urban heat.

Cevap

The correct assumptions are that suitable materials for green roofs are accessible to builders, and that installing these roofs will positively impact urban heat mitigation.

For the City Planning Commission's mandate to be logically sound and executable, two unstated premises must be true: First, it must be practically possible for builders to follow the rule (meaning materials are accessible). Second, the required action must actually serve the stated purpose (meaning green roofs effectively reduce urban heat).

Adım Adım Çözüm

Analyze the core objective and the corresponding action presented in the statement.

Objective: Reduce urban heat island effects. Action: Mandate green roofs for new, large commercial buildings.

Understanding the cause-and-effect relationship intended by the author is necessary to identify unstated premises.

Evaluate each candidate assumption against the statement to see if it is a necessary precondition.

The availability of materials and the effectiveness of the green roofs are necessary preconditions for the mandate to be logical and executable.

An assumption is an unstated fact that must be true for the argument or directive to hold up.

Identify and eliminate options that are logical conclusions (inferences) or external real-world facts not required by the statement.

The options discussing immediate temperature drops and maintenance costs are eliminated.

Inferences happen after the statement is accepted; external facts are independent of the author's logic.

Anahtar Kavram

Identifying Implicit Assumptions in Policy Mandates

Tahmini Süre:1m 30s

Soru 439Soru →

Match the following administrative scenarios with the core ethical or governance principle that primarily guides the appropriate course of action.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The scenarios match their respective governing principles as follows: The refusal of quid pro quo aligns with Probity; delaying the audit report violates Political Neutrality; bypassing procurement in emergencies uses the Doctrine of Necessity; and maintaining the welfare scheme despite minor leaks applies Utilitarianism.

Each scenario tests a specific ethical tension. Accepting community assets in exchange for regulatory favors violates probity. Delaying reports for elections violates neutrality. Bypassing financial rules to save lives is justified by the doctrine of necessity. Keeping a largely beneficial scheme despite minor flaws aligns with utilitarianism.

Adım Adım Çözüm

Analyze the hospital funding scenario.

Identified as a conflict of interest involving a transactional favor.

Matches 'Probity in Governance and Rejection of Quid Pro Quo'.

Analyze the audit report delay scenario.

Identified as an attempt to manipulate public perception for electoral gain.

Matches 'Administrative Objectivity and Political Neutrality'.

Analyze the emergency procurement scenario.

Identified as a deviation from protocol strictly to save lives during a crisis.

Matches 'Doctrine of Necessity and Administrative Expediency'.

Analyze the welfare scheme continuation scenario.

Identified as a decision maximizing overall benefit despite acknowledged minor flaws.

Matches 'Utilitarianism and the Greater Public Good'.

Anahtar Kavram

Application of core administrative ethics and governance principles to practical scenarios.

Soru 440Soru →

Six professionals — P, Q, R, S, T, and U — sit around a circular table, with some facing the center and others facing outward. Q faces the center. P sits second to the right of Q. U is not an immediate neighbor of Q, and T sits to the immediate right of U. R sits to the immediate left of P. S sits second to the right of R. P and R face the same direction, while U and P face opposite directions. The immediate neighbors of T face the same direction. Finally, S and T face the same direction as Q.

Based on the given information, who sits to the immediate right of P?

Cevabı ve açıklamayı göster

Cevap: S

Cevap

Based on the seating arrangement logic, P is seated at position 5 and is facing outward. For an individual facing outward from the center, their right side follows the clockwise direction. The person seated immediately clockwise to P is S (at position 6). Therefore, S sits to the immediate right of P.

Adım Adım Çözüm

Place Q and determine P's position.

Q is at position 1 facing the center. P is at position 5.

Since Q faces the center, the right side is counter-clockwise. P sits second to the right of Q (positions: 1 -> 6 -> 5).

Determine the positions of U and T.

U is at position 3 facing the center, and T is at position 2.

U cannot be adjacent to Q, leaving positions 3 and 4 available for U. If U is placed at 4, placing T to its immediate right causes a conflict with either P or R's required positions regardless of facing direction. Thus, U must be at position 3. T sits to the immediate right of U.

Determine the facing direction of P and place R.

P faces outward, placing R at position 4.

R is to the immediate left of P. If P faced the center, R would be at 6. S (second right of R) would then be at 4, forcing R to face inward. But U and P must face opposite directions, meaning if P is inward, U is outward, which breaks T's placement. Therefore, P must face outward, placing R at position 4.

Complete the arrangement with S and verify all conditions.

S is at position 6. R and P face outward. S, T, U, and Q face the center.

S is second to the right of R. Since R faces outward (same as P), right is clockwise (4 -> 5 -> 6). T and S face the same direction as Q (inward). All conditions are satisfied.

Identify the person to the immediate right of P.

S sits to the immediate right of P.

P is at position 5 facing outward. For outward-facing positions, right is clockwise. The position immediately clockwise to 5 is 6, which is occupied by S.

Anahtar Kavram

Analytical reasoning using circular seating constraints with mixed facing directions (inward and outward).

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