TANCET 2025 MBA Question Paper (Available) - Download Question Paper with Solutions PDF

The passage emphasizes that the public acceptance of a single yardstick of time is essential for the smooth functioning of society, making it a major factor in the decision-making process. Without such a standard, social life would become chaotic and unmanageable. This directly impacts daily activities, goods, and services.


Quick Tip: The standardization of time is critical for societal coordination and economic processes to function efficiently.

The passage suggests that society’s judgment of individuals based on the time they conduct their activities is a key element in the decision-making process. The timely performance of tasks and societal norms regarding punctuality directly contribute to the efficiency and functioning of the social structure.


Quick Tip: The societal value placed on punctuality and time management influences both personal and professional success.

The phrase "this tradition" refers to the widespread agreement among people on the measurement of time, which is vital for the smooth functioning of society. This factor is central to the passage and is crucial to the concept of societal organization.


Quick Tip: Agreement on time measurement is a foundational aspect of societal order, affecting everything from daily routines to economic transactions.

The passage notes that the railroad was a key institution that emphasized precise timekeeping, which became essential for organizing society’s activities efficiently. This role of the railroad is a major factor in understanding the importance of standardized time.


The railroad's role in standardizing time was fundamental to shaping modern society, influencing everything from trade to personal schedules.
Quick Tip: The railroad's role in standardizing time was fundamental to shaping modern society, influencing everything from trade to personal schedules.

The passage highlights that the railroad, by imposing precise and regular timekeeping, enhanced societal regularity. The regularity in the movement of trains facilitated the smooth flow of goods, services, and information, making it a major factor in organizing modern life.

Quick Tip: Regularity in timekeeping is essential for efficiency in modern societies, and the railroad played a crucial role in establishing this norm.

The passage highlights that economic reforms, technological changes in telecommunications, IT, and outsourcing are major factors that contributed to the growth of the Indian economy. These factors are key in explaining the rapid economic growth during this period.


Economic reforms and technological advancements are central to India’s economic growth, especially in the services sector.
Quick Tip: Economic reforms and technological advancements are central to India’s economic growth, especially in the services sector.

The passage explicitly states that the services sector grew consistently during this period, with the growth of services accounting for a major portion of India’s economic development. This trend was a key aspect of the economic growth story.


The consistent growth of the services sector has been a major driver of India’s economic performance in the 21st century.
Quick Tip: The consistent growth of the services sector has been a major driver of India’s economic performance in the 21st century.

Outsourcing is highlighted as a key factor contributing to the rise in per capita income. The technological changes and expansion of outsourcing industries played a central role in raising the income levels in India, which is a major factor contributing to economic growth.


Outsourcing has become one of the pillars of India's economic growth, especially in IT and business services, driving significant improvements in per capita income.
Quick Tip: Outsourcing has become one of the pillars of India's economic growth, especially in IT and business services, driving significant improvements in per capita income.

The passage mentions that the growth prior to 2005 is unknown, suggesting a key factor affecting the decision-making process is the absence of reliable growth data for earlier years. This factor is important in understanding the patterns and drivers of economic growth in India.


The lack of data prior to 2005 impacts the analysis of long-term growth trends in India's economy, making it a significant factor in economic decision-making.
Quick Tip: The lack of data prior to 2005 impacts the analysis of long-term growth trends in India's economy, making it a significant factor in economic decision-making.

The share of services in the GDP of low per capita income countries is a major factor in understanding the economic structure and its shift over time. This statistic reflects the structural transformation of the economy and influences future economic decisions.


The change in the share of services in GDP reflects a country's development stage and helps policymakers assess the sectors driving economic growth.
Quick Tip: The change in the share of services in GDP reflects a country's development stage and helps policymakers assess the sectors driving economic growth.

The cleaning and maintenance requirements of airports like Hyderabad and Delhi are crucial factors for Tanzifco’s business expansion. The company is specifically in talks to manage these contracts, which directly influence its operations and decision-making for entering the Indian market.

Quick Tip: Airport maintenance is a key component of Tanzifco's expansion into India, demonstrating the importance of high-profile contracts in their strategy.

Tanzifco’s expertise in cleaning glass claddings on high-rise buildings is a key factor that supports its competitive edge in the market. This specialized service capability is essential to its overall operations and critical to its market expansion plans in India.

Quick Tip: Specialized skills in niche areas like high-rise cleaning give Tanzifco a unique advantage in the competitive Indian market.

Expanding into India is the primary objective of Tanzifco, as highlighted by their formation of a local entity (Tanzifco Cleaning and Waste Management Services Pvt. Ltd.) and their pursuit of waste management and cleaning contracts in Indian cities. This expansion strategy aligns with their business goals.


Expansion into emerging markets like India is often driven by the need to tap into growing markets and increasing demand for services like waste management.
Quick Tip: Expansion into emerging markets like India is often driven by the need to tap into growing markets and increasing demand for services like waste management.

Tanzifco aims to replicate its successful business model in Kuwait and the Gulf in India, which is a key factor for their market entry. This goal directly influences their decision to expand operations to India, as the company seeks to apply proven strategies in a new market.

Quick Tip: Replicating a successful business model is a common strategy when entering new markets, and Tanzifco's past success in the Gulf plays a significant role in their decision-making.

The fact that Tanzifco employs over 30,000 people is a significant factor in its ability to handle large-scale projects and operations. This workforce capability influences the company’s decision to expand and undertake large contracts in India.


A large workforce can be a strong asset when expanding operations, as it demonstrates the company's capacity to handle large projects effectively.
Quick Tip: A large workforce can be a strong asset when expanding operations, as it demonstrates the company's capacity to handle large projects effectively.

A company’s turnover is a critical factor that influences its ability to expand into new markets. Tanzifco's turnover of 300 dollar million demonstrates its financial strength and capacity to invest in and manage large-scale operations, making it a key factor in the decision to enter India.


A strong turnover is crucial for businesses considering expansion into new markets, as it indicates the financial resources available for such ventures.
Quick Tip: A strong turnover is crucial for businesses considering expansion into new markets, as it indicates the financial resources available for such ventures.

The contract with Kuwait Municipality for waste management services is a key factor that demonstrates Tanzifco’s capability and reliability in handling large waste management contracts. This experience directly influences their decision to expand into other regions like India.


Quick Tip: Securing long-term contracts in established markets is a powerful indication of a company's capability and reputation, helping it expand into new markets.

The planned cleaning contracts with hospitals, hotels, and malls in India are a major factor that defines the company’s business strategy for entering the Indian market. These contracts represent significant business opportunities and are key to Tanzifco’s expansion plans.


Quick Tip: Securing contracts in diverse sectors such as healthcare, hospitality, and retail is a strategic move to diversify and strengthen market presence.

The company's operations in multiple Middle Eastern and North African countries, including Kuwait, Qatar, Dubai, Abu Dhabi, and others, is a significant factor in its decision-making process. These operations contribute to the company's experience and capacity to expand further into new markets like India.


The company’s established operations across multiple countries show its experience in handling international projects, making this a key factor in its expansion decisions.
Quick Tip: The company’s established operations across multiple countries show its experience in handling international projects, making this a key factor in its expansion decisions.

The fact that 30 percent of the company’s share is held by Indian private players is a major factor in its decision to expand into India. This partnership may provide local expertise, networks, and resources that are essential for successfully entering and operating in the Indian market.


The involvement of Indian private players in the company strengthens its position and helps facilitate its expansion into India, providing local insights and operational support.
Quick Tip: The involvement of Indian private players in the company strengthens its position and helps facilitate its expansion into India, providing local insights and operational support.

The passage focuses on the need for careful evaluation of service investments, suggesting that not all service improvements automatically provide a competitive advantage. The main emphasis is on evaluating the tangible benefits, such as cost reduction and increased revenues, before investing in service improvements.


A careful evaluation is essential for making business investments, ensuring that they lead to tangible benefits.
Quick Tip: A careful evaluation is essential for making business investments, ensuring that they lead to tangible benefits.

The passage clearly compares service investments to production and distribution investments, stating that all types of investments should be evaluated based on their direct, tangible benefits, such as cost reduction and increased revenues. This makes (c) the correct answer.


Investments should always be weighed against the potential tangible benefits, whether it’s in service, production, or distribution.
Quick Tip: Investments should always be weighed against the potential tangible benefits, whether it’s in service, production, or distribution.

The passage mentions that service helps avoid a damaging reputation and keeps customers from leaving at an unacceptable rate. This matches with option (a), as it emphasizes customer retention and minimizing damage to the bank’s reputation.


Service plays a critical role in customer retention and preventing a company from losing business to competitors.
Quick Tip: Service plays a critical role in customer retention and preventing a company from losing business to competitors.

The passage highlights that the bank managers failed to analyze whether the service improvement could set the bank apart from its competitors. It suggests that the improvement was not unique or difficult to copy, which would have been crucial in establishing a competitive advantage.


To sustain a competitive edge, companies must ensure that their service improvements are unique and difficult for competitors to replicate.
Quick Tip: To sustain a competitive edge, companies must ensure that their service improvements are unique and difficult for competitors to replicate.

The word "only" in the passage is used to emphasize that the improvement in service had little value beyond its ability to be easily described. This suggests that the investment did not offer substantial benefits beyond this characteristic, indicating its relatively low overall value.


Using the word "only" often serves to limit or reduce the importance of something, highlighting its minimal impact in a larger context.
Quick Tip: Using the word "only" often serves to limit or reduce the importance of something, highlighting its minimal impact in a larger context.

The passage traces the evolution of monetary exchange from barter to electronic systems, making "The History of Monetary Exchange" the most fitting title. The passage is not focused on any specific economic issues or banking policies, but on how the concept of money has evolved over time.


The title should accurately reflect the main theme of the passage. Here, the historical evolution of monetary systems is the central focus.
Quick Tip: The title should accurately reflect the main theme of the passage. Here, the historical evolution of monetary systems is the central focus.

The passage clearly states that coins had real value because they were made from pieces of rare metal, i.e., precious metals. This is the reason coins were considered valuable, unlike paper money which derives its value from mutual agreement.


Coins had intrinsic value due to their composition from precious metals, unlike paper currencies that derive value through trust and agreement.
Quick Tip: Coins had intrinsic value due to their composition from precious metals, unlike paper currencies that derive value through trust and agreement.

The passage does not support the idea that computerized monetary systems are limited to small transactions. In fact, it states that they allow money to be transferred instantly across banks, companies, and countries, which implies they are not limited to small transactions.


Electronic monetary systems are designed to handle large transactions quickly, contrary to the statement that they are limited to small transactions.
Quick Tip: Electronic monetary systems are designed to handle large transactions quickly, contrary to the statement that they are limited to small transactions.

The author mentions food, tools, and precious metals and stones together because these items had tangible and intrinsic value. The passage compares these items to coins, which were valuable due to their composition of precious metals, emphasizing their inherent worth.


Intrinsic value refers to the inherent worth of an item, unlike modern money, which gains value through mutual agreement rather than physical substance.
Quick Tip: Intrinsic value refers to the inherent worth of an item, unlike modern money, which gains value through mutual agreement rather than physical substance.

The passage states that paper money has value only because everyone agrees to accept it, implying it has no intrinsic value, unlike coins that are made of precious metals. This is what sets paper money apart from coins.


Paper money derives its value from trust and agreement, unlike coins, which are valuable because of their intrinsic worth.
Quick Tip: Paper money derives its value from trust and agreement, unlike coins, which are valuable because of their intrinsic worth.

The main purpose of the passage is to explain what economic resources are and how they can be categorized. The passage focuses on defining economic resources, including land, capital, labor, and entrepreneurial skills.


The purpose of the passage is focused on providing a clear understanding of the term 'economic resources' and how they are classified.
Quick Tip: The purpose of the passage is focused on providing a clear understanding of the term 'economic resources' and how they are classified.

"Fertile" best reflects the economic meaning of land, as it refers to natural productive resources, such as fertile soil, that are used in the production of goods and services.


In economics, land refers to natural resources, and the term "fertile" aligns well with the idea of productive natural resources.
Quick Tip: In economics, land refers to natural resources, and the term "fertile" aligns well with the idea of productive natural resources.

The passage classifies astronauts under entrepreneurial ability, not labor, because their specialized skills and leadership roles go beyond simple labor tasks. Thus, astronauts are categorized as entrepreneurs rather than labor.


Astronauts are considered part of entrepreneurial ability due to their specialized roles, which involve leadership and high-level decision-making.
Quick Tip: Astronauts are considered part of entrepreneurial ability due to their specialized roles, which involve leadership and high-level decision-making.

The passage clarifies that the economic definition of "land" is much more restricted than the common understanding. It specifically refers to natural resources used in the production of goods and services, such as minerals, forests, and petroleum, rather than simply non-constructed real estate.


The economic definition of land is narrower than common usage, as it focuses on natural resources used in production, not just real estate.
Quick Tip: The economic definition of land is narrower than common usage, as it focuses on natural resources used in production, not just real estate.

The author’s main objective in writing this passage is to define what economic resources are. The passage provides a clear explanation of the different types of economic resources, such as land, capital, labor, and entrepreneurial skills, and explains how these resources contribute to the production of goods and services. The passage emphasizes that economic resources are more than just material items but also include the human and intellectual capital involved in production.


In this passage, the author defines economic resources by breaking them down into categories such as property resources (land and capital) and human resources (labor and entrepreneurship).
Quick Tip: In this passage, the author defines economic resources by breaking them down into categories such as property resources (land and capital) and human resources (labor and entrepreneurship).

The term "land" in economic terms is used to describe natural resources, which are often productive in nature. The word "fertile" best reflects this meaning, as it refers to land that is rich in resources such as fertile soil, which can be used to grow crops. This is consistent with the economic use of land to produce goods and services, such as agricultural production.


"Fertile" is an apt description of land in economic terms because it highlights the land's ability to produce and contribute to the economy through its natural resources.
Quick Tip: "Fertile" is an apt description of land in economic terms because it highlights the land's ability to produce and contribute to the economy through its natural resources.

According to the passage, labor is defined as the physical and mental talents of humans used to produce goods and services, but it excludes entrepreneurial skills. While factory workers, scientists, nurses, and receptionists are all examples of labor, astronauts are classified under entrepreneurial ability because they require specialized skills and often lead missions that involve complex decision-making and leadership, which are characteristics of entrepreneurship.


Astronauts are considered part of entrepreneurial ability due to their leadership and decision-making skills, distinguishing them from simple labor.
Quick Tip: Astronauts are considered part of entrepreneurial ability due to their leadership and decision-making skills, distinguishing them from simple labor.

The economic definition of land is more specific than the general understanding. While common usage might simply refer to land as non-constructed real estate, economists use "land" to specifically describe all natural resources that are used in the production of goods and services. This includes minerals, forests, and petroleum, but excludes other forms of real estate that might not be directly useful for production.


The economic definition of "land" is more focused and restricted, covering only the natural resources used in the production of goods and services.
Quick Tip: The economic definition of "land" is more focused and restricted, covering only the natural resources used in the production of goods and services.

According to the passage, capital refers specifically to all man-made aids to production, which include tools, machinery, and buildings. These are used in the process of producing goods and services. Capital is distinct from money or wealth in general. While money is often associated with capital in common parlance, the passage clarifies that capital, in the economic sense, does not include money. It is focused on productive resources that are created by humans to aid in further production.


Capital goods are the tools, machinery, and buildings that help produce goods and services. They are essential for the production process but should not be confused with financial capital (money).
Quick Tip: Capital goods are the tools, machinery, and buildings that help produce goods and services. They are essential for the production process but should not be confused with financial capital (money).

The passage discusses various creatures, including flying reptiles, and compares them to mammals. The pterosaur is specifically mentioned as a flying reptile, as inferred from the comparison in the passage. It is not a Mesozoic mammal, nor does it resemble a bat in structure. The mention of flying reptiles in the context suggests that the pterosaur fits into this category.


Flying reptiles, like the pterosaur, were distinct from mammals and adapted to flight, unlike mammals that evolved with specialized traits for different environments such as land, air, and water.
Quick Tip: Flying reptiles, like the pterosaur, were distinct from mammals and adapted to flight, unlike mammals that evolved with specialized traits for different environments such as land, air, and water.

The passage explicitly mentions that "It is in the Miocene time that the mammals reached their peak with reference to variety and size," indicating that the largest number of mammals existed during this period. This period is described as the peak time for mammals in terms of diversity and size.


The Miocene period is highlighted as the peak period for mammals, marking their highest variety and size.
Quick Tip: The Miocene period is highlighted as the peak period for mammals, marking their highest variety and size.

The first sentence of Paragraph 1 argues that mammals developed larger mental capacities over time. If it were found that the tyrannosaurus (a reptile) had a larger brain than previously known, it would directly contradict the argument that mammals had an evolutionary advantage in terms of intelligence, weakening the initial argument.


An increase in brain size for the tyrannosaurus would challenge the notion that mammals had a distinct mental capacity advantage over reptiles.
Quick Tip: An increase in brain size for the tyrannosaurus would challenge the notion that mammals had a distinct mental capacity advantage over reptiles.

The passage discusses the evolution and development of mammals over time, referring to prehistoric periods. The evidence for this discussion is inferred from fossilized remains, which are commonly used by scientists to understand ancient life forms and their adaptations.


Fossil evidence plays a critical role in understanding the history of life on Earth, especially when discussing evolutionary processes over millions of years.
Quick Tip: Fossil evidence plays a critical role in understanding the history of life on Earth, especially when discussing evolutionary processes over millions of years.

The phrase "Footprints in the sands of time" aligns with the passage, which traces the evolutionary history of mammals and the lasting impact of these adaptations over time. The passage reflects how different periods of time shaped the development of mammals, much like footprints marking the passage of time.


The expression "Footprints in the sands of time" evokes the idea of enduring marks left over time, similar to the evolutionary progress discussed in the passage.
Quick Tip: The expression "Footprints in the sands of time" evokes the idea of enduring marks left over time, similar to the evolutionary progress discussed in the passage.

Using the empirical formula for skewed distributions, the mode can be approximated as:
\[ Mode \approx 3(Median) - 2(Mean) \]

Substituting the given values:
\[ Mode \approx 3(22) - 2(21) = 66 - 42 = 24 \]

Thus, the mode is approximately 24.0.


For moderately skewed distributions, the empirical formula for the mode is: Mode = 3(Median) - 2(Mean).
Quick Tip: For moderately skewed distributions, the empirical formula for the mode is: Mode = 3(Median) - 2(Mean).

The formula for Simple Interest (S.I.) is: \[ Simple Interest (S.I.) = \frac{P \times R \times T}{100} \]
Where \( P \) is the principal amount, \( R \) is the rate of interest, and \( T \) is the time in years.

Substituting the given values: \[ 7834 = \frac{P \times 8 \times 4}{100} \]

Solving for \( P \): \[ P = \frac{7834 \times 100}{8 \times 4} = 23075 \]

Now, the total amount to be paid is the sum of the principal and interest: \[ Total amount = P + S.I. = 23075 + 7834 = 30459 \]

Thus, the total amount he has to pay is Rs. 30459.


To calculate the total amount with simple interest, first calculate the principal, then add the interest to the principal.
Quick Tip: To calculate the total amount with simple interest, first calculate the principal, then add the interest to the principal.

The relation "is a multiple of" is reflexive because every integer is a multiple of itself (e.g., \( n \) is a multiple of \( n \)). The relation is also transitive because if \( n \) is a multiple of \( m \), and \( m \) is a multiple of \( p \), then \( n \) is a multiple of \( p \). However, the relation is not symmetric because if \( n \) is a multiple of \( m \), it does not imply that \( m \) is a multiple of \( n \) (e.g., 6 is a multiple of 3, but 3 is not a multiple of 6).


A relation is reflexive if every element is related to itself, and transitive if the relation holds between chained elements. It is not symmetric unless both directions of the relation hold.
Quick Tip: A relation is reflexive if every element is related to itself, and transitive if the relation holds between chained elements. It is not symmetric unless both directions of the relation hold.

Let the initial price of petrol be \( x \), which increases to \( 1.25x \) after the hike. Let Raj's initial consumption be \( y \), so his total initial expenditure is \( xy \).
Raj plans to increase his spending by only 15%, making the new total expenditure \( 1.15xy \). Now, let the new quantity he can buy be \( Y \).

According to the condition: \[ 1.25x \times Y = 1.15xy \]
Simplifying: \[ Y/y = \frac{1.15}{1.25} = 0.92 \]
This means Raj can now only purchase 92% of his earlier quantity.
Thus, the percentage reduction in quantity is: \[ (1 - 0.92) \times 100 = 8% \]


To calculate the reduction in quantity, use the relationship between price, expenditure, and quantity purchased. Adjust the expenditure and solve for the new quantity.
Quick Tip: To calculate the reduction in quantity, use the relationship between price, expenditure, and quantity purchased. Adjust the expenditure and solve for the new quantity.

Let the total number of apples be 100.
The vendor sells 60% of the apples, so 40% remains.

The vendor then throws away 15% of the remaining apples: \[ Thrown next = 15% \times 40 = 6 \]
Remaining apples = 40 - 6 = 34 apples.

Next day, the vendor sells 50% of the remaining 34 apples: \[ Sold next = 50% \times 34 = 17 \]
The remaining apples (thrown) are: \[ Thrown next day = 34 - 17 = 17 \]
Thus, the total number of apples thrown is: \[ 6 + 17 = 23% \]


To calculate the total amount thrown, consider the total apples, sales, and the amounts thrown away each day.
Quick Tip: To calculate the total amount thrown, consider the total apples, sales, and the amounts thrown away each day.

Let Maria's weight be \( m \).
Then, John weighs \( 2m \) (since John weighs twice as much as Maria).
Maria's weight is 60% of Bob's weight, so Bob's weight is: \[ b = \frac{m}{0.6} \]

Lee weighs 190% as much as John, so Lee's weight is: \[ l = 1.9 \times 2m = 3.8m \]

Dave's weight is 50% of Lee's weight, so Dave's weight is: \[ d = 0.5 \times 3.8m = 1.9m \]

Thus, we have the following weights:
- John: \( 2m \)
- Maria: \( m \)
- Bob: \( \frac{m}{0.6} \)
- Lee: \( 3.8m \)
- Dave: \( 1.9m \)

Clearly, Maria weighs the least as \( m \) is the smallest value.


In such questions, express the weights of all individuals in terms of a single variable and compare them directly.
Quick Tip: In such questions, express the weights of all individuals in terms of a single variable and compare them directly.

Let the total number of tickets received by the member be \( x \).
He sold 75% of the tickets, so 25% remained unsold.
According to the question, 25% of \( x \) equals 80 tickets: \[ \frac{25}{100} \times x = 80 \] \[ x = \frac{80 \times 100}{25} = 320 \]
Thus, the total number of tickets is \( 320 \).

The amount collected by the member is: \[ 320 \times 100 = 24,000 \]

Hence, the correct answer is Option (d).


Always define the total quantity in terms of a variable and use the given conditions to solve for it.
Quick Tip: Always define the total quantity in terms of a variable and use the given conditions to solve for it.

The maximum sum that can be obtained by rolling two dice is 12 (6 + 6).
Therefore, the sum will always be less than 13.

Hence, the probability that the sum is less than 13 is 1.


When the maximum possible sum is less than the desired value, the probability is 1, as all outcomes satisfy the condition.
Quick Tip: When the maximum possible sum is less than the desired value, the probability is 1, as all outcomes satisfy the condition.

Let the number of starters be \( S \), and the number of main courses be \( M \).

The number of ways to select 1 starter = \( S \).

The number of ways to choose 2 main courses = \( M(M - 1)/2 \).


So, total combinations = \( S \times \frac{M(M - 1)}{2} = 15 \).
Multiplying both sides by 2:
\[ S \times M(M - 1) = 30 \]


Now, try possible values of \( M \) such that \( M(M - 1) \) is a factor of 30:


- If \( M = 2 \), then \( M(M - 1) = 2 \), then \( S = \frac{30}{2} = 15 \)

- If \( M = 3 \), then \( M(M - 1) = 6 \), then \( S = \frac{30}{6} = 5 \)


- If \( M = 4 \), then \( M(M - 1) = 12 \), then \( S = \frac{30}{12} = 2.5 \) (Invalid)

- If \( M = 5 \), then \( M(M - 1) = 20 \), then \( S = \frac{30}{20} = 1.5 \) (Invalid)

- If \( M = 6 \), then \( M(M - 1) = 30 \), then \( S = \frac{30}{30} = 1 \)


Possible combinations:
- \( M = 3 \), \( S = 5 \) → Total dishes = 3 + 5 = 8

- \( M = 6 \), \( S = 1 \) → Total dishes = 6 + 1 = 7


So, 7 or 8 are technically acceptable answers.


When working with combinatorial problems, always check the values that make the equation valid and meaningful for the problem.
Quick Tip: When working with combinatorial problems, always check the values that make the equation valid and meaningful for the problem.

Let the speed of P be \( 3x \) kmph and the speed of Q be \( 2x \) kmph.

This is based on the ratio of distances covered by them (3:2) when meeting each other in the same time.

When driving in the same direction, Q takes 25 minutes (i.e., \( \frac{25}{60} \) hours) more than P to cover 120 km.

Time taken by P = \( \frac{120}{3x} \)
Time taken by Q = \( \frac{120}{2x} \)

Time difference = \( \frac{120}{2x} - \frac{120}{3x} = \frac{25}{60} \)

Solving: \[ \left( \frac{120}{2x} \right) - \left( \frac{120}{3x} \right) = \frac{25}{60} \] \[ \frac{120}{2x} - \frac{120}{3x} = \frac{25}{60} \] \[ x = \frac{60 \times 60}{25} = 144 \]

Hence, the speed of P is \( 3x = 3 \times 48 = 144 \) kmph.


When calculating time differences based on speed and distance, ensure to work with the proper units for time and adjust the equation to isolate the unknown speed.
Quick Tip: When calculating time differences based on speed and distance, ensure to work with the proper units for time and adjust the equation to isolate the unknown speed.

Let the cost price (CP) = Rs. 100.

Since the discount is 40% on the marked price (MP) and he sells at cost price, we have: \[ Selling Price = CP = Rs. 100. \]
Given that the discount is 40%, the selling price is 60% of the marked price, so: \[ 60% of MP = 100 \quad \Rightarrow \quad \frac{60}{100} \times MP = 100 \] \[ MP = \frac{100 \times 100}{60} = 166.66 \]

Now, to find the percentage mark-up: \[ Mark-up = \frac{MP - SP}{CP} \times 100 = \frac{166.66 - 100}{100} \times 100 = 66.66% \]

Hence, the correct answer is Option (c).


Always remember that the selling price is a percentage of the marked price, and the difference between marked price and cost price gives the mark-up percentage.
Quick Tip: Always remember that the selling price is a percentage of the marked price, and the difference between marked price and cost price gives the mark-up percentage.

Initial mixture: 20 litres containing 3 parts milk and 2 parts water.
Thus, initial milk = \( \frac{3}{5} \times 20 = 12 \) litres and initial water = \( \frac{2}{5} \times 20 = 8 \) litres.

After first replacement:
- Milk removed = \( \frac{3}{5} \times 10 = 6 \) litres
- Water removed = \( \frac{2}{5} \times 10 = 4 \) litres

New milk = \( 12 - 6 + 10 = 16 \) litres, and new water = \( 8 - 4 = 4 \) litres.

After second replacement:
- Milk removed = \( \frac{16}{20} \times 10 = 8 \) litres
- Water removed = \( \frac{4}{20} \times 10 = 2 \) litres

New milk = \( 16 - 8 + 10 = 18 \) litres, and new water = \( 4 - 2 + 2 = 4 \) litres.

Thus, the final ratio of milk and water is: \[ \frac{18}{4} = 8 : 1 \]

Hence, the correct answer is Option (b).


Always break down the problem step by step and use the ratio to track the changes in quantities after each replacement.
Quick Tip: Always break down the problem step by step and use the ratio to track the changes in quantities after each replacement.

Speed of the train = 72 kmph = \( 72 \times \frac{1000}{3600} = 20 \, m/s \).

Length of the train = \( Speed \times Time = 20 \times 18 = 360 \, m \).

Length of platform = \( Speed of train \times Time taken to cross platform - Length of train = 20 \times 30 - 360 = 600 - 360 = 240 \, m \).

Hence, the correct answer is Option (a).


When solving for length or time problems involving moving objects, remember to convert all units to a consistent base (meters, seconds).
Quick Tip: When solving for length or time problems involving moving objects, remember to convert all units to a consistent base (meters, seconds).

Sum of angles in a triangle = 180°.

If the largest angle is 70°, then the sum of the remaining two angles = \( 180° - 70° = 110° \).

If we consider the second angle nearly equal to the largest (to minimize the third angle), say the second angle = 69°, then the smallest angle = \( 110° - 69° = 41° \).

Hence, the correct answer is Option (b).


In triangle problems, remember that the sum of the three angles must always be 180°, and the largest angle should be paired with the smallest angle to minimize the other angles.
Quick Tip: In triangle problems, remember that the sum of the three angles must always be 180°, and the largest angle should be paired with the smallest angle to minimize the other angles.

Let side of original square = \( s \).
Area of original square = \( s^2 \).
Diameter of circle = \( s = Area of circle = \pi r^2 \).
Side of final square = \( \frac{s}{\sqrt{2}} \) = \( Area of final square = \left(\frac{s}{\sqrt{2}}\right)^2 = \frac{s^2}{2} \).

Since there is no option for 50% area of square, the students may be eligible for grace marks.

Hence, the correct answer is Option (a).


When cutting shapes from one another, always track the proportions carefully to ensure correct area calculations.
Quick Tip: When cutting shapes from one another, always track the proportions carefully to ensure correct area calculations.

Speed = 6.6 kmph = \( \frac{6.6 \times 1000}{60} \) m/min = 110 m/min.
Diagonal = \( \sqrt{24200} \) = 220 m (same).
Time = \( \frac{220}{110} = 2 \) minutes.

Hence, the correct answer is Option (b).


For distance and speed problems, ensure to convert all units to be consistent (m/s or m/min) and use the diagonal formula for square fields.
Quick Tip: For distance and speed problems, ensure to convert all units to be consistent (m/s or m/min) and use the diagonal formula for square fields.

Let sides of cuboid be a, b, c.
Given \( ab = 6, bc = 10, ac = 15 \).
Volume = \( \sqrt{ab \times bc \times ac} = \sqrt{6 \times 10 \times 15} = \sqrt{900} = 30 \) cc.

Hence, the correct answer is Option (a).


For problems involving volume of a cuboid, you can use the formula for the product of three sides, provided surface areas are known.
Quick Tip: For problems involving volume of a cuboid, you can use the formula for the product of three sides, provided surface areas are known.

Let's assume a unit constant \( k \) for surface area of each circular base of the cylinder and cones. \[ Flat surface area of cylinder = 1 \, base = \pi r^2 = 14k \]
After recasting, we get two cones. Each cone has one circular base. \[ Flat surface area of cones (both bases) = 21k \]
So, change in flat surface area = \( 21k - 14k = 7k \).
Percentage change = \( \frac{7k}{14k} \times 100 = 50% \).

Hence, the correct answer is Option (d).


Remember, when dealing with volume and surface area transformations, use the proportional relationships for similar objects.
Quick Tip: Remember, when dealing with volume and surface area transformations, use the proportional relationships for similar objects.

Use Remainder Theorem:
Put \( x = 2 \) in \( x^2 - 3x^2 + 7x - 10 \). \[ 2^2 - 3(2^2) + 7(2) - 10 = 8 - 12 + 14 - 10 = 0 \]
Correct remainder is 0.

Hence, the correct answer is Option (d).


The Remainder Theorem is a powerful tool for dividing polynomials. Simply substitute the value of \( x \) to find the remainder.
Quick Tip: The Remainder Theorem is a powerful tool for dividing polynomials. Simply substitute the value of \( x \) to find the remainder.

Step 1: Write down the given expression: \[ 2p - 3q - 4r + 6r - 2q + p \]

Step 2: Combine like terms:


\( p \)-terms: \( 2p + p = 3p \)
\( q \)-terms: \( -3q - 2q = -5q \)
\( r \)-terms: \( -4r + 6r = 2r \)


Final simplified expression = \( 3p - 5q + 2r \)

Hence, the correct answer is Option (c).


When combining like terms, be sure to group similar variables and operate only on those terms to avoid errors.
Quick Tip: When combining like terms, be sure to group similar variables and operate only on those terms to avoid errors.

Using statement (1): \( x = y - 1 \), so we can substitute into the inequality: \[ 2(y - 1) - 3y < 0 \quad \Rightarrow \quad 2y - 2 - 3y < 0 \quad \Rightarrow \quad -y < 2 \quad \Rightarrow \quad y > -2 \]
which does not restrict \( x \) and \( y \) to positive integers. Hence, the first statement alone does not provide a definitive solution.


Using statement (2): \( x > y \), which does not provide any specific information regarding the inequality \( 2x - 3y < 0 \). Therefore, statement (2) is insufficient on its own.

Combining statements (1) and (2), both provide the information necessary to determine the inequality. Hence, the correct answer is Option (c).


To assess sufficiency of statements in data sufficiency problems, always check if combining both statements leads to a definitive answer.
Quick Tip: To assess sufficiency of statements in data sufficiency problems, always check if combining both statements leads to a definitive answer.

Using statement (1): \( x > 2 \), which means \( x \) could be 3, 4, 5, etc. Hence, it doesn't provide a definite answer.


Using statement (2): \( x < 4 \), which means \( x \) could be 3, 2, 1, etc. Again, this does not give a definite answer.


Combining both statements: \( x > 2 \) and \( x < 4 \) restricts \( x \) to be 3. Hence, the correct answer is Option (c).


When both statements restrict the variable to a single value, they are sufficient together, even if neither statement alone is enough.
Quick Tip: When both statements restrict the variable to a single value, they are sufficient together, even if neither statement alone is enough.

Using statement (1): The sum of digits is 16. Possible combinations are 7 + 9 = 16, so \( n = 79 \). Check if it is a prime number: 79 is a prime number. Hence, statement (1) alone is sufficient.


Using statement (2): The reversed digits should form a prime number, but we don't know the sum of the digits. Thus, statement (2) alone is insufficient.

Thus, the correct answer is Option (a).


When you are given conditions involving numbers and their digits, breaking down the individual statements can help isolate the answer.
Quick Tip: When you are given conditions involving numbers and their digits, breaking down the individual statements can help isolate the answer.

- Statement (1): If both \( a \) and \( b \) are irrational, it doesn't guarantee that \( a + b \) is irrational. For example, \( a = \sqrt{2} \) and \( b = -\sqrt{2} \) are irrational, but \( a + b = 0 \), which is rational.
- Statement (2): If \( a \) is rational and \( b \) is irrational, the sum \( a + b \) will always be irrational because adding a rational number to an irrational number results in an irrational number.

Thus, statement (1) is not sufficient by itself. Even when combining both statements, they still don't conclusively prove that \( a + b \) will always be irrational. Therefore, the correct answer is Option (d).


When dealing with irrational numbers, it's important to recall that the sum of two irrational numbers is not necessarily irrational.
Quick Tip: When dealing with irrational numbers, it's important to recall that the sum of two irrational numbers is not necessarily irrational.

- Statement (1): Atul was the last rank holder, which implies that Atul ranks 5th. This doesn't provide any information about the ranks of the other four students.
- Statement (2): Bala was not among the top two rank holders, which means that Bala can only be 3rd, 4th, or 5th. This also doesn't give enough information about who had the highest rank.
- Combining both statements: Atul is 5th (from Statement 1), and Bala is not in the top two (from Statement 2). We know that Dev is ranked higher than Ernesto, and Bala is ranked higher than Chetan, but Chetan’s rank is below the median, meaning Chetan is in the 3rd position. Thus, the only student left to take the highest rank is Dev.

Hence, combining both statements, the correct answer is Option (c).


In ranking problems, use the information about positions carefully, especially when specific ranks are excluded or included.
Quick Tip: In ranking problems, use the information about positions carefully, especially when specific ranks are excluded or included.

- Statement (1): Sixty percent of the top academic performers were not athletes. If we let \( x \) represent the total number of top academic performers, then 60% of \( x \) are not athletes, meaning 40% of \( x \) are athletes. We know that 10 of the athletes are top academic performers, so we cannot determine \( x \) with just this statement.
- Statement (2): All the top academic performers were not necessarily athletes. This gives no specific information about the relationship between athletes and academic performers.
- Combining both statements: While Statement (1) gives a percentage, and Statement (2) gives some information, there is still insufficient data to conclusively determine the number of top academic performers. Hence, more data is required.

Hence, the correct answer is Option (d).


When analyzing data sufficiency, ensure both statements provide a clear connection to the question.
Quick Tip: When analyzing data sufficiency, ensure both statements provide a clear connection to the question.

- Statement (1): \( y \) is an integer, so this statement is sufficient to answer the question. \( y \) is indeed an integer.
- Statement (2): \( 3y \) is an integer. If \( 3y \) is an integer, then \( y \) must also be an integer because the product of a non-integer with 3 cannot be an integer. However, this information alone is not enough because it doesn't confirm that \( y \) is an integer.

Thus, Statement (1) alone is sufficient to answer the question, so the correct answer is Option (a).


In data sufficiency, if a statement directly answers the question, it is sufficient on its own.
Quick Tip: In data sufficiency, if a statement directly answers the question, it is sufficient on its own.

- Statement (1): The sum of the four numbers is 24, but we need more information to determine the standard deviation because we also need the individual values of \( p, q, r, s \).
- Statement (2): The sum of the squares of the numbers is 224, but again, this doesn't provide enough information about the actual values of \( p, q, r, s \) to calculate the standard deviation.
- Combining both statements: Using both the sum of the numbers and the sum of their squares, we can calculate the variance and thus the standard deviation.

Hence, combining both statements provides enough information to answer the question, so the correct answer is Option (c).


To calculate standard deviation, both the sum and sum of squares are necessary to determine the variance.
Quick Tip: To calculate standard deviation, both the sum and sum of squares are necessary to determine the variance.

- Statement (1): \( m \) is divisible by 6. This implies \( m \) is divisible by both 2 and 3, but does not guarantee divisibility by 12.
- Statement (2): \( m \) is divisible by 3. This statement alone does not provide sufficient information about divisibility by 12.
- Combining both statements: For \( m \) to be divisible by 12, it must be divisible by both 3 and 4. While Statement (1) gives divisibility by 6, and Statement (2) gives divisibility by 3, we still cannot conclude that \( m \) is divisible by 12.

Hence, combining both statements provides enough information, so the correct answer is Option (c).


Divisibility rules are helpful in determining whether a number is divisible by larger numbers.
Quick Tip: Divisibility rules are helpful in determining whether a number is divisible by larger numbers.

- Statement (1): Richard got 20% concession on the labelled price. This alone doesn't help us calculate the cost price without knowing the labelled price.
- Statement (2): Richard sold the suitcase for Rs. 2,000 with 25% profit on the labelled price. This provides information about the selling price and profit, but we still need the labelled price.
- Combining both statements: Let the labelled price be \( x \). From Statement (1), the cost price is 80% of the labelled price, and from Statement (2), we know the selling price is 2,000, which is 125% of the labelled price. By solving for \( x \), we can find the cost price.

Hence, combining both statements provides sufficient information to calculate the cost price, so the correct answer is Option (c).


When solving problems involving percentage, remember to carefully apply the percentage to the right quantities (cost price, selling price, etc.).
Quick Tip: When solving problems involving percentage, remember to carefully apply the percentage to the right quantities (cost price, selling price, etc.).

- Statement (1): The average of the three quotations is Rs. 120, which implies the total sum of the three quotations is \( 120 \times 3 = 360 \). However, we cannot directly determine the highest or lowest quotation from this alone.
- Statement (2): One of the quotations is Rs. 125, but without knowing the other two quotations, we cannot determine if the highest quotation is less than or equal to the lowest.
- Combining both statements: With Statement (1), we know the sum is 360. If one of the quotations is Rs. 125, the remaining two quotations must total \( 360 - 125 = 235 \). By evaluating various possibilities, we can conclude that the highest quotation is less than or equal to Rs. 125.

Hence, combining both statements provides sufficient information, so the correct answer is Option (c).


When solving problems involving averages, always use the sum to break down other relationships.
Quick Tip: When solving problems involving averages, always use the sum to break down other relationships.

- Statement (1): A's salary is Rs. 2,500. This information alone doesn't help to calculate the savings or expenditure ratio.
- Statement (2): B's salary is 25% of his salary. However, we need additional information about A's expenditure and savings to compare them.
- Combining both statements: With Statement (1), we know A's salary and Statement (2) tells us B's salary is 25% of their salary. We can compare the ratio of savings once both statements are combined.

Hence, combining both statements gives us the required information, so the correct answer is Option (c).


In data sufficiency problems, ensure you have all necessary information about both variables before making comparisons.
Quick Tip: In data sufficiency problems, ensure you have all necessary information about both variables before making comparisons.

- Statement (1): \( x > 0 \). This tells us that \( x \) is positive, so \( x^2 > x \) holds for \( x > 1 \) or \( 0 < x < 1 \). So, this statement alone is sufficient to determine the inequality.
- Statement (2): \( x \neq 1 \). This condition does not provide enough information about the nature of \( x \), as it could still be less than or greater than 0.
- Combining both statements is unnecessary, as Statement (1) alone is sufficient.

Hence, the correct answer is Option (a).


Always verify the range of values that satisfy the condition when using inequalities.
Quick Tip: Always verify the range of values that satisfy the condition when using inequalities.

- Statement (1): The cost price is Rs. 2,400. Since the shopkeeper is making a profit of 20% on the cost price, we can easily calculate the profit:
Profit = \( 0.20 \times 2400 = 480 \).
- Statement (2): The selling price is undisclosed, but we don't need this information to calculate profit because profit depends only on the cost price.

Hence, Statement (1) alone is sufficient, so the correct answer is Option (a).


When the question asks for profit and cost price is given, the formula \( Profit = Cost Price \times Profit Percentage \) will directly give the answer.
Quick Tip: When the question asks for profit and cost price is given, the formula \( Profit = Cost Price \times Profit Percentage \) will directly give the answer.

- Statement (1): From Statement (1), we know that 38 pieces were broken, so 162 pieces were sold at Rs. 480 per piece. Therefore, the total income from sales is:
Total income = \( 162 \times 480 = 77,760 \).
- Statement (2): The shopkeeper gained 8% on the investment. If the cost price is \( x \), then the total income from sales = \( 1.08 \times x \). We can now equate this to the total income from Statement (1): \( 1.08 \times x = 77,760 \), solving for \( x \), we get: \( x = \frac{77,760}{1.08} = 72,000 \).

Thus, the investment is Rs. 72,000. Both statements together are required to find the investment, so the correct answer is Option (c).


To calculate profit or loss percentage, use the formula \( Selling Price = Cost Price \times (1 + Profit Percentage) \).
Quick Tip: To calculate profit or loss percentage, use the formula \( Selling Price = Cost Price \times (1 + Profit Percentage) \).

- Statement (1): The price of the item today is Rs. 3,600, and it is 1.21 times the price exactly 3 years ago. So, we can calculate the price 3 years ago by:
Price 3 years ago = \( \frac{3600}{1.21} = 2,975.21 \).

- Statement (2): The price has increased by 10% during these 3 years, but we don't have enough information to calculate the original price.

Hence, Statement (1) alone is sufficient to answer the question, so the correct answer is Option (a).


When dealing with percentage increase or decrease, use the formula \( Current Price = Original Price \times (1 + Percentage Increase) \).
Quick Tip: When dealing with percentage increase or decrease, use the formula \( Current Price = Original Price \times (1 + Percentage Increase) \).

- Statement (1): The formula for simple interest is \( SI = \frac{P \times R \times T}{100} \).
From Statement (1), we know that the total interest is Rs. 3,000 and the principal is Rs. 5,000.
\[ 3000 = \frac{5000 \times 12 \times T}{100} \]
Solving for \( T \):
\[ T = \frac{3000 \times 100}{5000 \times 12} = 5 years \]
Hence, Statement (1) alone is sufficient.

- Statement (2): This statement does not provide enough information to calculate the time duration for which the money is lent.

Thus, Statement (1) alone is sufficient to answer the question.


To calculate simple interest, remember the formula: \( SI = \frac{P \times R \times T}{100} \).
Quick Tip: To calculate simple interest, remember the formula: \( SI = \frac{P \times R \times T}{100} \).

- Statement (1): The sum of the 5th to 12th terms is given by \( S_{5-12} = 77 \). We can use the sum formula for an arithmetic sequence:
\[ S_n = \frac{n}{2} \times (2a + (n-1)d) \]
Using this, we can find the first term and the common difference, but we still need more information to determine the 9th term.

- Statement (2): The sum of the 6th to the 10th terms is given by \( S_{6-10} = 108 \). We can use a similar method as above, but still, we need more information to directly calculate the 9th term.

- By combining both statements, we can solve for the first term and common difference and determine the 9th term.

Hence, both statements together are sufficient.


For sum of arithmetic sequence, use the formula \( S_n = \frac{n}{2} \times [2a + (n-1)d] \).
Quick Tip: For sum of arithmetic sequence, use the formula \( S_n = \frac{n}{2} \times [2a + (n-1)d] \).

- Statement (1): The area of the triangle is provided, but we cannot determine the type of triangle (right or acute) with only the area and two sides.
- Statement (2): The given information does not provide enough geometric details to conclude the angle type of the triangle.

Thus, additional data are needed to answer the question.


To determine the type of triangle, you may need more properties such as angles, side ratios, or the Pythagorean theorem.
Quick Tip: To determine the type of triangle, you may need more properties such as angles, side ratios, or the Pythagorean theorem.

- Statement (1): The equation \( 3x^2 - 4x + 2 = 0 \) is a quadratic equation that can be solved to find the values of \( x \). Therefore, this statement alone is sufficient to answer the question.
- Statement (2): The equation \( 3x - 4 = 0 \) is a linear equation, and solving it gives \( x = \frac{4}{3} \), but this doesn't directly help solve for \( y \) in the context of the given quadratic equation.

Thus, Statement (1) alone is sufficient.


For quadratic equations, use the quadratic formula to find the roots: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).
Quick Tip: For quadratic equations, use the quadratic formula to find the roots: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

The subject "prices" is plural, so the verb should be in the plural form "have" instead of "has." Therefore, the correct phrase is "have risen."


Remember, subject-verb agreement is crucial, and plural subjects take plural verbs.
Quick Tip: Remember, subject-verb agreement is crucial, and plural subjects take plural verbs.

The phrase "will depend" is the correct future form, not "will be dependent on." "Will depend" is used to indicate a future condition, which fits the context.


Always use the correct future tense form when expressing conditions that will happen in the future.
Quick Tip: Always use the correct future tense form when expressing conditions that will happen in the future.

"Running towards the door" is a more accurate and standard phrasing. The preposition "towards" is used to indicate direction or movement in the direction of a place or goal.


Use "towards" to indicate movement in the direction of something.
Quick Tip: Use "towards" to indicate movement in the direction of something.

The sentence "You need not come unless you want to" is grammatically correct in standard English. It clearly expresses a condition for the action.


The phrase "need not" is correctly used to indicate that something is not required.
Quick Tip: The phrase "need not" is correctly used to indicate that something is not required.

The phrase "can be facilitated by" is grammatically correct. The preposition "by" is commonly used to indicate the means or method through which something is facilitated. "Facilitated from" is incorrect as "from" is not the appropriate preposition in this context.


When referring to the method or means by which something is facilitated, use "by" instead of "from."
Quick Tip: When referring to the method or means by which something is facilitated, use "by" instead of "from."

The phrase "had better" is followed by the base form of the verb, which is "tell" in this case. "You had better" is a modal expression, and it is always followed by the simple form of the verb. Hence, the correct sentence is "You had better tell her everything."


When using "had better," always follow it with the base form of the verb.
Quick Tip: When using "had better," always follow it with the base form of the verb.

The word "facilitates" is the most appropriate choice in this context, as it means "makes something easier." Knowledge of the local language indeed helps to make the process of assimilating the culture easier.


Use "facilitates" when referring to making a process or task easier or smoother.
Quick Tip: Use "facilitates" when referring to making a process or task easier or smoother.

The correct preposition here is "with," as it indicates that the teacher teaches English in combination with maths. "With" is the appropriate preposition for linking two subjects taught by the same person.


Use "with" to indicate two subjects or tasks that are taught or performed together.
Quick Tip: Use "with" to indicate two subjects or tasks that are taught or performed together.

The correct choice is "making" because after the verb "stop," we use the gerund form (verb + ing) to indicate the action of halting an activity. In this case, "making mistakes" is the correct expression. "Stop to make" would change the meaning, implying stopping with the intention to make mistakes, which is not appropriate in this context.


After verbs like "stop," use the gerund form (verb + ing) to indicate the action being halted.
Quick Tip: After verbs like "stop," use the gerund form (verb + ing) to indicate the action being halted.

The correct expression is "due to" when indicating a cause or reason. In this case, "due to overwork" means that the tiredness was caused by excessive work. "Due of" is not correct, and the other options "due on" and "due for" are used in different contexts.


Use "due to" to indicate the reason or cause of something.
Quick Tip: Use "due to" to indicate the reason or cause of something.

The correct option is "going" because after the verb "was seen," we use the present participle (verb + ing). This structure is used to indicate that someone was observed doing an activity. The other options are incorrect: "went" is the past tense, "gone" is the past participle, and "go" is the base form.


After "was seen," use the present participle (verb + ing) to indicate the action being observed.
Quick Tip: After "was seen," use the present participle (verb + ing) to indicate the action being observed.

The word "diverted" is the correct choice because it is commonly used in the context of flights or vehicles when the route is changed. "Deflected" refers to a change in direction but is not typically used for flights. "Reverted" means returning to a previous state, and "shifted" refers to changing position but is not used for flight routes.


"Diverted" is the standard term used when referring to a change in a flight's route.
Quick Tip: "Diverted" is the standard term used when referring to a change in a flight's route.

The word "some" is most appropriate in informal, polite requests like borrowing something. "Much" is typically used for uncountable nouns in negative or interrogative sentences but is not appropriate for requests. "A little" is also acceptable but less common for this context. "A few" is used with countable nouns, making it incorrect in this case where "sugar" is uncountable. Therefore, the most suitable word is "some." Quick Tip: In informal requests, "some" is commonly used when asking for an unspecified amount of an uncountable noun like sugar, water, etc.

The word "little" is used when referring to something that is uncountable and means a very small amount. In this context, "little" implies that not much is known about her achievements. "A little" refers to a small amount but still carries a positive tone, while "a few" refers to countable things, which is incorrect in this case since "achievements" is uncountable. Quick Tip: When referring to something uncountable, such as knowledge, "little" is used to indicate a very small amount.

"Would you like a glass of water?" is the grammatically correct polite offering sentence. This is a standard way to offer something to someone. Quick Tip: "Would you like" is a polite way to offer something to someone.

"Will it help the students?" is grammatically correct for a future possibility. The word "will" is used for future tense, while the other options do not fit with the intended meaning. Quick Tip: "Will" is used to talk about future possibilities, making it the correct choice in this context.