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Question 401Question →

As the Chief Executive Authority of a Special Economic Zone (SEZ), you are confronted with an escalating crisis. A coalition of local villagers and environmentalists has blockaded the site of a multi-billion dollar foreign manufacturing plant, claiming the construction will destroy a traditional water reservoir essential for their livelihoods. The foreign investors have issued a strict 48-hour ultimatum: clear the site immediately or they will relocate their investment to a competing state. The local police superintendent advises a forced, unannounced midnight dispersal of the protesters to prevent media attention and quickly secure the site. Arrange the following courses of action from the most ethically and administratively sound to the least appropriate.

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Answer

The correct sequence from most to least appropriate is: 1) Initiate multi-stakeholder dialogue and verify claims, 2) Use lawful daylight eviction with guaranteed tribunal hearings, 3) Use unannounced midnight police force, and 4) Offer secret financial bribes to protest leaders.
The ethically sound sequence prioritizes transparency, dialogue, and constitutional values first. Lawful procedural action follows as a secondary legitimate tool. Abuse of police force represents a severe ethical failure, but outright corruption (bribery) is the absolute lowest standard of administrative conduct.

Step-by-Step Solution

1
Identify the core ethical conflicts in the scenario.
The conflict lies between economic development (foreign investment), environmental preservation (water reservoir), human rights (peaceful protest), and institutional integrity.
Administrative decisions must balance these competing values while upholding constitutional principles and the rule of law.
2
Evaluate the highest standard of administrative response.
Temporarily halting construction for a joint stakeholder dialogue is identified as the best approach.
It addresses the root cause transparently, verifies facts, and seeks a collaborative solution without violence or coercion.
3
Assess the remaining lawful option.
Securing a court injunction for a daylight clearance is placed second.
It relies on due process, avoids arbitrary executive action, and maintains transparency, even though it is less participatory than open dialogue.
4
Rank the unethical and compromised options.
Midnight police dispersal is placed third, and secret bribery is placed last.
Midnight dispersal is an abuse of power and violates procedural safeguards, but secret bribery represents the total collapse of administrative integrity and constitutes a criminal act.

Key Concept

Administrative Ethics, Conflict Resolution, and Procedural Propriety
Question 402Question →

A state-backed wind energy corporation's plan to expand its farm into traditional grazing territories has triggered aggressive blockades by local pastoralists. Concurrently, local wildlife NGOs are threatening litigation over procedural lapses in the project's environmental clearance. As the appointed District Collector handling this volatile situation, arrange the following administrative interventions in the most optimal sequence to de-escalate the standoff and achieve a sustainable negotiated settlement.

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Answer

The optimal sequence is to first enforce a status quo and conduct fact-finding, followed by separate confidential consultations, then form a joint committee, conduct mediated joint negotiations, and finally ratify a formal MoU.
The correct sequence adheres to the standard public administration protocol for complex stakeholder conflicts: immediate de-escalation (status quo), independent assessment (fact-finding), private trust-building (separate consultations), structured dialogue (joint committee), active mediation (joint negotiation), and final institutionalization (MoU). This progressive approach systematically builds trust and manages volatility before opposing parties face each other.

Step-by-Step Solution

1
Establish immediate control and gather objective facts.
Temporary status quo enforced and fact-finding team deployed.
Prevents immediate violence and provides an objective administrative baseline for all future discussions.
2
Understand individual stakeholder positions privately.
Separate, confidential consultations are held.
Allows parties to express genuine concerns and bottom lines without losing face in front of their opponents.
3
Create a structured, transparent platform for dialogue.
Constitution of a formal multi-stakeholder joint committee.
Brings all parties to a single, officially recognized forum once the necessary groundwork and trust-building are complete.
4
Conduct the core conflict resolution process.
Mediated joint negotiation sessions occur.
Facilitates direct problem-solving, expectation management, and trade-offs between the conflicting groups.
5
Formalize the negotiated agreement.
Drafting and ratification of a legally binding MoU.
Ensures the negotiated settlement is recognized by the state and holds all parties accountable to the agreed terms.

Key Concept

Sequential Administrative Conflict Resolution and Negotiation Strategy
Question 403Question →

Consider the standard sequence of events in criminal justice. In what chronological order do the following events naturally occur?

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Answer

The events occur in the following chronological sequence: Crime, Police, Arrest, Trial, Judgment, Punishment.
The logical flow begins when an offense is committed (Crime). This immediately triggers the involvement of law enforcement (Police), who then take the suspect into custody (Arrest). The suspect is brought before a court for hearings (Trial). After examining the case, the court issues a verdict (Judgment), which results in a penalty (Punishment) if the suspect is found guilty.

Step-by-Step Solution

1
Identify the initial triggering event.
'Crime' is placed first.
The entire legal framework is initiated by the commission of an offense, making it the undeniable starting point.
2
Determine the immediate response and subsequent action.
'Police' followed by 'Arrest'.
Law enforcement must respond to the incident before they have the authority or opportunity to formally apprehend a suspect.
3
Arrange the judicial proceedings.
'Trial' followed by 'Judgment', and finally 'Punishment'.
The suspect must face court proceedings first. These proceedings conclude with a verdict, which then dictates the final consequence.

Key Concept

Logical Sequence and Chronological Classification
Estimated Time:1m 0s
Question 404Question →

Arrange the following words in a logical sequence as they would appear in an English dictionary:

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Answer

The correct dictionary order is: Objection, Objective, Obligation, Oblivion, Obscure.
By strictly applying alphabetical ordering rules, we group the words by their initial letters and then differentiate within groups. 'Objection' precedes 'Objective' because 'o' comes before 'v'. 'Obligation' precedes 'Oblivion' because 'g' comes before 'v'. 'Obscure' is last because 's' comes after 'j' and 'l'.

Step-by-Step Solution

1
Compare the first three letters of all words.
All words start with 'Ob'. The third letters are 'j' (Objection, Objective), 'l' (Obligation, Oblivion), and 's' (Obscure).
Dictionary order strictly follows alphabetical order from left to right.
2
Sort the groups based on the third letter.
The 'j' group comes first, followed by the 'l' group, and finally the 's' group (Obscure).
In the alphabet, 'j' precedes 'l', which precedes 's'.
3
Order the words within the 'j' group (Objection, Objective).
'Objection' comes before 'Objective'.
The first seven letters (O-b-j-e-c-t-i) are identical. The eighth letter 'o' in Objection comes before the 'v' in Objective.
4
Order the words within the 'l' group (Obligation, Oblivion).
'Obligation' comes before 'Oblivion'.
The first three letters (O-b-l) are identical, and the fourth letter is 'i' for both. The fifth letter 'g' in Obligation comes before the 'v' in Oblivion.
5
Combine the sorted groups into the final sequence.
Objection, Objective, Obligation, Oblivion, Obscure.
This maintains the strict alphabetical sorting established in the previous steps.

Key Concept

Dictionary Arrangement and Alphabetical Order
Question 405Question →

Six colleagues—Farah, Gauri, Hasan, Imran, Jamal, and Kiran—are seated in a single straight row facing North for a team meeting.

Read the following information to determine their exact seating positions:
1. Jamal sits third to the right of Farah.
2. Neither Jamal nor Farah sits at the extreme ends of the row.
3. Hasan sits to the immediate left of Gauri.
4. Kiran does not sit at the extreme right end of the row.

Arrange the colleagues in their correct seating order from left (Position 1) to right (Position 6).

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Answer

The correct seating order from left to right is: Kiran, Farah, Hasan, Gauri, Jamal, and Imran.
The correct sequence from left to right is Kiran, Farah, Hasan, Gauri, Jamal, and Imran. By deducing the fixed spacing between Farah and Jamal (who must occupy positions 2 and 5 to avoid the ends), the remaining adjacent seats (3 and 4) are strictly restricted to Hasan and Gauri. Kiran is assigned to the left end (Position 1) because the right end is forbidden for her by the constraints, leaving Imran to take the final open seat at the right end (Position 6).

Step-by-Step Solution

1
Determine the seating positions of Farah and Jamal.
Farah sits at Position 2 and Jamal sits at Position 5.
Jamal is third to the right of Farah. Since neither can sit at the extreme ends (Positions 1 and 6), Farah must be at Position 2, which places Jamal at Position 5 (2 + 3 = 5).
2
Determine the seating positions of Hasan and Gauri.
Hasan sits at Position 3 and Gauri sits at Position 4.
Hasan is immediately to the left of Gauri. The only two adjacent empty seats in the row (which currently has Positions 1, 3, 4, and 6 empty) are Positions 3 and 4.
3
Determine the seating positions of Kiran and Imran.
Kiran sits at Position 1 and Imran sits at Position 6.
The remaining empty seats are Positions 1 and 6. Since Kiran cannot sit at the extreme right end (Position 6), Kiran must sit at Position 1. Consequently, Imran takes the last remaining seat at Position 6.

Key Concept

Linear Seating Arrangement with Negative Constraints
Question 406Question →

You are the Municipal Commissioner of a rapidly expanding city. A severe outbreak of a vector-borne disease has occurred in a densely populated, unauthorized slum settlement. The slum is situated on prime municipal land previously earmarked for a commercial complex. While local health workers request the immediate deployment of emergency medical camps, some municipal officials advise you to use this health crisis as an opportunity to evict the squatters, arguing that the area is inherently unhygienic and illegal.

Arrange the following courses of administrative action from the most ethically sound to the least ethically sound.

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Answer

The most ethical approach prioritizes immediate humanitarian relief and public health containment inside the settlement. This is followed by offering external medical access (which is bureaucratically safe but lacks compassion), then withholding aid to leverage eviction, and finally, the most unethical action: exploiting the crisis to forcibly demolish the settlement under the guise of health measures.
The correct sequence prioritizes the fundamental right to life and immediate disaster containment over bureaucratic enforcement. An ethical administrator must first mitigate the immediate threat to human life before addressing the long-term legal status of the land. The sequence moves progressively from proactive humanitarian aid, to passive bureaucratic aid, to unethical coercion, and finally to outright abuse of power.

Step-by-Step Solution

1
Analyze the core ethical tension in the scenario.
The conflict is between the immediate humanitarian need to save lives during a health crisis and the administrative desire to clear illegal land encroachment.
Identifying the competing values at stake is necessary to evaluate administrative priorities.
2
Identify the most ethically sound action.
Deploying medical camps inside the settlement is ranked first.
The constitutional Right to Life and public health safety absolutely supersede property disputes or zoning laws.
3
Evaluate the intermediate actions.
Directing residents to outside hospitals is ranked second, while withholding aid to issue eviction notices is ranked third.
The former offers some medical help despite bureaucratic rigidity, whereas the latter weaponizes the crisis to force evictions, which is coercive and unethical.
4
Identify the least ethically sound action.
Using police force to demolish the settlement under the guise of sanitization is ranked last.
Deceiving the public and using a health disaster as a cover for violent displacement is a severe abuse of power and violates basic human dignity.

Key Concept

Administrative compassion, proportionality, and prioritization of the Right to Life over procedural enforcement during crises.
Question 407Question →

Four identical delivery vans have different amounts of fuel remaining in their tanks. Arrange the vehicles based on their remaining fuel fraction from the least amount to the greatest amount.

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Answer

The correct ascending sequence of fuel remaining is Van R, Van P, Van S, and Van Q.
By converting all given amounts into decimals (0.600.60, 0.750.75, 0.500.50, and 0.650.65), the values can be directly compared. 0.500.50 is the smallest and 0.750.75 is the largest, resulting in the correct ascending order of Van R, Van P, Van S, and Van Q.

Step-by-Step Solution

1
Convert all fractional fuel values into decimal form for straightforward comparison.
Van P (35\frac{3}{5}) becomes 0.60, and Van R (12\frac{1}{2}) becomes 0.50.
Converting all amounts to decimals provides a uniform format that is easier to logically order.
2
Order the decimal values from smallest to largest.
0.50<0.60<0.65<0.750.50 < 0.60 < 0.65 < 0.75.
The question specifically requires arranging the vehicles from the least amount of fuel to the greatest amount.

Key Concept

Converting basic fractions to decimals to compare and order numerical values.
Question 408Question →

As the Chief Executive Officer of a City Municipal Corporation, you are facing widespread protests. Formal shop owner associations are demanding the immediate removal of informal street vendors who are allegedly causing traffic bottlenecks. Meanwhile, the street vendors' union is protesting the exorbitant fees of the newly constructed municipal vending zones and refusing to relocate. The situation is escalating into daily physical clashes. Arrange the following administrative actions in the most optimal sequential order to resolve this stakeholder conflict effectively and peacefully.

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Answer

The optimal sequence of administrative actions begins with halting evictions to de-escalate the crisis. This is followed by gathering objective data through a socio-economic assessment. After establishing the facts, a tripartite negotiation committee is convened. The resulting consensus is used to draft a revised fee policy, which is finally tested through a pilot relocation program.
The correct sequence ensures that immediate threats to public order are neutralized first. Only then can reliable data be collected to inform a collaborative negotiation process, which in turn leads to a sustainable policy that is safely tested through a pilot program.

Step-by-Step Solution

1
De-escalate the immediate crisis.
Temporarily halt coercive eviction drives.
Public order must be restored and hostilities neutralized before any constructive dialogue or data collection can occur.
2
Gather objective baseline data.
Commission a socio-economic assessment.
Effective negotiations require factual, unbiased data regarding the true number of vendors and their financial capabilities.
3
Facilitate stakeholder mediation.
Convene a tripartite negotiation committee.
Direct negotiation between conflicting parties, mediated by the administration and backed by data, builds mutual trust and identifies common ground.
4
Develop a consensus-based policy.
Draft a revised fee structure and vending policy.
The outcomes of the negotiation must be formalized into an actionable, mutually acceptable administrative policy.
5
Execute and evaluate.
Implement a pilot relocation program.
A phased rollout minimizes systemic risk and allows the administration to address unforeseen on-the-ground challenges before full-scale enforcement.

Key Concept

Sequential conflict resolution requires immediate de-escalation, followed by objective fact-finding, collaborative negotiation, policy formalization, and phased implementation.
Estimated Time:1m 30s
Question 409Question →

Five candidates—Aarav, Bhavna, Chirag, Divya, and Esha—are sitting on a bench from left to right. Based on the clues provided, arrange the candidates in their correct seating order from the leftmost position to the rightmost position.

1. Divya is sitting exactly in the middle of the bench.
2. Bhavna is sitting to the immediate right of Aarav.
3. Esha is not sitting at either of the extreme ends of the bench.
4. Chirag is sitting somewhere to the right of Divya, but he is not sitting immediately next to her.

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Answer

The correct order from left to right is Aarav, Bhavna, Divya, Esha, and Chirag.
Based on the clues, Divya is in the middle (Seat 3). Chirag is to her right but not adjacent, so he must be at Seat 5. Aarav and Bhavna must sit together with Bhavna on the right, which only fits Seats 1 and 2 respectively. Esha takes the remaining Seat 4, which correctly places her away from the extreme ends. Therefore, the left-to-right sequence is Aarav, Bhavna, Divya, Esha, and Chirag.

Step-by-Step Solution

1
Identify Divya's position.
Divya is in Seat 3.
The problem states she is sitting exactly in the middle of the five candidates.
2
Determine Chirag's position.
Chirag is in Seat 5.
Chirag is to the right of Divya (Seats 4 or 5) but not adjacent to her (not Seat 4).
3
Locate Aarav and Bhavna.
Aarav is in Seat 1 and Bhavna is in Seat 2.
They must sit together with Bhavna on the immediate right of Aarav. The only two consecutive empty seats remaining are 1 and 2.
4
Place the remaining candidate.
Esha is in Seat 4.
Esha is the only candidate left and Seat 4 is the only seat left. This also satisfies the condition that she is not at an extreme end.

Key Concept

Linear Seating Arrangement
Question 410Question →

Five cargo ships—Apex, Beacon, Crest, Dawn, and Echo—arrived at a port one after another. Based on the following conditions, arrange the ships in the correct order of their arrival from first to last:

1. Crest arrived exactly two places after Beacon.
2. Dawn arrived before Echo but after Beacon.
3. Apex did not arrive first or last.
4. Echo arrived immediately after Apex.

Arrange the cargo ships in chronological order from the first to arrive to the last.

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Answer

The correct chronological order of arrival is Beacon, Dawn, Crest, Apex, and Echo.
The conditions are uniquely satisfied when Beacon is 1st, Dawn is 2nd, Crest is 3rd, Apex is 4th, and Echo is 5th. Beacon must be first because placing it anywhere else either pushes Crest too far back or prevents Dawn and Echo from following their respective constraints.

Step-by-Step Solution

1
Determine the relative positions of Beacon and Crest.
Beacon is in position xx, and Crest is in position x+2x+2.
The condition states that Crest arrived exactly two places after Beacon.
2
Determine the possible positions for Apex and Echo.
Apex and Echo must occupy consecutive positions, with Apex directly before Echo. Since Apex cannot be first or last, they can only occupy positions 2 and 3, 3 and 4, or 4 and 5.
Echo arrived immediately after Apex, and Apex has boundary restrictions.
3
Test position assignments to satisfy all constraints.
If Beacon is 1st, Crest is 3rd. This leaves positions 4 and 5 for Apex and Echo. Dawn must arrive after Beacon and before Echo, so Dawn perfectly fits into the remaining 2nd position.
If Beacon were placed 2nd or later, it would create unresolvable conflicts with the spacing needed for Apex and Echo, or violate Dawn's placement.

Key Concept

Relative ordering and positional constraints
Question 411Question →

You are the Chief Medical Officer (CMO) of a district hospital during a severe outbreak of a novel viral fever. The hospital is operating at full capacity. A highly influential local politician demands that you clear a general ward—currently occupied by recovering, but still vulnerable, patients—to create an exclusive isolation unit for his extended family, who are exhibiting mild symptoms. The politician subtly threatens to block the hospital's discretionary emergency medicine funding if you do not comply. Arrange the following courses of action from the most ethically sound and administratively appropriate to the least appropriate.

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Answer

The correct sequence begins with adhering strictly to triage and reporting the threat, followed by offering standard admission without reporting, then abandoning the post, and ends with the most unethical act of evicting vulnerable patients.
The most appropriate action directly addresses both the medical reality (triage) and the administrative threat (reporting to superiors). The next best action maintains medical ethics but ignores the threat. Dereliction of duty is severe, but actively harming existing vulnerable patients for political favor is the ultimate breach of administrative and medical ethics, placing it last.

Step-by-Step Solution

1
Evaluate the primary administrative and medical duty in the scenario.
The paramount duty of a CMO is non-maleficence (do no harm) and fair, objective triage of patients regardless of political influence.
Medical ethics and administrative impartiality dictate that healthcare resources must be allocated based strictly on medical need.
2
Assess the ethical standing of each proposed action.
Reporting the threat shows highest integrity. Offering standard admission is ethical but passive. Abandoning the post is a passive failure. Evicting patients is an active, corrupt harm.
Administrative actions must be judged on adherence to statutory rules, the courage to face coercion, and the protection of the public interest.

Key Concept

Administrative Objectivity, Medical Ethics, and Resistance to Undue Influence
Question 412Question →

A financial analyst is evaluating the long-term performance of four mutual funds. The average annualized yield rates of the funds are given below. Arrange the funds in descending order based on their yield rates (from highest to lowest).

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Answer

The correct descending order is Fund X, Fund Y, Fund W, then Fund Z.
By converting all values to their extended decimal forms, we determine their precise magnitudes: Fund X is 8.166...%8.166...\%, Fund Y is 8.155...%8.155...\%, Fund W is 8.151...%8.151...\%, and Fund Z is 8.142...%8.142...\%. Ordering these from highest to lowest yields Fund X, Fund Y, Fund W, then Fund Z.

Step-by-Step Solution

1
Convert Fund W's yield to extended decimal form for precise comparison.
Fund W = 8.15‾%=8.1515...%8.\overline{15}\% = 8.1515...\%
Expanding the recurring decimals reveals the sequence of digits beyond the hundredths place.
2
Convert Fund X's yield to decimal form.
Fund X = 816%=8+0.1666...%=8.1666...%8 \frac{1}{6}\% = 8 + 0.1666...\% = 8.1666...\%
Converting the mixed fraction standardizes the format to match the others.
3
Convert Fund Y's yield to extended decimal form.
Fund Y = 8.15‾%=8.1555...%8.1\overline{5}\% = 8.1555...\%
Properly expanding the specific repeating digit distinguishes it from Fund W.
4
Convert Fund Z's yield to decimal form.
Fund Z = 577%=817%≈8.1428...%\frac{57}{7}\% = 8 \frac{1}{7}\% \approx 8.1428...\%
Division provides the decimal equivalent needed for a direct comparison.
5
Compare the decimal values digit by digit from left to right.
Highest is 8.166...8.166... (Fund X), then 8.155...8.155... (Fund Y), then 8.151...8.151... (Fund W), and lowest is 8.142...8.142... (Fund Z).
Sorting by the tenths, hundredths, and thousandths digits establishes the definitive descending sequence.

Key Concept

Converting mixed fractions, improper fractions, and different notations of recurring decimals into standard decimal form for accurate comparison.
Question 413Question →

A civil engineer is evaluating the thickness of four different structural panels, measured in centimeters (cm). To meet safety standards, the panels must be stacked from the thinnest to the thickest. Arrange the following panel thicknesses in ascending order.

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Answer

The correct ascending order from thinnest to thickest is: Panel Z, Panel X, Panel W, Panel Y.
The correct sequence is determined by converting all measurements into standard decimal forms. Panel Z is exactly 1.3751.375 cm, Panel X is approximately 1.4281.428 cm, Panel W is 1.444...1.444... cm, and Panel Y is exactly 1.4501.450 cm. Sorting these values in ascending order yields Panel Z, Panel X, Panel W, Panel Y.

Step-by-Step Solution

1
Convert the thickness of Panel Z into a standard decimal format.
Panel Z = 138=1+0.375=1.3751\frac{3}{8} = 1 + 0.375 = 1.375 cm.
Converting a mixed fraction to a decimal allows for direct magnitude comparison.
2
Convert the thickness of Panel X into a standard decimal format.
Panel X = 107≈1.42857...\frac{10}{7} \approx 1.42857... cm.
An improper fraction must be divided out to identify its exact decimal value.
3
Expand the thickness of Panel W to clearly see its decimal value.
Panel W = 1.4‾=1.4444...1.\overline{4} = 1.4444... cm.
The overline indicates a recurring decimal that continues infinitely with the digit 4.
4
Compare all four decimal values and arrange them from smallest to largest.
1.375<1.42857...<1.4444...<1.4501.375 < 1.42857... < 1.4444... < 1.450. Therefore, Panel Z < Panel X < Panel W < Panel Y.
The stem requires ordering from thinnest to thickest.

Key Concept

Converting mixed fractions, improper fractions, and recurring decimals into a common decimal format to accurately compare and order them.
Question 414Question →

During a physical endurance test, four candidates completed different portions of a 10-kilometer cross-country course before a mandatory rest period. The fraction or decimal representing the portion of the course completed by each candidate is given below. Arrange the candidates in ascending order based on the portion of the course they completed (from least to most).

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Answer

Candidate Q, Candidate S, Candidate R, Candidate P
To correctly order the candidates, all values must be evaluated in a uniform format. Candidate P is exactly 0.85. Candidate Q is approximately 0.818. Candidate R is approximately 0.844. Candidate S is approximately 0.833. Arranging these numerical values from least to most gives: Q (0.818...), S (0.833...), R (0.844...), P (0.850).

Step-by-Step Solution

1
Convert the portion completed by Candidate P into a standard decimal format.
1720=17×520×5=85100=0.85\frac{17}{20} = \frac{17 \times 5}{20 \times 5} = \frac{85}{100} = 0.85
Converting all values to standard decimals makes it easier to directly compare their magnitudes.
2
Convert the portion completed by Candidate Q into an expanded decimal format.
0.81‾=0.818181…0.\overline{81} = 0.818181\dots
Expanding the recurring bar notation clarifies the digits beyond the hundredths place.
3
Convert the portion completed by Candidate R into an expanded decimal format.
0.84‾=0.844444…0.8\overline{4} = 0.844444\dots
Expanding the single recurring digit makes its exact magnitude clear for comparison.
4
Convert the portion completed by Candidate S into a decimal format.
56=5÷6=0.833333…\frac{5}{6} = 5 \div 6 = 0.833333\dots
Performing the division provides the decimal value needed to compare against the others.
5
Compare the resulting decimal values and arrange them in ascending order.
0.8181⋯<0.8333⋯<0.8444⋯<0.85000.8181\dots < 0.8333\dots < 0.8444\dots < 0.8500
Sorting the decimals from smallest to largest yields the order: Candidate Q, Candidate S, Candidate R, Candidate P.

Key Concept

Converting mixed fraction types and recurring decimals into a uniform decimal format to accurately compare their relative magnitudes.
Question 415Question →

An aerospace engineering facility is calibrating a pressure sensor using four specialized metallic foils. To prevent calibration errors, a technician must stack these foils in strictly ascending order of their thickness (from thinnest to thickest).

The thicknesses of the four foils are:
- Foil P: 0.3450.345 mm
- Foil Q: 1132\frac{11}{32} mm
- Foil R: 0.34‾0.\overline{34} mm
- Foil S: 720\frac{7}{20} mm

Arrange the foils in the correct ascending order of their thickness.

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Answer

The correct ascending sequence from thinnest to thickest is Foil R, Foil Q, Foil P, and Foil S.
By converting all foil thicknesses into uniform decimal representations, we establish the values: Foil R (0.3434...0.3434...), Foil Q (0.343750.34375), Foil P (0.3450.345), and Foil S (0.350.35). Comparing these exact decimal values digit-by-digit confirms that the ascending sequence must be R, Q, P, then S.

Step-by-Step Solution

1
Convert the fraction for Foil S to a decimal.
720=7×520×5=35100=0.35\frac{7}{20} = \frac{7 \times 5}{20 \times 5} = \frac{35}{100} = 0.35 mm
Converting all measurements to a uniform decimal format allows for direct magnitude comparison.
2
Convert the fraction for Foil Q to a decimal.
11÷32=0.3437511 \div 32 = 0.34375 mm
Using long division provides the exact decimal expansion necessary to compare against closely grouped measurements.
3
Expand the recurring decimal for Foil R.
0.34‾=0.343434...0.\overline{34} = 0.343434... mm
Expanding the repeating digits to at least 4 decimal places makes place-value comparison clear.
4
Compare all four decimal values place-by-place and sequence them from smallest to largest.
0.343434...<0.34375<0.34500<0.350000.343434... < 0.34375 < 0.34500 < 0.35000
Aligning the decimals by their thousandths and ten-thousandths places reveals the exact ascending sequence.

Key Concept

Converting fractions and recurring decimals into standard decimals to accurately evaluate and compare their magnitudes.
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