Question 1

M, A, N and K stand in a row; based on the given information about their heights, which statements are sufficient to decide who stands last when arranged from shortest to tallest?

Accepted Answer

Introduction / Context: This is a data sufficiency question about ordering by height. The goal is not to find exact heights but to check whether the given statements are enough to determine who will stand last when the four persons are arranged from shortest to tallest. Given Data / Assumptions: Persons: M, A, N and K are standing in a row. Main question: If we arrange them from shortest to tallest, who is standing last? Statement 1: A is shorter than K. Statement 2: M is shorter than A. Concept / Approach: We need enough information to identify the tallest person uniquely. One or more inequality statements may give partial order, but unless every person's relative position is fixed, the data are insufficient. We test each statement alone and then both together to see whether N's position remains unspecified. Step-by-Step Solution: Step 1: From statement 1 alone, A is shorter than K, so K is taller than A. We know nothing about M or N relative to them. Step 2: From statement 2 alone, M is shorter than A, so A is taller than M. N's height is still unknown, and K's height is also unknown. Step 3: Combine both statements. We obtain M < A < K (M is shorter than A, A is shorter than K). K is taller than both M and A. Step 4: However, we still do not know where N stands. N could be shorter than M, between M and A, between A and K, or taller than K. Step 5: Because N's relative height is not fixed, we cannot decide who is tallest and hence who will stand last. Verification / Alternative check: Construct two scenarios. In scenario one, N is the tallest: let heights be M = 150 cm, A = 160 cm, K = 170 cm and N = 180 cm. In scenario two, K is the tallest: M = 150 cm, A = 160 cm, K = 180 cm and N = 165 cm. Both scenarios satisfy A < K and M < A, but the identity of the tallest person differs. This proves that the data do not fix a unique last person. Why Other Options Are Wrong: Option B claims that together the statements are sufficient, but our examples show otherwise. Options C and D incorrectly treat one statement alone as sufficient, which is clearly not the case since they say nothing about two of the persons. Option E also overstates sufficiency since neither statement alone answers the question. Common Pitfalls: A common mistake is to focus only on the three persons connected by the statements and ignore the fourth person whose position remains free. Always check whether every person's relative order is uniquely determined before calling the data sufficient. Final Answer: The correct evaluation is that statements 1 and 2 together are not sufficient to identify who will stand last.

Question 2

Some boys are hardworking and no intelligent person is a boy; based on this, which of the given conclusions logically follow?

Accepted Answer

Introduction / Context: This syllogism type question involves three sets: boys, hardworking people and intelligent people. You must use the given statements to check which of the provided conclusions are logically forced. Given Data / Assumptions: Statement I: Some boys are hardworking. Statement II: No intelligent person is a boy. Conclusion I: Some hardworking people are not intelligent. Conclusion II: All hardworking people are intelligent. Conclusion III: Some intelligent people are not hardworking. Concept / Approach: We interpret the statements with Venn diagrams. Some boys are hardworking means there is an overlap between boys and hardworking people. No intelligent person is a boy means the sets intelligent and boys do not overlap at all. We then translate these into implications for the three conclusions. Step-by-Step Solution: Step 1: From some boys are hardworking, pick one person who is both a boy and hardworking. Step 2: From no intelligent person is a boy, we know that no boy can belong to the intelligent set. Step 3: Therefore, the boy who is hardworking cannot be intelligent. This directly means some hardworking people are not intelligent, so conclusion I follows. Step 4: Conclusion II says all hardworking people are intelligent, which directly contradicts the existence of at least one hardworking boy who is not intelligent. So conclusion II is false. Step 5: Conclusion III says some intelligent people are not hardworking. The given statements say nothing about whether intelligent people are hardworking or not; they only say intelligent people are not boys. So conclusion III is not forced. Verification / Alternative check: Construct an example set. Let boys be {b1, b2}, hardworking be {b1, h1} and intelligent be {i1, i2}. Here b1 is both a boy and hardworking, and intelligent contains no boys. Some hardworking people, such as b1, are not intelligent. However, we could choose to make i1 hardworking or not hardworking without contradicting the statements, so conclusion III is not fixed. Why Other Options Are Wrong: Option B includes conclusion III, which is not compelled by the data. Option C treats all conclusions as valid, but conclusions II and III are not. Option D says no conclusion follows, which ignores the clear implication in conclusion I. Option E selects only conclusion II, which is contradicted by the existence of a hardworking boy who is not intelligent. Common Pitfalls: A frequent mistake is to assume that if no intelligent person is a boy, then intelligent people must form a completely separate category with some forced properties such as not being hardworking. The statements do not say that. They only exclude overlap with boys, not with hardworking people in general. Final Answer: The correct evaluation is that only conclusion I follows from the given statements.

Question 3

Poverty is described as a symptom as well as a consequence of social disorder; which of the given assumptions about poverty and social order can definitely be drawn?

Accepted Answer

Introduction / Context: This reasoning question asks you to interpret a statement about poverty and social disorder and decide which assumptions can definitely be drawn from it. The statement links poverty with social disorder in two ways, and the assumptions suggest different interpretations of that link. Given Data / Assumptions: Statement: Poverty is a symptom as well as a consequence of social disorder. Assumption I: Poverty is a type of social order. Assumption II: Poverty is related to social order. We must treat the statement as true and see which assumptions are supported. Concept / Approach: A symptom and a consequence of social disorder are both effects related to that disorder. The phrase social order refers to the structure and functioning of society, and social disorder refers to its breakdown. From this, we can infer that poverty has a relationship with social order or disorder. However, that does not mean poverty itself is a form of social order. Step-by-Step Solution: Step 1: The statement says poverty is a symptom and consequence of social disorder. This clearly links poverty with social disorder. Step 2: If something is a symptom and consequence of social disorder, it is obviously related to the condition of social order and its breakdown. So assumption II is directly supported. Step 3: Assumption I claims that poverty is a type of social order. The statement does not call poverty a form of order, but rather an outcome of disorder. This is a different concept. Step 4: Therefore assumption I goes beyond what is said and is not supported by the statement. Verification / Alternative check: Think of an illness analogy. Saying fever is a symptom and consequence of infection does not mean fever is a type of infection. It only means fever is related to infection. Similarly, saying poverty is a symptom and consequence of social disorder means poverty is linked to the state of social order, but it does not redefine poverty as a form of social order itself. Why Other Options Are Wrong: Option A selects only assumption I, which is clearly not justified. Option C claims both are correct, which wrongly includes assumption I. Option D says neither assumption is correct, which ignores the clear relationship described in the statement. Option E suggests that exactly one is correct without specifying which, but you are expected to identify the specific valid assumption, which is assumption II. Common Pitfalls: A common error is to read the phrase related to social order as meaning poverty is part of the structure of social order, rather than an effect of its breakdown. Another mistake is to treat every word in the statement as a definition, which leads to over interpretation of the term social disorder. Final Answer: The correct conclusion is that only assumption II is correct, because poverty is clearly related to social order but is not itself a type of social order.

Question 4

Some principals are teachers and all teachers are students; based on this, which of the given conclusions about principals and students logically follows?

Accepted Answer

Introduction / Context: This syllogism style question involves three sets: principals, teachers and students. You must check which of the two conclusions about principals and students are logically forced by the given statements. Given Data / Assumptions: Statement 1: Some principals are teachers. Statement 2: All teachers are students. Conclusion I: All principals are students. Conclusion II: Some students are principals. Concept / Approach: Some principals are teachers means there is at least one person who is both a principal and a teacher. All teachers are students means the entire set of teachers lies inside the set of students. By combining these, we consider what we can say about principals and students. Step-by-Step Solution: Step 1: From some principals are teachers, pick at least one person who belongs to both sets: principal and teacher. Step 2: From all teachers are students, anyone who is a teacher must also be a student. Step 3: Therefore the person who is both a principal and a teacher must also be a student. This means there exists at least one person who is both a principal and a student. Step 4: Thus some students are principals is definitely true, and conclusion II follows. Step 5: Conclusion I says all principals are students. We only know that some principals are teachers and thus students. There may be other principals who are not teachers and whose student status is unknown. So conclusion I is not forced. Verification / Alternative check: Construct an example. Let the set of principals be {p1, p2}, teachers be {p1, t1} and students be {p1, t1, s1}. Some principals (p1) are teachers, and all teachers are students. Here, some students (p1) are principals, so conclusion II holds. However, principal p2 is not necessarily a student in this example, so conclusion I fails. This confirms that only conclusion II is logically valid. Why Other Options Are Wrong: Option A chooses only conclusion I, which overgeneralises the relation between principals and students. Option C says both conclusions follow, which is not correct because we cannot include all principals. Option D says neither follows, which ignores the clear existence of at least one principal who is a student. Option E suggests an ambiguous either or, but the question requires the specific conclusion that holds, which is conclusion II. Common Pitfalls: A frequent mistake is to misread some as all and immediately assume that all principals are teachers or all principals are students. Another error is to ignore that there can be principals who are not teachers and whose relation to the student set is not defined by the given statements. Final Answer: The correct evaluation is that only conclusion II follows from the given statements.

Question 5

To achieve economic development, people should work hard; based on this, which of the given conclusions about development and hard work logically follows?

Accepted Answer

Introduction / Context: This reasoning question connects economic development with people's hard work. You must determine which conclusion is directly supported by the given statement when it is treated as true. Given Data / Assumptions: Statement: To achieve economic development, people should work hard. Conclusion I: Economic development is directly related to people's hard work. Conclusion II: Working hard by all the people is impossible. No further information about feasibility or other factors is provided. Concept / Approach: The statement sets up a necessary condition: for economic development to happen, hard work by people is required. This means there is a direct connection between development and hard work. However, the statement does not discuss whether hard work by all people is practically possible or impossible, so we cannot conclude that part. Step-by-Step Solution: Step 1: The expression to achieve economic development, people should work hard indicates that hard work is required for development. Step 2: This clearly supports the idea that there is a direct relationship between economic development and hard work of people. If people do not work hard, development is unlikely. Step 3: Conclusion I restates this as economic development is directly related to people's hard work, which matches the essence of the statement. Step 4: Conclusion II claims that it is impossible for all people to work hard. The original statement does not talk about possibility or impossibility of everyone working hard; it only advises that they should do so. Step 5: Therefore conclusion II goes beyond the given information and does not follow. Verification / Alternative check: Consider two situations. In one, many people work hard and development is achieved. In another, many people are lazy and development is slow. Both situations are consistent with the idea that hard work is important for development. Neither case proves that it is impossible for everyone to work hard. The statement is a prescription, not a claim about impossibility. Why Other Options Are Wrong: Option B chooses only conclusion II, which is unsupported. Option C says both follow, wrongly including the stronger claim about impossibility. Option D says neither follows, which ignores the clear link between development and hard work stated in the problem. Option E proposes an either or condition that is not relevant here, since exactly one conclusion follows. Common Pitfalls: A common error is to assume that an obligation (people should work hard) automatically implies impossibility (people cannot all work hard). These are very different ideas. Another pitfall is to overlook direct restatements of the given condition, such as conclusion I, which is precisely what the original sentence suggests. Final Answer: The correct evaluation is that only conclusion I follows from the given statement.

Question 6

In each of the following logical reasoning questions, a set of statements is followed by suggested conclusions. Taking the given statements to be true, even if they appear to differ from commonly known facts, read all the conclusions carefully and d…

Accepted Answer

Introduction / Context: This question belongs to the standard category of syllogism based logical reasoning. You are given universal statements about insects, machines, and the property of being dangerous, and then asked to test different possible conclusions. The task is to decide which conclusion must logically follow if we accept the statements as absolutely true, even when they may not agree with real world knowledge. The focus is on set relations, not on general knowledge about insects or machines. Given Data / Assumptions: Statement (I): All insects are dangerous. Statement (II): All machines are dangerous. Conclusion (I): All dangerous things are insects. Conclusion (II): All dangerous things are machines. Conclusion (III): Some machines are insects. We assume only the information given in the statements and do not add any extra facts. Concept / Approach: The problem uses the idea of sets and subsets. A statement like “All insects are dangerous” means that the set of insects is completely contained inside the set of dangerous things. In set language, insects are a subset of dangerous things. However, this does not mean that all dangerous things are insects. Similarly, “All machines are dangerous” says that machines form another subset of dangerous things. The key idea is to check whether each conclusion must be true in every possible diagram that satisfies the given statements. Step-by-Step Solution: Step 1: Represent insects as a subset of the set of dangerous things, based on statement (I).Step 2: Represent machines as a subset of the same set of dangerous things, based on statement (II).Step 3: Observe that the two subsets, insects and machines, may or may not overlap. There is no information that forces any machine to be an insect or any insect to be a machine.Step 4: Check conclusion (I): “All dangerous things are insects.” This would mean that the entire dangerous set is equal to the insect set. But statements only say that insects are inside dangerous, not that dangerous has nothing else. So conclusion (I) is not necessary.Step 5: Check conclusion (II): “All dangerous things are machines.” By the same reasoning, machines are inside dangerous, but dangerous can contain other things as well. So conclusion (II) is also not necessary.Step 6: Check conclusion (III): “Some machines are insects.” This requires an overlap between machines and insects. The statements do not force any such overlap, so it is possible to draw a diagram in which the two subsets do not intersect at all. Therefore this conclusion is also not guaranteed. Verification / Alternative check: A quick way to verify is to mentally draw a Venn diagram. Draw a large circle for dangerous things. Inside it, draw one smaller circle for insects and another separate smaller circle for machines, with no overlap. This picture satisfies both statements: every insect and every machine is dangerous. In this picture, none of the three given conclusions is true. This confirms that no conclusion logically follows from the statements. Why Other Options Are Wrong: Option A, claiming only conclusion (I) follows, is wrong because the statements never say that every dangerous thing is an insect. Option B, claiming only conclusion (II) follows, is wrong for the same reason with machines. Option C, claiming only conclusion (III) follows, is wrong because it is possible that machines and insects are two completely separate subsets inside the dangerous group. There is no forced overlap. Thus none of the listed conclusions must be true. Common Pitfalls: A very common mistake is to reverse the direction of the statements. Learners often read “All insects are dangerous” and mentally convert it into “All dangerous are insects,” which is logically incorrect. Another typical error is to assume that two different groups contained in a larger group must overlap, which is again not guaranteed. Always remember that A subset of C and B subset of C does not imply any relation between A and B. Exam questions of this type test whether you can avoid such intuitive but invalid jumps. Final Answer: The only logically correct decision is that no conclusion follows from the given statements.

Question 7

In the following logical reasoning question, a couple of statements is followed by suggested conclusions. Taking the given statements to be true, even if they appear to be at variance with commonly known facts, read both conclusions carefully and de…

Accepted Answer

Introduction / Context: This question tests standard syllogism reasoning about the relations between three categories: cups, plates, and glasses. You are asked to work only with the logical content of the statements, ignoring real world experience. The aim is to see whether you can correctly judge which conclusions must follow and which are only possibilities or may even be false in some valid arrangement. Given Data / Assumptions: Statement (I): All cups are plates. Statement (II): Some plates are glass. Conclusion (I): Some glasses are cups. Conclusion (II): All glasses are cups. We assume no further information beyond what is explicitly stated. Concept / Approach: The language “All cups are plates” indicates that the set of cups is a subset of the set of plates. The phrase “Some plates are glass” indicates that there is at least one element which belongs to both the set of plates and the set of glass. To decide whether a conclusion logically follows, we must check if it is true in every possible diagram that respects the statements. If a conclusion fails even in one valid diagram, then it does not logically follow. Step-by-Step Solution: Step 1: Draw a large circle for plates. Place a smaller circle for cups completely inside the plates circle, representing “All cups are plates.”Step 2: Place at least one point or region inside the plates circle that represents plates which are glass, based on “Some plates are glass.” However, the problem does not say that this glass region must intersect the cups circle.Step 3: Analyse conclusion (I): “Some glasses are cups.” For this to be necessarily true, at least one of the plates that are glass must also be a cup. But the statements never force the overlap between the cups region and the glass region inside plates. It is perfectly possible that all plates that are glass are outside the cups circle. Hence conclusion (I) is not guaranteed.Step 4: Analyse conclusion (II): “All glasses are cups.” This is even stronger. It claims that every glass item lies within the set of cups. The data only says some plates are glass and that all cups are plates. Glass items can very well exist outside the cups region, as long as they are plates. Therefore conclusion (II) also does not necessarily follow. Verification / Alternative check: To verify, construct a concrete example. Suppose there are 10 plates. Out of them, 3 are cups and 2 are glass, but these 2 are not cups. All other objects are neither cups nor plates. These numbers satisfy both given statements: all cups are plates, and there exist some plates that are glass. In this example, there is no glass that is a cup, so conclusion (I) is false, and clearly not all glasses are cups, so conclusion (II) is also false. Because there exists at least one valid situation where both conclusions fail, neither conclusion logically follows. Why Other Options Are Wrong: Option A claims that only conclusion (I) follows, which is wrong because we just showed a valid case where no glass object is a cup. Option B claims that only conclusion (II) follows, but that is even stronger and definitely not supported by the statements. Option D says both conclusions follow, which clearly contradicts our counterexample. The only defensible choice is the one that accepts that neither conclusion is logically forced. Common Pitfalls: A frequent error in such problems is to assume that “Some plates are glass” automatically implies an overlap with cups simply because cups are also plates. In reality, a subset inside a bigger set is free to occupy any part of that set. Another mistake is to casually convert “All cups are plates” into “All plates are cups,” which reverses the logical relation and leads to wrong conclusions. Careful diagram drawing and strict reading of the statements help avoid these traps. Final Answer: The correct logical assessment is that neither conclusion (I) nor conclusion (II) follows from the given statements.

Question 8

In the following logical reasoning question, a pair of statements about pens, pencils, and erasers is followed by two suggested conclusions. Accept the statements as true, even if they do not match real life experience, read both conclusions careful…

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Introduction / Context: This question examines your understanding of set relations involving pens, pencils, and erasers. You are given one statement about partial overlap between pens and pencils and another statement that fully connects pencils to erasers. Two conclusions are proposed, and your task is to judge whether any of them must be true in every case consistent with the statements. The emphasis is on what is logically forced, not on what is merely possible. Given Data / Assumptions: Statement (I): Some pens are pencils. This means there is at least one object that is both a pen and a pencil. Statement (II): All pencils are erasers. Every pencil lies inside the set of erasers. Conclusion (I): Some pencils are not pens. Conclusion (II): Some erasers are not pens. We must not assume anything extra beyond these two statements. Concept / Approach: From the statements we know there is an overlapping region between pens and pencils, and that all pencils lie inside the larger set of erasers. So the set of pencils is fully contained in the eraser set. However, we do not know whether every pencil is also a pen or whether there are additional erasers that are not pencils. Logical conclusions require certainty: a conclusion follows only if it holds in every possible Venn diagram that satisfies the statements. Step-by-Step Solution: Step 1: Represent the pencil set as a subset of the eraser set, because all pencils are erasers.Step 2: Represent the pen set so that it overlaps the pencil set at least in one point, because some pens are pencils.Step 3: Check conclusion (I): “Some pencils are not pens.” This needs at least one pencil outside the pen region. But the given statements do not force any such extra pencil. All pencils might coincide with pens. For example, every pencil could be a pen, while still being an eraser, and the statements would still hold. Hence conclusion (I) is not necessary.Step 4: Check conclusion (II): “Some erasers are not pens.” This requires at least one eraser outside the pen set. However, it is possible that there are no erasers except those pencils which are also pens. In such a scenario, every eraser is also a pen, and conclusion (II) fails. Since the statements allow such a diagram, conclusion (II) is also not guaranteed. Verification / Alternative check: To verify, create a concrete model. Suppose there is exactly one object, and that object is a pen, a pencil, and an eraser at the same time. Then “Some pens are pencils” is true, and “All pencils are erasers” is also true. However, in this picture there is no pencil which is not a pen, and no eraser which is not a pen. Both conclusions (I) and (II) turn out false. Because we have found at least one valid case in which both conclusions fail, neither conclusion logically follows from the original statements. Why Other Options Are Wrong: Option A claims that only conclusion (I) follows, which is incorrect because we have displayed a valid arrangement where every pencil is also a pen. Option B claims that only conclusion (II) follows, but our example also shows a case where every eraser is a pen, so conclusion (II) is not forced. Option D asserts that both conclusions follow, which is clearly contradicted by the same counterexample. The only correct choice is the one that admits that neither conclusion is logically compelled. Common Pitfalls: Learners often confuse what is possible with what is necessary. It is easy to imagine real world situations where there are erasers unrelated to pens, or pencils that are not pens. But logical questions are stricter: unless the statement guarantees such an element in every case, we cannot accept the conclusion. Another frequent mistake is to assume that when two sets overlap, there must also be elements in each set that do not belong to the other, which is not mandatory. Final Answer: Therefore, based on strict syllogistic reasoning, neither conclusion (I) nor conclusion (II) follows from the given statements.

Question 9

In this statement and conclusion type logical reasoning question, you are given two categorical statements about mangoes, their colour, and their price. Treat the statements as true, even if they appear unrealistic, and then decide which conclusion …

Accepted Answer

Introduction / Context: This question is a classic example of syllogism based reasoning used in many competitive exams. You are given two statements about mangoes, golden colour, and cheapness, and then two possible conclusions. The task is to see which conclusion must follow logically if both statements are accepted as absolutely true. Real life knowledge about mangoes or prices is irrelevant; only the internal logic matters. Given Data / Assumptions: Statement 1: All mangoes are golden in colour. Statement 2: No golden coloured things are cheap. Conclusion I: All mangoes are cheap. Conclusion II: Golden coloured mangoes are not cheap. Assume the statements hold without exception as long as the question is considered. Concept / Approach: The first statement tells us that the set of mangoes is fully contained inside the set of golden coloured things. The second statement tells us that there is no overlap between golden coloured things and cheap things. In set language, golden things and cheap things are disjoint. To decide which conclusion follows, we combine these two relations carefully. A conclusion follows only when it must be true in every diagram that satisfies both statements. Step-by-Step Solution: Step 1: Represent the set of golden coloured things as a large circle.Step 2: Draw the set of mangoes as a smaller circle completely inside the golden circle, because every mango is golden.Step 3: Represent the set of cheap things as another circle that does not intersect the golden circle at all, since no golden thing is cheap.Step 4: Consider conclusion I: “All mangoes are cheap.” This would require the mangoes circle to be completely contained in the cheap circle. But our diagram shows that mangoes are inside the golden region and golden things do not intersect cheap things at all. So mangoes cannot be cheap. Conclusion I directly contradicts the combined effect of the statements, so it cannot follow.Step 5: Consider conclusion II: “Golden coloured mangoes are not cheap.” Every mango is golden, and every golden thing is not cheap. So if we talk about golden coloured mangoes, they must also be not cheap. This conclusion simply restates the logical consequence of the two statements and therefore follows. Verification / Alternative check: We can also reason symbolically. From statement 1, mango implies golden. From statement 2, golden implies not cheap. By linking these, mango implies not cheap. Therefore, any mango cannot be cheap. Conclusion II talks exactly about golden coloured mangoes being not cheap, which agrees with this chain. Conclusion I, on the other hand, says the opposite. It would require mango implies cheap, which contradicts mango implies not cheap. Hence only conclusion II is logically valid. Why Other Options Are Wrong: Option A, which claims only conclusion I follows, is wrong because conclusion I conflicts with the second statement. Option C, which suggests that either conclusion I or conclusion II follows, is wrong since they are not both possible logical consequences; only the second can be correct. Option D claims that both follow, which is impossible because they say opposite things about the same set of mangoes. Only option B, supporting conclusion II alone, matches the derived logic. Common Pitfalls: A common mistake is to misread the second statement and think that no cheap thing is golden, then confuse the direction and assume that no golden thing is cheap means nothing else can be cheap either. Another error is to ignore the word “no” and accidentally treat golden items as possibly cheap. Always track the direction of implications and the presence of negative words like “no” and “not.” Drawing a clear Venn diagram usually prevents such confusion. Final Answer: Therefore, the correct reasoning shows that only conclusion II follows from the given statements.

Question 10

In this logical reasoning question on statements and conclusions, you are given three statements about stars, the colour white, and the moon being blue or not. Treat the statements as true even when they differ from real astronomy, read all four con…

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Introduction / Context: This problem checks your ability to handle chained categorical statements about stars, white objects, moons, and blue objects. Although the content looks like astronomy, you must ignore actual science and work purely with the logical structure. The three statements define how the sets “stars,” “white,” “moon,” and “blue” relate, and you are asked to judge which conclusions are forced by these relationships. Given Data / Assumptions: Statement (I): All stars are white. Statement (II): All white things are moon. Statement (III): No moon is blue. Conclusion (I): Some moon are stars. Conclusion (II): No blue is stars. Conclusion (III): Some white are stars. Conclusion (IV): Some blue are white. Assume that stars exist, so “all stars are white” implies at least some stars and some white objects. Concept / Approach: When one statement says “All A are B” and another says “All B are C,” we can chain them to conclude “All A are C.” Likewise, “No C is D” creates a disjoint relationship between sets. Here we chain stars to white and then to moon, and then apply the restriction that moons are never blue. Conclusions are evaluated by checking if they must hold in every Venn diagram that respects all three statements. Step-by-Step Solution: Step 1: Draw a large circle for moon.Step 2: Place the white circle completely inside the moon circle because all white things are moon.Step 3: Place the stars circle completely inside the white circle because all stars are white. Therefore, stars are also inside the moon circle.Step 4: Draw a separate region for blue such that it does not intersect the moon circle at all, since no moon is blue.Step 5: Check conclusion (I): “Some moon are stars.” Because the stars circle lies inside the moon circle and we assume there is at least one star, at least one moon is also a star. So conclusion (I) follows.Step 6: Check conclusion (II): “No blue is stars.” All stars lie inside the moon circle, and no moon is blue. Thus stars cannot be blue, so no blue is stars. Conclusion (II) follows.Step 7: Check conclusion (III): “Some white are stars.” Stars lie inside the white circle, and stars exist, so there is at least one object that is both white and star. Therefore conclusion (III) follows.Step 8: Check conclusion (IV): “Some blue are white.” The blue region is completely outside the moon circle, while white lies completely inside moon. So there is absolutely no intersection between blue and white. Conclusion (IV) contradicts the diagram and does not follow. Verification / Alternative check: Symbolically, from statement (I), star implies white. From statement (II), white implies moon. Combining, star implies moon. From statement (III), moon implies not blue. Thus star implies not blue. Conclusion (II) matches this reasoning. Since there exists at least one star, there must be at least one white moon that is a star, which supports conclusions (I) and (III). Conclusion (IV) would require some object to be both blue and white, but if white implies moon and moon objects are never blue, such an object cannot exist. Why Other Options Are Wrong: Option B claims only conclusions (III) and (IV) follow, but we have already established that (I) and (II) also follow and (IV) is false. Option C includes (IV), which contradicts the condition that moon and blue do not overlap. Option D again includes (IV), so it cannot be correct. Only option A, which includes (I), (II), and (III) while excluding (IV), correctly matches the logical deductions. Common Pitfalls: One frequent error is to ignore existence and treat “All stars are white” as not implying any stars, which can cause confusion about conclusions with “some.” In competitive exam conventions, when such chains are used, it is usually intended that there are at least some objects in the mentioned sets. Another mistake is to overlook that white objects are also moon objects, so any restriction on moons automatically restricts white things and thereby restricts stars as well. Final Answer: The correct assessment is that only conclusions (I), (II) and (III) follow from the given statements.

Question 11

In this logical reasoning question on statements and conclusions, you are given information about managers, boys, and people who are young. Accept the statements as true even if they differ from common sense, then examine the conclusions and decide …

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Introduction / Context: This question checks your ability to reason about overlapping sets when only partial information is given. You are told something about managers, boys, and young people, and then asked whether there is any guaranteed overlap between managers and boys. The key challenge is to avoid assuming more than what is stated and to distinguish possible situations from logically necessary ones. Given Data / Assumptions: Statement 1: Some managers are young. Statement 2: All boys are young. Conclusion I: Some boys are managers. Conclusion II: Some managers are boys. We assume no extra relationship between “managers” and “boys” beyond what is directly provided. Concept / Approach: Both statements talk about the set of young people. Some managers lie inside the young group, and all boys lie inside the young group. However, there is no direct relation given between the set of managers and the set of boys. When two different subsets of a larger set are mentioned, we must not assume they overlap unless the statements specifically say so. To test conclusions, we try to construct at least one diagram that satisfies the statements but makes a conclusion false. If such a diagram exists, the conclusion does not logically follow. Step-by-Step Solution: Step 1: Draw a large circle representing young people.Step 2: Place a region for managers that partially lies inside the young circle, because some managers are young. There may also be managers outside the young group, but that is not important here.Step 3: Place the boys group completely inside the young circle, because all boys are young. This does not tell us whether boys and managers have any overlap inside young people.Step 4: Consider conclusion I: “Some boys are managers.” This would require that the boys region and the manager region overlap. But the statements allow a situation where all boys are young but none of them are managers. Therefore conclusion I is not necessary.Step 5: Consider conclusion II: “Some managers are boys.” This is the same overlap viewed from the other side. Again, nothing in the statements forces any boy to be a manager. It is possible that all young managers are adults who are not boys, while all boys are young students and none of them manage anything. So conclusion II is not forced either. Verification / Alternative check: Take a simple numerical example. Suppose there are 10 young people. Out of them, 3 are managers and 7 are boys. It is entirely possible that these 3 managers are different individuals from the 7 boys. Then “Some managers are young” is true (those 3 managers), and “All boys are young” is also true (all 7 boys are in the young group). However, there is no boy who is a manager, and no manager who is a boy, so both conclusions fail. Since such a situation obeys the statements but makes both conclusions false, neither conclusion follows logically. Why Other Options Are Wrong: Option A claims that only conclusion I follows, but we have seen that there can be zero overlap between boys and managers. Option B claims that only conclusion II follows, which is the same error seen from the managers side. Option D says both conclusions follow, which clearly contradicts the counterexample. Only option C correctly acknowledges that neither conclusion is guaranteed. Common Pitfalls: Many learners automatically assume that if two groups share a common attribute, such as being young, then the groups must overlap. This is not logically necessary. Both managers and boys are contained within the larger group of young people, but they can occupy completely different parts of that group. Another mistake is to unconsciously rely on real world stereotypes about managers and boys, which should be avoided in formal reasoning questions. Final Answer: Therefore, the logically correct decision is that neither conclusion I nor conclusion II follows from the given statements.

Question 12

In this statement and conclusion based reasoning question, you are given two statements about bags, tables, and the colour red. Accept the statements as true even if they contradict real life, and then decide which of the given conclusions logically…

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Introduction / Context: This question presents you with two statements involving bags, tables, and the property of being red. You must treat the statements as perfectly true for the purpose of the problem and then decide which conclusions are logically forced. The challenge is to track how being a bag connects to being a table and how tables relate to the colour red. Given Data / Assumptions: Statement (I): All bags are tables. Statement (II): No table is red. Conclusion (I): Some bags are red. Conclusion (II): All bags are red. We assume nothing about bags or colours beyond what these statements provide. Concept / Approach: The first statement says that the entire set of bags lies inside the set of tables. The second statement says that the set of tables does not intersect the set of red objects at all. Combined, this means that bags, which are all tables, also cannot be red. Conclusions that talk about bags being red must therefore be checked against this restriction. A conclusion follows only if it is compatible with the statements in every possible interpretation. Step-by-Step Solution: Step 1: Draw a large circle for tables.Step 2: Draw a smaller circle completely inside the tables circle to represent bags, because every bag is a table.Step 3: Draw another circle for red objects such that it lies totally outside the tables circle, since no table is red.Step 4: Consider conclusion (I): “Some bags are red.” Since every bag is inside the tables circle and tables do not overlap with red objects, there cannot be any bag that is red. So conclusion (I) is directly contradicted by the combined statements.Step 5: Consider conclusion (II): “All bags are red.” This is even stronger and would require the entire bags circle to lie inside the red circle. But the bags circle lies inside the tables circle, and tables are completely disjoint from red objects. Therefore, it is impossible for any bag to be red, let alone all of them. Conclusion (II) is also incompatible with the statements. Verification / Alternative check: We can verify logically by simple implication chains. From statement (I), bag implies table. From statement (II), table implies not red. Therefore, bag implies not red. That is, no bag can be red. Conclusion (I) claims that some bags are red, which contradicts bag implies not red. Conclusion (II) claims that all bags are red, which is an even stronger contradiction. Since both conclusions conflict with the necessary implication bag implies not red, neither can be accepted. Why Other Options Are Wrong: Option A claims only conclusion (I) follows; this is clearly wrong because conclusion (I) states the opposite of what the statements imply. Option B claims only conclusion (II) follows, which is again impossible for the same reason. Option D suggests that both conclusions follow, which would mean we accept that some and all bags are red, which directly violates both statements. Only option C, indicating that neither conclusion follows, agrees with the logic. Common Pitfalls: Students sometimes get confused by the phrase “All bags are tables” and misinterpret it as “Some tables are bags,” then assume that some of those tables might be red. However, the second statement clearly prohibits any table from being red. Another common error is overlooking the effect of a “no” type statement, which creates completely disjoint sets. Whenever you see “No A is B,” ensure that the A and B sets do not overlap anywhere in your mental diagram. Final Answer: Hence, the correct decision is that neither conclusion (I) nor conclusion (II) follows from the given statements.

Question 13

In each of the following statement and conclusion questions, a pair of statements about books, sharpeners, and erasers is followed by some conclusions. Taking the given statements to be true even if they appear unrealistic, read both conclusions car…

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Introduction / Context: This syllogism style question deals with the logical relationships between three sets: books, sharpeners, and erasers. You are given two universal statements and then asked to determine which conclusions must follow. The question tests your ability to chain subset relations correctly and to distinguish guaranteed facts from possibilities. Given Data / Assumptions: Statement (I): All books are erasers. Statement (II): All sharpeners are books. Conclusion (I): All sharpeners are erasers. Conclusion (II): Some books are sharpeners. We assume that the statements can be represented by sets and subset relations, with no extra information added. Concept / Approach: When one statement says “All A are B” and another says “All B are C,” we can logically combine them to obtain “All A are C.” This is the idea of chaining subsets. However, such universal statements do not automatically guarantee the existence of any elements unless there is a “some” type statement. Therefore, it is important to treat conclusions about existence, such as “some books are sharpeners,” with extra care. A conclusion follows only if it is true in every possible diagram that satisfies the given statements. Step-by-Step Solution: Step 1: Represent erasers as a large set.Step 2: Place the books set completely inside the erasers set, because all books are erasers.Step 3: Place the sharpeners set completely inside the books set, because all sharpeners are books. As a result, sharpeners are automatically inside the erasers set as well.Step 4: Analyse conclusion (I): “All sharpeners are erasers.” Since sharpeners lie inside books and books lie inside erasers, every sharpener must also be an eraser. This is a direct consequence of the chain sharpeners subset books subset erasers, so conclusion (I) definitely follows.Step 5: Analyse conclusion (II): “Some books are sharpeners.” This statement asserts the existence of at least one object that is both a book and a sharpener. But the original statements never say that there is at least one sharpener, nor that there is at least one book. It is logically possible, though unrealistic, that there are no books and no sharpeners at all. In that empty model, the statements “All books are erasers” and “All sharpeners are books” still hold, while conclusion (II) fails. Therefore conclusion (II) does not logically follow. Verification / Alternative check: To verify, use symbolic reasoning. From statement (II), sharpener implies book. From statement (I), book implies eraser. Combining them, sharpener implies eraser, which is exactly what conclusion (I) says. So conclusion (I) is correct in every scenario. However, the statements never include the word “some,” so they do not guarantee the presence of any actual sharpeners or books. A universal statement like “All sharpeners are books” is logically true even if there are no sharpeners at all. Because of this, the existence claim in conclusion (II) is not ensured. Why Other Options Are Wrong: Option B claims that only conclusion (II) follows, which contradicts the direct deduction that sharpeners must be erasers. Option C says that both conclusions follow, but we have shown that conclusion (II) might fail in a valid interpretation. Option D suggests that neither conclusion follows, which ignores the clear chain from sharpeners to erasers. Only option A, which asserts that only conclusion (I) follows, is consistent with proper logical analysis. Common Pitfalls: Many students assume that “All sharpeners are books” implies there is at least one sharpener, but in pure logic that is not required. Another common mistake is to forget that once a set is contained inside another, any further container also contains it. Here, because books are inside erasers, and sharpeners are inside books, sharpeners are automatically inside erasers. Careful diagram drawing and awareness of existence assumptions help avoid these errors. Final Answer: Therefore, the correct conclusion is that only conclusion (I) follows from the given statements.

Question 14

Read the following information carefully and answer the question that follows. The municipal authority has made English language one of the compulsory subjects in all primary schools under its control from the current academic year. Based on this de…

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Introduction / Context: This is an assumptions based critical reasoning question. The statement talks about a new policy decision by a municipal authority: making English a compulsory subject in all primary schools under its control. You are asked to identify which option can be reasonably taken as an assumption behind this decision. An assumption is an unstated idea that the decision maker accepts as true and which supports the action taken. Given Data / Assumptions: Statement: The municipal authority has made English language one of the compulsory subjects in all primary schools under its control from the current academic year. Option A: Students in municipal primary schools were not taught English so far. Option B: Parents of primary school students do not have working knowledge of English. Option C: All primary schools outside municipal control already teach English as a compulsory subject. Option D: Other subjects can be changed according to the will of the students. We must choose the assumption that is necessary or very closely linked to the decision. Concept / Approach: In assumption questions, we look for a statement that must be true, or is at least strongly presumed, for the given action to make sense. The assumption should be directly connected to the decision and should help explain why the authority considered the step necessary. Very broad, unrelated, or external claims that are not essential for the decision are usually not assumptions. Also, an assumption should not contradict the statement. Step-by-Step Solution: Step 1: Understand the decision. The municipal authority is changing the curriculum to make English compulsory in its primary schools. This indicates that English had a lesser or optional role earlier, or that the authority feels English education needs strengthening.Step 2: Examine option A. If students were not taught English earlier, then introducing English as a compulsory subject is a natural corrective measure. The authority can be assumed to believe that the absence of English in the curriculum is a problem. So option A provides a strong underlying reason for the decision.Step 3: Examine option B. Parents lacking working knowledge of English might be true, but it is not necessary for changing the school curriculum. The policy is about what students learn in school, not about parents abilities.Step 4: Examine option C. Whether schools outside municipal control teach English compulsorily is external information. The municipal authority can decide its own curriculum without assuming anything about other schools. This option goes beyond what is required.Step 5: Examine option D. The idea that other subjects can be changed according to the will of students is unrelated to making English compulsory. Curriculum design is generally driven by educational priorities, not by students wishes alone. So this option does not connect logically to the decision. Verification / Alternative check: Think about what would make the municipal authority feel a need to act. A natural and strong reason is that earlier their schools did not offer English at all, or did not emphasise it sufficiently. If teachers were already systematically teaching English as a compulsory subject, then formally declaring it compulsory would add little. Hence, the authority is likely assuming that English has been missing from or weak in the curriculum so far. Option A closely captures this sense, even if it is a somewhat strong wording. The other options are not required for the decision to make sense. Why Other Options Are Wrong: Option B focuses on parents, not students, and though it might be interesting, it is not necessary for deciding to change the school curriculum. Option C speculates about all schools outside municipal control, which the authority does not need to assume in order to modify its own schools. Option D introduces a claim about students controlling subject choices, which has no connection to the stated decision. Only option A directly addresses the likely earlier absence of English teaching in municipal primary schools. Common Pitfalls: Candidates sometimes confuse an assumption with a mere possibility or an effect. They may also be attracted to options containing general or emotional statements, even when those are not linked to the action. Another typical mistake is to pick an option that would be nice to have true, rather than one that is needed for the decision to be meaningful. Always ask yourself: if this option were false, would the decision in the statement still make sense? Final Answer: Thus, the most reasonable assumption is that the students in the primary schools run by the municipal authority were not taught English so far, which corresponds to option A.

Question 15

Read the following statements about peak hour travel in city M and answer the question that follows. During peak hours the local trains of city M are chaotic. Peak hours usually refer to the morning time when people go to work and the evening time w…

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Introduction / Context: This is a critical reasoning question focused on weakening a perception or claim. The perception here is that the state government has not taken any measures in the past two years to address chaos in local trains during peak hours. Your job is to identify which option, if taken as true, weakens this belief by showing that the government has in fact taken some relevant action. Given Data / Assumptions: Context statement: During peak hours the local trains of city M are chaotic. Additional information: Peak hours are the morning and evening work commute periods. Perception: Some people believe that the state government has taken no measures in the past two years to manage this chaos. Option A: In the past one year the government has increased train frequency in peak hours and capacity per train. Option B: In the past two years the government has received many petitions demanding improvement. Option C: First class passengers feel their condition is worse than that of second class passengers. Option D: Population is increasing due to migration and better job opportunities, leading to more train users. Concept / Approach: To weaken a claim, you look for information that directly contradicts or undermines the basis of that claim. The perception is that no measures have been taken. Therefore, any option that shows the government has taken some reasonable and relevant measures during the specified time period would weaken this perception. Options that merely describe complaints, feelings, or external factors like population growth do not show government action and hence do not weaken the claim. Step-by-Step Solution: Step 1: Examine option A. It explicitly states that in the past one year the state government increased the frequency of trains during peak hours and increased the number of passengers each train can carry. Both actions are directly aimed at managing peak hour chaos by increasing capacity and supply. This directly contradicts the idea that the government took no measures.Step 2: Examine option B. Receiving many petitions only shows that citizens complained and suggested improvements. It does not show that the government acted. In fact, it might support the perception that more needs to be done, but it does not weaken the claim regarding lack of measures.Step 3: Examine option C. The feeling of first class passengers that their plight is worse than that of second class passengers merely comments on the nature of the problem and relative discomfort. It says nothing about government measures and therefore does not weaken the perception.Step 4: Examine option D. This option explains why there is a surge in the number of people travelling by trains by pointing to population growth and migration. This can even support the idea that chaos is natural under these conditions but does not show the government took any steps. Verification / Alternative check: If option A is true, then people who claim that the government has taken no measures in the last two years are clearly mistaken, because increasing frequency and capacity are concrete measures. On the other hand, options B, C, and D are compatible with the belief that the government has not actually intervened. Only one option provides direct evidence of action that targets the problem, and that option must therefore weaken the original perception. Why Other Options Are Wrong: Option B highlights citizen petitions but not government response. It may even strengthen the idea that the problem continues. Option C focuses on passenger feelings and relative discomfort, which is irrelevant to the question of whether any measures were taken. Option D gives a reason for the chaos, namely increasing population and commuters, but again does not mention any governmental steps. Since the question is specifically asking for an option that weakens the perception about lack of measures, these options are unsuitable. Common Pitfalls: Test takers often confuse explaining a problem with weakening a claim about solutions. An explanation of why trains are crowded does not show any action by the authorities. Another pitfall is to choose an option that increases sympathy for passengers, assuming that such an option responds to the issue; however, the question is about measures taken, not about who suffers more. Always align your choice precisely with what the question stem is asking you to do. Final Answer: Hence, the statement that weakens the perception that no measures have been taken is that in the past one year the state government has increased the frequency of trains in peak hours and also increased the number of passengers per train, that is, option A.

Question 16

Read the following statement about drinking behaviour among U.S. fraternity and sorority members and answer the question that follows. According to a recent study in the journal Psychology of Addictive Behaviours, U.S. fraternity and sorority member…

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Introduction / Context: This is a critical reasoning question asking for a logical extension of a short passage. The passage states a research finding about U.S. fraternity and sorority members: those who drink heavily while in school do not tend to drink heavily after graduation. A logical extension is a statement that naturally continues the line of reasoning or offers a plausible explanation consistent with the given fact, without introducing unrelated or overly broad claims. Given Data / Assumptions: Study finding: Fraternity and sorority members who drink heavily in school usually do not continue heavy drinking after graduation. Option A: Most men end a drinking binge after they cross thirty. Option B: Graduation brings a sense of responsibility that makes students avoid such vices. Option C: Drinking begins as a group activity, and as students leave these groups, the habit of drinking is also left behind. Option D: Heavy drinking during college makes most students realize the harmful effects of alcohol. We seek the option that directly connects the college group context to the reduction in heavy drinking after college. Concept / Approach: The passage emphasises two elements: heavy drinking and the specific environment of fraternities and sororities. These are social groups where drinking is strongly influenced by peer behaviour and group culture. A strong logical extension will usually highlight this group influence and show how its disappearance after graduation can explain the observed change in drinking behaviour. Options that talk about age in general, vague responsibility, or generic learning from harm may be plausible, but they are less tightly linked to the group-based nature of fraternity and sorority life. Step-by-Step Solution: Step 1: Examine option A. It speaks about men reducing drinking after they cross thirty years of age. The passage, however, specifically focuses on the transition from being in school to after graduation, not on age thirty. Many graduates are in their early or mid twenties, so this statement is not closely aligned with the passage.Step 2: Examine option B. It claims that graduation brings a sense of responsibility which makes students avoid vices like heavy drinking. While this might be partially true, it is generic and does not mention fraternities, sororities, or the group influence that the passage highlights.Step 3: Examine option C. It explicitly states that drinking begins as a group activity and that, as students leave these specific groups, they leave the habit behind. This matches the passage very closely: fraternities and sororities are exactly such groups, and leaving them at graduation would naturally reduce the group driven drinking behaviour.Step 4: Examine option D. It says heavy drinking makes most students realize the harmful effects of alcohol. While this can explain why some people might stop drinking heavily, it does not tie in the fraternity and sorority context. It also introduces a new claim about learning from harm, which the passage does not mention. Verification / Alternative check: To verify the best extension, ask which option you could add as the next sentence in the passage so that the paragraph reads smoothly and remains focused on fraternity and sorority culture. Adding option C creates a coherent continuation: heavy drinking is common while in these social groups, and once students graduate and leave the groups, the context that encouraged heavy drinking disappears, so their drinking reduces. Options A, B, and D either shift the focus to age, general responsibility, or health realization, all of which are not specifically rooted in fraternity or sorority dynamics. Why Other Options Are Wrong: Option A generalizes about men and a particular age threshold, which is neither mentioned nor implied in the study. Option B is too broad and attributes reduced drinking solely to responsibility after graduation; it does not explain why the effect is especially noticeable among fraternity and sorority members. Option D introduces an assumption that heavy drinking itself teaches a lesson through harmful effects, which the passage does not support, and it still ignores the group based nature of the original observation. Common Pitfalls: A common mistake in such questions is to select an option that feels morally satisfying, such as the idea that students learn from harm, rather than focusing on logical fit. Another pitfall is to pick an option that is plausible in real life but not tightly connected to the specific details of the passage. Always pay attention to any special groups or conditions mentioned, like fraternities and sororities here, and prefer options that directly leverage those details. Final Answer: The most appropriate logical extension is that drinking begins as a group activity and as students leave these groups, the habit of drinking is also left behind, which corresponds to option C.

Question 17

In the following statement and conclusion question, you are given two statements relating banks, private entities, and industry. Treat the statements as true even if they conflict with common knowledge, read the conclusions, and decide which of them…

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Introduction / Context: This question belongs to the standard syllogism type where you must reason about set relationships involving banks, private entities, and industry. The statements are to be taken as logically true, and your task is to check which conclusions must hold in every possible interpretation that respects these statements. It is essential to distinguish between definite conclusions and overgeneralizations. Given Data / Assumptions: Statement (I): Some banks are private. Statement (II): All private are industry. Conclusion (I): Some banks are industry. Conclusion (II): All banks are industry. We assume the words “some” and “all” carry their usual logical meanings. Concept / Approach: The phrase “Some banks are private” indicates there is at least one bank that belongs to the subset of private entities. The second statement, “All private are industry,” means that the set of private entities is completely contained within the set of industry. We can chain these ideas: if some banks are private and all private are industry, then those particular banks are also part of industry. This directly supports a “some” type conclusion. However, we must be careful not to overextend this to “all banks.” Step-by-Step Solution: Step 1: Represent the set of industry as a large circle.Step 2: Place the private set completely inside the industry set, because all private are industry.Step 3: Place the banks set such that it overlaps the private region in at least one area, because some banks are private. It may have additional parts outside the private region, about which we know nothing.Step 4: Check conclusion (I): “Some banks are industry.” The banks that lie in the private region are also in industry, since private is inside industry. Therefore, there is at least one bank that belongs to industry. So conclusion (I) must be true in every valid diagram.Step 5: Check conclusion (II): “All banks are industry.” This would require the entire banks set to lie completely inside the industry set. The original statements, however, only restrict the private part of banks. They do not say that all banks are private or that banks have no part outside the private or industry regions. It is possible that some banks lie outside the industry set, which would still satisfy the statements. So conclusion (II) does not necessarily follow. Verification / Alternative check: Symbolically, we can express the logic as follows. From statement (I), there exists at least one object x such that x is a bank and x is private. From statement (II), for any object y, if y is private then y is industry. Combining these, for that object x, x is bank, x is private, and x is industry. Thus, there exists at least one bank that is industry, which confirms conclusion (I). However, the statements never assert that for every bank z, z is industry, so conclusion (II) cannot be guaranteed. Why Other Options Are Wrong: Option B claims that only conclusion (II) follows, ignoring the fact that (II) goes beyond the information given. Option C suggests that neither conclusion follows, which is incorrect because we have a clear chain proving conclusion (I). Option D states that both conclusions follow, but this overstates what the statements support by including the unjustified universal claim in conclusion (II). Only option A, which accepts conclusion (I) and rejects conclusion (II), aligns with rigorous logical analysis. Common Pitfalls: Students sometimes misread “Some banks are private” as “All banks are private,” which leads them to conclude “All banks are industry.” This is a classic error of replacing “some” with “all.” Another common mistake is to think that if part of a set is inside a larger set, then the whole set must also be inside, which is not true. Always pay close attention to quantifiers like “some” and “all,” as they significantly change the meaning of statements. Final Answer: Thus, the correct conclusion is that only conclusion (I) follows from the given statements.

Question 18

In this statement and conclusion question, you are given two statements relating stars, satellites, and the property of twinkling. Accept the statements as true, even if they differ from real world facts, then read the conclusions and decide which o…

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Introduction / Context: This is a basic syllogism question involving stars, satellites, and the act of twinkling. The statements describe two different sets, both fully contained within a larger conceptual set of twinkling objects. Your task is to decide which of the given conclusions necessarily follows from these statements under strict logical interpretation. Given Data / Assumptions: Statement (I): All stars twinkle. Statement (II): All satellites twinkle. Conclusion (I): Some stars are satellites. Conclusion (II): Some stars twinkle. We assume that stars exist, so “all stars twinkle” implies at least one twinkling star. Concept / Approach: Both statements are universal. “All stars twinkle” means that the set of stars is a subset of the set of twinkling objects. “All satellites twinkle” means that the set of satellites is another subset of the same set. The key question is whether these two subsets are forced to overlap and whether we can infer existence of stars that twinkle. Logical conclusions must hold in every Venn diagram that respects the statements, not just in diagrams we find intuitive. Step-by-Step Solution: Step 1: Draw a large circle representing all twinkling objects.Step 2: Place the stars set completely inside this circle, as all stars twinkle.Step 3: Place the satellites set also completely inside the twinkling circle, because all satellites twinkle.Step 4: Notice that the problem does not say anything about stars being satellites or satellites being stars. So the two subsets can be disjoint inside the twinkling set or they may overlap; both arrangements are allowed.Step 5: Evaluate conclusion (I): “Some stars are satellites.” This requires at least one object that is both a star and a satellite. However, we can construct a valid diagram where stars and satellites are two separate non-overlapping regions inside the twinkling set. In that case, no star is a satellite. Therefore conclusion (I) is not guaranteed.Step 6: Evaluate conclusion (II): “Some stars twinkle.” Since all stars twinkle and we assume there is at least one star, it follows directly that at least one star twinkles. Consequently, conclusion (II) must be true in every acceptable diagram. Verification / Alternative check: Symbolically, from statement (I), for any object x, if x is a star then x twinkles. If there exists at least one star, call it s, then s is a star and therefore s twinkles. This is exactly what conclusion (II) expresses. For conclusion (I), we would need an object that is both star and satellite, but the statements do not establish any such link. Because it is logically possible that there is no object that belongs to both groups, we cannot accept conclusion (I) as a necessary consequence. Why Other Options Are Wrong: Option A says only conclusion (I) follows, but we just saw that conclusion (I) is not forced. Option C claims that neither conclusion follows, which ignores the straightforward implication that some stars twinkle. Option D says that both conclusions follow, which again overstates what is supported by the statements by including conclusion (I). Only option B, which accepts conclusion (II) and rejects conclusion (I), is consistent with correct logical reasoning. Common Pitfalls: Many learners mistakenly assume that if two categories share a common property, such as twinkling, then they must have some elements in common. This is not true in logic: two distinct subsets can be completely disjoint yet share the same superset property. Another error is to overlook the implicit existence of stars, which supports the move from “all stars twinkle” to “some stars twinkle” in the exam context. Final Answer: Therefore, the correct conclusion is that only conclusion (II) follows from the given statements.

Question 19

In the following statement and conclusion problem, you are given two statements involving dens, spirals, and cards. Accept the statements as true, read all the conclusions carefully, and decide which of them logically follow from the information giv…

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Introduction / Context: This question examines your ability to reason about partial information using Venn style logic. The statements connect the sets “dens,” “spirals,” and “cards.” You must check each proposed conclusion to see whether it is forced by the statements, or whether there is at least one valid arrangement in which the conclusion fails. Only those conclusions that must hold in every such arrangement are said to logically follow. Given Data / Assumptions: Statement (I): All dens are spiral. Statement (II): Some spirals are cards. Conclusion (I): Some spirals are not cards. Conclusion (II): Some dens are not cards. Conclusion (III): Some cards are den. We accept the statements as true and avoid adding any extra assumptions. Concept / Approach: The first statement tells us that the set of dens is contained within the set of spirals. The second statement says that there is at least one spiral that is also a card. However, nothing is said about whether all spirals are cards or only some of them are, and nothing is directly said about dens being cards or not. To test each conclusion, we construct diagrams that satisfy the statements and see whether a conclusion can be false in any of them. Step-by-Step Solution: Step 1: Draw a large circle for spirals.Step 2: Draw the dens set completely inside the spirals circle, because all dens are spiral.Step 3: Represent cards as a separate circle that intersects the spirals circle in at least one region to account for “Some spirals are cards.” We do not yet fix the overlap with dens.Step 4: Analyse conclusion (I): “Some spirals are not cards.” This requires that there exist spirals outside the card region. But the statements allow the possibility that all spirals happen to be inside the cards set. For example, every spiral could also be a card, which still satisfies “Some spirals are cards.” Thus conclusion (I) is not necessary.Step 5: Analyse conclusion (II): “Some dens are not cards.” Dens lie inside spirals, but the statements do not say how the dens region relates to the cards region. It is possible that all dens happen to lie in the overlapping part of spirals and cards, making every den a card. In such a case, conclusion (II) would be false while the statements remain true. So conclusion (II) does not follow.Step 6: Analyse conclusion (III): “Some cards are den.” This would require at least one card that lies in the dens region. However, the overlap required by “Some spirals are cards” can occur entirely outside the dens region. For example, some spirals that are not dens may be cards. In that scenario, no card is a den, and yet both statements are still satisfied. Hence conclusion (III) also does not necessarily follow. Verification / Alternative check: We can verify by constructing explicit examples. Suppose there are spirals that are not dens and are also cards. Let all dens be spirals and let every spiral be a card. Then statements (I) and (II) are true: dens are spiral, and some spirals are cards. In this arrangement, there is no spiral that is not a card, so conclusion (I) fails. If we let all dens lie inside the overlapping region of spirals and cards, there is no den that is not a card, so conclusion (II) fails. Furthermore, if no card lies inside the dens region in a different diagram, conclusion (III) fails there while the statements still hold. Therefore none of the conclusions is forced. Why Other Options Are Wrong: Option A claims that conclusions (I) and (II) follow, but we have shown that both can be false in valid interpretations. Option B claims only conclusion (III) follows, which again is not justified by the statements. Option C asserts all three conclusions follow, which is the strongest and most incorrect claim. Only option D, which states that no conclusion follows, matches the careful analysis. Common Pitfalls: Many candidates think that once “Some spirals are cards” is given, there must also be spirals that are not cards, which is not logically necessary. Another common mistake is to assume that if a set is contained in another, it must have some portion outside the intersection with a third set. Visualising multiple possible diagrams and checking whether a conclusion must hold in all of them is essential for this type of reasoning question. Final Answer: Therefore, the correct decision is that no conclusion follows from the given statements.

Question 20

In this statement and conclusion problem, you are given information about pens, pencils, and erasers. Treat the statements as true, even if they do not look realistic, and then decide which of the given conclusions logically follow. Statements: (I) …

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Introduction / Context: This question deals with partial overlaps among three sets: pens, pencils, and erasers. The statements tell you that some pens are pencils and some pens are erasers. You must then check whether this limited information is sufficient to conclude that some pencils are also erasers or that all erasers are pens. The exercise tests whether you can avoid drawing unjustified connections from partial overlaps. Given Data / Assumptions: Statement (I): Some pens are pencils. Statement (II): Some pens are erasers. Conclusion (I): Some pencils are erasers. Conclusion (II): All erasers are pens. We accept the statements as true and do not add any extra relations. Concept / Approach: Each statement of the form “Some pens are pencils” indicates the existence of at least one object that belongs to both sets. However, these existence statements do not specify whether the same pen is both a pencil and an eraser or whether completely different pens are being referred to. Therefore, the safe way is to try to construct diagrams where the overlaps are separate. If you can find at least one arrangement that satisfies the statements but makes a conclusion false, then that conclusion does not logically follow. Step-by-Step Solution: Step 1: Draw a large set for pens.Step 2: Inside the pen set, mark a region where pens and pencils overlap, to represent “Some pens are pencils.” This region may be small and need not include all pencils or all pens.Step 3: Also inside the pen set, mark another region where pens and erasers overlap, to represent “Some pens are erasers.” Importantly, this region can be drawn disjoint from the pens that are pencils.Step 4: Analyse conclusion (I): “Some pencils are erasers.” This requires at least one object that is both a pencil and an eraser. However, we can draw the overlapping region between pens and pencils separate from the overlapping region between pens and erasers. Then there is no common element of pencils and erasers, even though both statements remain true. So conclusion (I) is not guaranteed.Step 5: Analyse conclusion (II): “All erasers are pens.” The statements only tell us that some pens are erasers. They say nothing about erasers that might lie outside the pen set. It is perfectly possible that some erasers are pens while others are not. Hence, the idea that all erasers are pens is an unjustified generalization. Verification / Alternative check: Consider a concrete example. Suppose there are three pen objects: P1, P2, and P3. Let P1 also be a pencil but not an eraser. Let P2 also be an eraser but not a pencil. Let P3 be only a pen. Further, suppose there are other erasers that are not pens at all. In this situation, “Some pens are pencils” is true because of P1, and “Some pens are erasers” is true because of P2. But there is no object that is both pencil and eraser, so conclusion (I) is false. Also, there are erasers that are not pens, so conclusion (II) is false. The statements hold, yet both conclusions fail. Why Other Options Are Wrong: Option A claims that only conclusion (I) follows, which is incorrect because we just built a valid case where no pencil is an eraser. Option B claims that only conclusion (II) follows, but we have shown erasers can exist outside the pen set. Option C claims that both conclusions follow, which is the strongest and most unjustified claim. Only option D, which states that neither conclusion follows, matches the logical analysis. Common Pitfalls: Learners often think that if one set overlaps with two other sets, those two must overlap with each other as well. This is a false intuition. A single set can intersect two other sets at different points without creating an intersection between those other sets. Another pitfall is to assume that a “Some A are B” statement eliminates the possibility of A elements outside B or B elements outside A, which it does not. Final Answer: Therefore, the correct decision is that neither conclusion (I) nor conclusion (II) follows from the given statements.

Statement and Conclusion Questions