All practice questions

A regional energy transition board reviewed the adoption of residential solar panels across three counties: County Alpha, County Beta, and County Gamma. At the beginning of $2025$, there were a total of $4,000$ households equipped with solar panels across these three counties. The number of such households in County Alpha was $1,500$. At that time, County Beta had $50\%$ more solar-equipped households than County Gamma.

Over the course of $2025$, the number of solar-equipped households in County Alpha increased by $20\%$, while County Gamma saw a $40\%$ increase. By the end of $2025$, the total number of solar-equipped households across all three counties reached $5,000$.

Based on the information provided, which of the following statements are correct?

You are the Municipal Commissioner of a rapidly growing tier-2 city. A major downtown intersection is facing severe daily traffic bottlenecks. To resolve this, the city's traffic department has finalized the blueprint for a new flyover. However, the proposed alignment requires demolishing a portion of a century-old public library and felling several heritage trees. Environmental activists and citizen groups have formed a coalition, staging continuous sit-ins and physically blocking the preliminary survey work. Concurrently, the city's trade association is heavily pressuring your office to expedite the flyover construction to reduce daily logistical losses. Media coverage is intensifying the polarization between the groups. What is the most appropriate initial course of action to resolve this stakeholder conflict?

In a consolidated merit list of 90 applicants for a university fellowship, Marcus is ranked $25^{\text{th}}$ from the top, while Elena is ranked $44^{\text{th}}$ from the bottom. If David is positioned exactly in the middle of Marcus and Elena in this merit list, what is David's rank from the bottom?

The board of directors of a closely-held company consists of five family members: Samar, Kiran, Harpreet, Daksh, and Ekta. The following relational conditions apply:

- Daksh is the son of Kiran, but Kiran is not the mother of Daksh.
- Samar and Kiran are a married couple.
- Ekta is the sibling of Kiran.
- Harpreet is the daughter of Samar.

Based on these statements, what is the exact relationship of Ekta to Harpreet?

A historian finds a perfectly preserved wall calendar for the year 1892. In which of the following subsequent years could this exact same calendar be used for the entire year without any discrepancies?

The city council recently published a new environmental directive. Based on the text below, which underlying assumptions must the council be relying upon? (Select all that apply)

Directive:
To combat the alarming decline in the local sparrow population, the council has initiated a program distributing free wooden birdhouses and urging citizens to install them in their balconies and gardens.

Consider the following policy statements:
1. Most municipal waste management upgrades are designed to reduce methane emissions.
2. Any initiative designed to reduce methane emissions qualifies for special environmental grants.

Based solely on the statements above, it logically follows that all municipal waste management upgrades qualify for special environmental grants.

Eight city planners—Aldo, Bianca, Cyrus, Diana, Ethan, Fiona, Gavin, and Hazel—are seated around a square discussion table. Four of them sit at the corners of the table facing the center, while the remaining four sit at the middle of each of the four sides facing outward.

- Cyrus sits third to the left of Aldo.
- Aldo sits at one of the corners.
- Only two planners sit between Cyrus and Ethan.
- Bianca sits to the immediate right of Ethan.
- Fiona sits second to the left of Bianca.
- Diana is not an immediate neighbor of Aldo.
- Gavin sits second to the right of Diana.

Based on this arrangement, who sits third to the right of Fiona?

An event organizer needs to pack $144$ apples, $180$ oranges, and $216$ bananas into identical fruit baskets. Each basket must contain only one type of fruit, and all baskets must contain exactly the same number of fruits. What is the minimum total number of fruit baskets the organizer must prepare?

Based on the specific letter transformation rule demonstrated in the first pair, which letter cluster correctly completes the second pair?

PLUM : NJXK :: BEAR : ?

Read the following announcement from a transportation agency:

"The regional transport authority has decided to replace all human-operated toll booths on the central highway with automated electronic scanning systems to eliminate traffic bottlenecks and decrease operational overhead."

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

In a digital encryption protocol, a security key is generated based on a master integer $N$. When $N$ is successively divided by $6$, $8$, and $9$, the resulting remainders are $4$, $3$, and $7$, respectively. If $N$ is the smallest possible positive integer that satisfies these conditions, what is the remainder when $N$ is divided by $19$?

Three electronic metronomes are set to tick at regular intervals of $\frac{2}{3}$ of a second, $\frac{3}{4}$ of a second, and $\frac{4}{5}$ of a second, respectively. If they all tick simultaneously at a given moment, after how many seconds will they next tick together simultaneously?

A commemorative time capsule was sealed by a city council on Tuesday, August 15, 1876. The municipal charter mandates that it must be opened exactly 50 years later, on August 15, 1926. Based on the standard Gregorian calendar, on what day of the week will the capsule be opened?

A network administrator is establishing a 5-step automated security protocol. The five steps—Backup Creation, Database Sync, Malware Scan, System Initialization, and User Authentication—must be arranged in a specific sequence based on the following constraints:

1. The Database Sync must occur exactly two steps after User Authentication.
2. The Malware Scan must occur sometime after System Initialization, but before Backup Creation.
3. The Database Sync cannot be the final step, and User Authentication cannot be the first step.

Arrange the five security steps in the correct chronological order from first to last.

A technology company manufactured a total of $400$ units (where $1$ unit = $1,000$ smartphones) across five different models (M1, M2, M3, M4, and M5) in 2026.

The percentage distribution of the total smartphones manufactured is as follows:
M1: $25\%$
M2: $20\%$
M3: $30\%$
M4: $15\%$
M5: $10\%$

The following table shows the ratio of Domestic Sales to Exports for each model:

Based on the provided data, what is the positive difference between the number of M2 smartphones exported and the number of M4 smartphones sold domestically?

A data verification algorithm analyzes inputs based on their fundamental mathematical classifications. During a specific test run, the system is fed four distinct variables:

- $w = \frac{22}{7}$
- $x =$ an arbitrary irrational number
- $y =$ the additive identity of the real number system
- $z =$ an arbitrary prime number strictly greater than 2

Based on the strict mathematical definitions and properties of numbers, which of the following statements are ALWAYS true? (Select all that apply)

Match the following administrative scenarios with the core civil service value they either violate or uphold:

The following facts are recorded in the annual operations report of a government municipality:

1. All departments that implement the new digital archiving system reduce their paper consumption by half.
2. No department in the grievance redressal wing has reduced its paper consumption by half.
3. Some priority task forces are operating within the grievance redressal wing.

Based strictly on these records, which of the conclusions logically follow? (Select all correct options)

Determine the correct chronological progression of the following entities, from their foundational biological origin to the finalized consumer product: