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Question 1 / 20
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1
Consider the statements: (1) All cups are books. (2) All books are shirts. Which of the following conclusions are valid: (1) Some cups are not shirts. (2) Some shirts are cups.
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Solution: Step 1: Represent the statements using Venn diagrams or logical notation: - Statement 1: All Cups are Books (C ⊆ B) - Statement 2: All Books are Shirts (B ⊆ S) Step 2: Evaluate Conclusion 1: "Some cups are not shirts." - From Statement 1 (C ⊆ B) and Statement 2 (B ⊆ S), it logically follows that all cups are shirts (C ⊆ S). - Therefore, the conclusion "Some cups are not shirts" is false. This conclusion does not logically follow. Step 3: Evaluate Conclusion 2: "Some shirts are cups." - From the combined statements (C ⊆ S), if all cups are shirts, then it logically follows that some shirts must be cups (specifically, the ones that are cups). - This conclusion logically follows. Step 4: Based on the analysis, only Conclusion (2) follows.
2
How many New Year's greeting cards were sold in your shop this year? Determine if the given statements are sufficient.
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Solution: Step 1: Analyze Statement I: 'Last year 2935 cards were sold'. This provides the baseline sales figure from the previous year. Step 2: Analyze Statement II: 'The number of cards sold this year was 1.2 times that of last year'. This provides the multiplier for this year's sales relative to last year's. Step 3: To find this year's sales, both the last year's sales (from Statement I) and the multiplication factor (from Statement II) are required. Step 4: Combine Statement I and Statement II: Number of cards sold this year = 2935 * 1.2. Step 5: Calculate: 2935 * 1.2 = 3522. Step 6: Since both statements together allow for the exact calculation of this year's card sales, 'Both I and II are sufficient'.
3
Determine the relationship between the following statements: Statement I: Many individuals in the area are reportedly suffering from Malaria. Statement II: Private Medical Practitioners in the area have decided to close their clinics for a few days.
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Solution: Step 1: Analyze Statement I. It describes a public health situation: many people suffering from Malaria. This is an effect of an epidemic or poor sanitation. Step 2: Analyze Statement II. It describes an action by private medical practitioners: closing their clinics. This is an effect, potentially due to various reasons. Step 3: Evaluate direct causal links. While an increase in Malaria cases (Statement I) would normally *increase* the workload for doctors, leading them to stay open, it is not a direct cause for them to *close* their clinics. Conversely, doctors closing their clinics (Statement II) does not cause Malaria (Statement I). The solution explanation confirms that their decisions are due to other, unstated causes. Step 4: Conclude the relationship. Both statements are effects of independent causes. The cause of the Malaria outbreak is distinct from the cause of doctors closing their clinics (e.g., threat to their safety, protest, lack of supplies, etc.).
4
Identify the cause-and-effect link between these statements: Statement I: Over the past three months, prices of food grains and other essential goods in the open market have sharply increased. Statement II: The opposition political party has called for a general strike to protest the government's economic policy.
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Solution: Step 1: Analyze Statement I. It describes a situation: a sharp increase in the prices of essential commodities. This is an economic condition that can provoke public or political reactions. Step 2: Analyze Statement II. It describes an action: an opposition party calling for a general strike to protest government policy. This is a political response. Step 3: Determine the causal link. A sharp rise in the prices of essential goods (Statement I) is a common reason for public discontent and political opposition, leading to protests against government economic policies. Therefore, the price increase directly causes the opposition's call for a strike. Step 4: Conclude the relationship. Statement I is the cause, and Statement II is its effect.
5
Determine the total number of speeches delivered during a two-day program using the provided statements.
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Solution: Step 1: Analyze Statement I. '18 speakers were invited... one-sixth of the speakers could not come.' Number of speakers who did not come = (1/6) * 18 = 3 speakers. Number of speakers who attended = 18 - 3 = 15 speakers. Statement I alone is insufficient to find total speeches as each could give 1 or 2 speeches. Step 2: Analyze Statement II. 'One-third of the speakers gave two speeches each.' This statement alone is insufficient as the total number of speakers is not known. Step 3: Combine Statement I and Statement II. From Statement I, 15 speakers attended. From Statement II, one-third of the attending speakers gave two speeches: (1/3) * 15 = 5 speakers gave two speeches. The remaining speakers = 15 - 5 = 10 speakers. Since each speaker gave at least one speech, these 10 speakers gave one speech each. Total speeches = (5 speakers * 2 speeches/speaker) + (10 speakers * 1 speech/speaker) = 10 + 10 = 20 speeches. Step 4: Conclude. Both Statement I and Statement II together are sufficient to determine the total number of speeches.
6
Is Ritesh eligible to retire from Office X in January 2006 with full pension benefits? Statement I: Ritesh will complete 30 years of service in Office X in April 2000 and expresses a desire to retire. Statement II: As per Office X rules, an employee must complete a minimum of 30 years of service and attain the age of 60. Ritesh has three years left to reach the age of 60.
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Solution: Step 1: Identify the question: Can Ritesh retire in January 2006 with full pension benefits? Step 2: Analyze Statement I. Ritesh completes 30 years of service in April 2000. By January 2006, he would have served for 30 + (2006 - 2000) = 36+ years, satisfying the service requirement. This statement, however, provides no information about his age. Statement I alone is not sufficient. Step 3: Analyze Statement II. Office X rules require a minimum of 30 years of service AND attainment of 60 years of age. Ritesh has 3 years to complete the age of 60. Assuming this statement is in reference to the time of the question (or January 2006), Ritesh would be 57 years old in January 2006. He would turn 60 in 3 years (i.e., in 2009). This statement provides age information but no direct information about service years in context of Jan 2006. Statement II alone is not sufficient. Step 4: Combine Statement I and II. From Statement I, Ritesh meets the 30 years service criteria by January 2006. From Statement II, Ritesh will be 57 years old in January 2006 and will not reach 60 years until 2009. Therefore, in January 2006, Ritesh meets the service requirement but not the age requirement. Step 5: Thus, Ritesh cannot retire in January 2006 with full pension benefits. Both statements together are necessary and sufficient to answer the question (with a 'No').
7
Determine the relationship between the following two statements regarding cause and effect: Statement I: The Meteorological Department has issued a statement mentioning deficient rainfall during monsoon in many parts of the country. Statement II: The Government has lowered the revised estimated GDP growth from the level of earlier estimates.
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Solution: Step 1: Analyze Statement I. This statement describes a natural phenomenon (deficient rainfall) caused by meteorological conditions. It's an environmental event. Step 2: Analyze Statement II. This statement describes an economic decision/projection (lowered GDP growth estimate) based on various economic indicators and forecasts. Step 3: Evaluate direct causation between I and II. While deficient rainfall can impact agricultural output and thus contribute to lower GDP, it is not the sole cause, nor is Statement I itself a cause of Statement II in an exclusive or direct manner. Furthermore, Statement II is not the cause of Statement I. Step 4: Evaluate for a common cause. There is no readily apparent single common cause that would lead to both a meteorological event and a government's economic forecast revision. Step 5: Conclude the relationship. Both statements are effects or observations resulting from their own distinct and independent sets of causes. Statement I results from atmospheric conditions, and Statement II results from complex economic analysis and various influencing factors (one of which *could* be rainfall, but not as the definitive, singular cause implied by a direct cause-effect relationship between the statements).
8
Initially, 'A' used three sheets of paper with two carbon sheets to produce two duplicate copies of an original document. Subsequently, 'A' aimed for more copies, folding the paper so the upper half of the sheets lay over the lower half, and then typed. How many carbon copies were produced in this second attempt?
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Solution: Step 1: Understand the mechanism of carbon copying. Each carbon sheet, placed between two regular sheets of paper, can transfer an impression from the upper sheet to the lower sheet, creating one copy. Step 2: In the initial setup, 'A' had three sheets of paper and two carbon sheets. This arrangement would be (Original) -> Carbon 1 -> Sheet 2 (Copy 1) -> Carbon 2 -> Sheet 3 (Copy 2). This correctly yields two copies. Step 3: In the second attempt, 'A' uses the *same* number of carbon sheets (two), but folds the paper. The act of folding the paper might create more layers of paper, but it does not increase the number of actual carbon sheets available to create impressions. Step 4: Regardless of how the paper is folded or layered, the number of copies that can be generated is limited by the number of carbon sheets used. Since there are still only two carbon sheets, only two carbon copies can be produced. Step 5: The folding affects *where* the impressions appear on the paper, potentially creating multiple impressions on a single sheet or partial copies, but not the total count of distinct 'carbon copies' as full duplicates of the original typed content. Step 6: Therefore, 'A' got 2 carbon copies.
9
Analyze the relationship between these two statements: (I) The government reduced petroleum product prices by five percent a week after increasing them by ten percent. (II) The rate of inflation marginally decreased during the last week.
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Solution: Step 1: Analyze Statement I: The government's actions on petroleum prices involve both an increase and a subsequent reduction within a short period. This is a policy decision influenced by various factors. Step 2: Analyze Statement II: A marginal drop in the inflation rate occurred last week. Inflation is a complex economic indicator influenced by numerous factors, including but not limited to fuel prices. Step 3: Evaluate for cause-effect: While petroleum prices do influence inflation, a *marginal* drop in inflation over the *last week* (Statement II) is unlikely to be solely caused by a *five percent reduction in petroleum prices* (Statement I), especially when that reduction followed a *ten percent increase*. The net effect of the government's recent actions on fuel price is complex, and many other market forces contribute to inflation. Step 4: Conclude that both statements describe effects that likely stem from independent, or at least distinct, economic and policy factors. The timing and magnitudes do not strongly suggest a direct cause-effect relationship between these two specific events.
10
Identify the cause-and-effect relationship between these statements: Statement I: A large number of people flocked to the temple last Sunday, the 15th of the month. Statement II: The temple authority had decided to close the temple for repairs from the 17th of the month.
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Solution: Step 1: Analyze Statement I. It describes a large crowd at the temple on a specific day (15th). This is an effect of some strong motivation for people to visit. Step 2: Analyze Statement II. It describes a decision by the temple authority to close the temple for repairs starting from the 17th. This decision would likely be announced in advance. Step 3: Determine the causal link. If people knew the temple was going to close for repairs starting on the 17th (Statement II), they would naturally rush to visit before the closure, especially on a weekend like the 15th. Therefore, the announcement of the impending closure would be a direct cause of the huge rush of visitors. Step 4: Conclude the relationship. Statement II is the cause, and Statement I is its effect.
11
Examine the relationship between these statements: Statement I: Car manufacturing companies have recently raised the prices of mid-sized cars. Statement II: The Government recently increased the duty on mid-sized cars.
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Solution: Step 1: Analyze Statement I. It describes an action by car companies: increasing prices. This is an effect, typically in response to increased costs or demand. Step 2: Analyze Statement II. It describes a government action: increasing duty (taxes) on mid-sized cars. This directly increases the cost of manufacturing or importing these cars. Step 3: Determine the causal link. An increase in government duty (Statement II) means higher production or import costs for car manufacturers. To maintain profit margins, companies would pass these increased costs onto consumers by raising car prices (Statement I). Therefore, the government's action is a direct cause. Step 4: Conclude the relationship. Statement II is the cause, and Statement I is its effect.
12
Identify the relationship between these two statements: (I) Domestic market petrol and diesel prices have remained stable for several months. (II) International crude oil prices have substantially increased over the past few months.
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Solution: Step 1: Analyze Statement I: Domestic petrol and diesel prices are unchanged. This suggests a stable domestic pricing policy or regulation, possibly involving government subsidies or price controls. Step 2: Analyze Statement II: International crude oil prices have significantly increased. This indicates a global market trend. Step 3: Evaluate the relationship: While international crude prices typically influence domestic fuel prices, Statement I explicitly states domestic prices have 'remained unchanged'. This implies that domestic pricing mechanisms are acting independently of the international market fluctuations described in Statement II. Step 4: Conclude that both statements describe distinct situations that are not directly causing or affecting each other within the given context. Therefore, they are independent causes (or facts that exist independently).
13
Analyze the relationship between two statements to determine if one is the cause and the other its effect: Statement I: The standard of living among the middle-class society has been consistently rising for the past few years. Statement II: The Indian Economy is experiencing remarkable growth.
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Solution: Step 1: Understand Statement I. A rising standard of living for a significant portion of society, like the middle class, implies increased consumer spending, demand for goods and services, and overall economic activity. Step 2: Understand Statement II. Remarkable growth in the Indian Economy refers to a significant increase in its GDP and other economic indicators. Step 3: Evaluate the causal link. An increase in consumption and economic activity (implied by Statement I) directly contributes to and drives national economic growth (Statement II). Step 4: Conclude that Statement I (rising standard of living) is a direct cause, and Statement II (remarkable economic growth) is its effect.
14
Analyze the relationship between the two statements: Statement I: Many residents from low-lying areas have been relocated to safer places in the last few days. Statement II: The Government has promptly dispatched relief supplies to residents in the affected areas.
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Solution: Step 1: Analyze Statement I. It describes an action taken: evacuation of people from low-lying areas. This is an effect, likely due to an impending or actual disaster like floods. Step 2: Analyze Statement II. It describes another action: the government rushing relief supplies. This is also an effect, a response to a disaster or emergency situation. Step 3: Evaluate direct causal links. Evacuation (Statement I) does not directly cause the rushing of relief supplies (Statement II), nor vice-versa. Both are distinct, albeit related, components of a disaster response. Step 4: Consider a common cause. Both evacuation and the provision of relief supplies are typical responses to a natural disaster (e.g., severe floods, storms) affecting low-lying areas. The disaster itself is the common underlying cause that necessitates both actions. Step 5: Conclude the relationship. Both statements are effects of some common cause (a natural disaster or emergency situation).
15
Identify the cause-and-effect relationship between the statements: Statement I: The literacy rate in the district has been rising for the past four years. Statement II: The district administration has conducted extensive training programs for workers involved in the literacy drive.
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Solution: Step 1: Analyze Statement I. It states an observation: the literacy rate has been increasing. This is an effect, indicating progress in education. Step 2: Analyze Statement II. It describes an action taken by the district administration: conducting extensive training programs for literacy workers. This is an initiative designed to improve literacy efforts. Step 3: Determine the causal link. Extensive training programs for literacy workers (Statement II) would equip them better to perform their duties, making the literacy drive more effective. An effective literacy drive would directly lead to an increase in the literacy rate (Statement I). The phrase 'for the last four years' aligns with 'conducted extensive training programme' suggesting a sustained effort leading to the observed effect. Step 4: Conclude the relationship. Statement II is the cause, and Statement I is its effect.
16
Calculate the number of gift boxes sold on Monday using the provided sales and visitor information.
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Solution: Step 1: Analyze Statement I. 'It was 10% more than the boxes sold on the earlier day i.e. Sunday.' This gives a percentage relationship (Monday sales = Sunday sales + 10% of Sunday sales). Statement I alone is insufficient as Sunday's sales are unknown. Step 2: Analyze Statement II. 'Every third visitor to the shop purchased the box and 1500 visitors were there on Sunday.' From this, Sunday's sales can be calculated: (1/3) * 1500 = 500 boxes. Statement II alone is insufficient for Monday's sales. Step 3: Combine Statement I and Statement II. From Statement II, Sunday's sales = 500 boxes. From Statement I, Monday's sales = 500 + (0.10 * 500) = 500 + 50 = 550 boxes. Step 4: Conclude. Both Statement I and Statement II together are sufficient to determine the number of gift boxes sold on Monday.
17
Two vehicles moving in opposite directions need to cross each other. Statement A: Both vehicles are of equal length of 350m. Statement B: One vehicle moves at 83 km/hr while the other at 86 km/hr. Are these statements sufficient to determine the crossing time?
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Solution: Step 1: Relative speed = 83 + 86 = 169 km/hr = 169 * 5/18 m/s Step 2: Total distance to cross = 350 + 350 = 700m (from Statement A) Step 3: Time = Distance / Speed = 700 / (169 * 5/18) Step 4: Without Statement A, total distance cannot be determined Step 5: Without Statement B, relative speed cannot be determined Step 6: Both statements are necessary to calculate crossing time
18
Determine the relationship between these two statements: (I) Modern life is excessively fast-paced and demanding, full of variety in all aspects, which often leads to stressful situations. (II) The number of suicide cases among teenagers is increasing.
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Solution: Step 1: Analyze Statement I: Modern life is characterized by speed, demands, and variety, leading to stress. This is a general observation about societal conditions. Step 2: Analyze Statement II: There is an increasing trend of suicide cases among teenagers. This is a specific social trend or outcome. Step 3: Evaluate for direct cause-effect: While the stressful environment described in Statement I could contribute to the issue in Statement II, it is more accurate to view both as consequences of deeper, interconnected societal pressures rather than one directly causing the other in a simple linear fashion. Step 4: Consider a common cause: The stressors of modern life (as described in Statement I) and the rise in teenage suicides (Statement II) can both be seen as effects of underlying societal factors such as increased academic pressure, social media influence, family dynamics, economic uncertainty, or a general decline in mental health support systems. These broader issues contribute to both the overall stressful environment and the specific tragic outcome. Step 5: Conclude that both statements are effects of some common, complex societal causes.
19
Examine the relationship between these statements: Statement I: The State Government has announced a special tax package for new industries establishing in the State. Statement II: Last year, the State Government increased taxes for all industrial activities in the State.
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Solution: Step 1: Analyze Statement I. It describes a current government action: offering tax benefits for new industries. This is an incentive. Step 2: Analyze Statement II. It describes a past government action: hiking taxes for all industrial activities. This would likely have had a negative impact on industrial growth. Step 3: Determine the causal link. If taxes were hiked last year (Statement II), it might have deterred new industries or even caused existing ones to consider leaving. To counteract this negative effect and attract new investment, the government might then decide to offer special tax packages (Statement I) as an incentive. The current action (Statement I) is a response to the previous action's likely negative impact or a need to balance the overall tax environment after a general hike. The solution explanation supports this interpretation. Step 4: Conclude the relationship. Statement II is the cause, and Statement I is its effect.
20
What is the combined total amount of money Vivek and Suman possess? Determine if the provided statements are sufficient to answer the question.
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Solution: Step 1: Let the amount of money Suman has be S, Vivek's money be V, and Tarun's money be T. Step 2: From Statement I, we know: S = T - 20 (Suman has 20 rupees less than Tarun). Step 3: From Statement II, we know: V = T + 30 (Vivek has 30 rupees more than Tarun). Step 4: To find the combined amount (V + S), substitute the expressions from both statements: V + S = (T + 30) + (T - 20). Step 5: Simplify the expression: V + S = 2T + 10. Step 6: Since the value of T (Tarun's money) is unknown, the exact combined amount of Vivek and Suman cannot be determined. Step 7: Therefore, neither Statement I nor Statement II alone or together is sufficient to answer the question.
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