Question 1

In this statement and conclusion reasoning question, two statements relate LED lights, bulbs, and tube lights. Accept the statements as true even if they differ from real electrical knowledge, then read the conclusions and decide which of them logic…

Accepted Answer

Introduction / Context: This problem explores logical relationships among three categories: LED, bulbs, and tube lights. The statements describe how LED items and some bulbs relate to tube lights, and the conclusions speculate about LED objects that are tube lights. The test is whether you can avoid overinterpreting limited data and correctly identify which conclusions are not forced by the statements. Given Data / Assumptions: Statement (I): All LED are bulb. Statement (II): Some bulbs are not tube light. Conclusion (I): Some tube lights are LED. Conclusion (II): All LED are tube lights. We accept the statements as true and do not add any further facts about LED or tube lights. Concept / Approach: Statement (I) tells us that the set of LED is fully contained inside the set of bulbs. Statement (II) tells us that there exist some bulbs that are not tube lights. Important point: neither statement says that any bulb is a tube light or that any tube light is a bulb, nor do they link LED directly to tube lights. Therefore, any conclusion stating a definite relation between LED and tube lights needs strong justification. We test each conclusion by seeing whether we can draw a diagram satisfying the statements while making the conclusion false. Step-by-Step Solution: Step 1: Draw a large set for bulbs.Step 2: Place the LED set completely inside the bulbs set, because all LED are bulb.Step 3: Ensure that there is a region of bulbs that lies outside the tube lights set, because some bulbs are not tube lights. This is required by statement (II).Step 4: Notice that the statements say nothing about where tube lights lie relative to the LED region. Tube lights might partially overlap with bulbs, they might overlap with none of the LED bulbs, or they might even extend beyond bulbs.Step 5: Evaluate conclusion (I): “Some tube lights are LED.” This would require at least one object in the intersection of the tube lights set and the LED set. However, we can construct a valid diagram where tube lights overlap only with non LED bulbs or do not overlap with bulbs at all. In such a picture, none of the tube lights is an LED, yet both statements remain true. So conclusion (I) is not necessary.Step 6: Evaluate conclusion (II): “All LED are tube lights.” This requires that the LED region, which lies inside bulbs, also lies completely inside the tube lights set. But statement (II) explicitly guarantees the existence of some bulbs that are not tube lights. There is no rule that these non tube light bulbs cannot be LED. We can easily let all LED bulbs be in that non tube light region. Then no LED is a tube light, and conclusion (II) fails. Since this configuration still satisfies the given statements, conclusion (II) does not follow either. Verification / Alternative check: Consider a concrete scenario. Suppose there are 10 bulbs. Two of them are LED, and none of these LED bulbs are tube lights. Among the remaining 8 bulbs, some may be tube lights, and some may not. Additionally, imagine a separate set of tube lights that are not bulbs at all, or tube lights that are bulbs but not LED. This arrangement fulfills statement (I) because all LED are bulbs. It fulfills statement (II) because there are bulbs that are not tube lights. In this setup, no tube light is LED, and not all LED are tube lights. Thus both conclusions can fail while the statements are true. Why Other Options Are Wrong: Option A claims that only conclusion (I) follows, but we provided a valid situation where no tube light is an LED. Option B claims that only conclusion (II) follows, which is even less supported because statement (II) suggests some bulbs are not tube lights, and LED could easily be among those. Option D, which says both conclusions follow, clearly contradicts the counterexample. Only option C, which states that neither conclusion follows, fits the logical analysis. Common Pitfalls: Many students see “All LED are bulb” and “Some bulbs are not tube light” and intuitively think of real world lighting fixtures, then insert additional knowledge about how LED and tube lights work in practice. Logical reasoning questions require you to ignore such outside information. Another common mistake is to jump from “no information” to “some information,” for example, assuming that if nothing is said about LED tube lights, then some must exist. Final Answer: Therefore, the correct conclusion is that neither conclusion (I) nor conclusion (II) follows from the given statements.

Question 2

In this question on statements and conclusions, you are given information about girls who are clever and hardworking. Accept the statements as true even if they seem unrealistic, then read all the conclusions carefully and decide which of them logic…

Accepted Answer

Introduction / Context: This question explores logical relationships involving girls, clever individuals, and hardworking individuals. The statements link cleverness with hard work and assert that some girls are clever. You are asked to determine which of the three possible conclusions necessarily follow from this information. The key is to use Venn style reasoning and avoid assuming more about the groups than what is stated. Given Data / Assumptions: Statement (I): Some girls are clever. Statement (II): All clever are hardworking. Conclusion (I): Some girls are not hardworking. Conclusion (II): Some girls are hardworking. Conclusion (III): Some hardworking are not girls. We accept the statements as true and do not introduce extra relationships. Concept / Approach: The two statements can be chained: some girls belong to the clever group, and every clever person belongs to the hardworking group. Therefore, those clever girls must also belong to the hardworking group. This directly supports one conclusion. However, the information does not specify anything about girls who are not clever or about hardworking individuals who are not girls. To test each conclusion, we construct possible diagrams and see whether a conclusion fails in at least one of them. Step-by-Step Solution: Step 1: Draw a large set representing hardworking individuals.Step 2: Place the clever set completely inside the hardworking set, because all clever are hardworking.Step 3: Represent the girls set so that at least some girls lie inside the clever region, capturing “Some girls are clever.” There may be other girls outside the clever region about whom nothing is said.Step 4: Evaluate conclusion (II): “Some girls are hardworking.” The girls who are clever are automatically hardworking, since all clever are hardworking. Therefore, there is at least one girl who is hardworking. Conclusion (II) must follow.Step 5: Evaluate conclusion (I): “Some girls are not hardworking.” This would require at least one girl outside the hardworking set. However, it is logically possible that all girls happen to be hardworking, with some of them clever and some not clever. The statements do not prevent that. In such a scenario, conclusion (I) would be false while statements remain true. Therefore, conclusion (I) does not necessarily follow.Step 6: Evaluate conclusion (III): “Some hardworking are not girls.” This requires at least one hardworking individual who is not a girl. But the statements allow the possibility that the only hardworking individuals are girls. For example, all clever people could be girls and all hardworking people could be exactly those clever girls. In that case, conclusion (III) fails, yet both statements are satisfied. So conclusion (III) also does not follow. Verification / Alternative check: Symbolically, from statement (I) we know there exists a person g such that g is a girl and g is clever. From statement (II), for any person x, if x is clever then x is hardworking. Putting these together, g is a girl and g is hardworking. This guarantees that some girls are hardworking, which supports conclusion (II). However, nothing in the statements guarantees the existence of a girl who is not hardworking or the existence of a hardworking individual who is not a girl. Those are possibilities, not necessities. Why Other Options Are Wrong: Option A says that conclusions (I) and (II) follow, but conclusion (I) can be false in a valid arrangement where every girl is hardworking. Option C says that conclusions (I) and (III) follow, yet we have seen that both are merely possible, not forced. Option D claims that all three conclusions follow, which is clearly incorrect because we find diagrams where two of them fail. Only option B, which accepts conclusion (II) alone, is consistent with exact logical reasoning. Common Pitfalls: Students often confuse “some” and “all,” and may think that if some girls are clever, then some girls must also be not clever, or if some people are hardworking, then some must not be girls. These are not valid inferences unless explicitly stated. Another common mistake is to import real world notions that most hardworking people are not girls or vice versa, which should be avoided in formal logic questions. Final Answer: Thus, the only conclusion that logically follows is that some girls are hardworking, corresponding to conclusion (II) and option B.

Question 3

In this statement and conclusion type question, you are given three statements about cups, plates, spoons, and the colour blue. Accept the statements as true even if they appear unrealistic, read all the conclusions carefully, and then decide which …

Accepted Answer

Introduction / Context: This question explores a slightly more complex web of relations involving cups, plates, spoons, and blue objects. You are given three statements and four candidate conclusions, and you must carefully evaluate each conclusion. The problem tests your ability to combine several set relations and to handle both “some” and “no” statements at the same time. Given Data / Assumptions: Statement (I): Some cups are plates. Statement (II): All spoons are blue. Statement (III): No plates are spoon. Conclusion (I): Some cups are not spoon. Conclusion (II): Some plates are not blue. Conclusion (III): Some cups are not blue. Conclusion (IV): Some blue are not plates. We accept the conventional exam assumption that when a universal statement like “All spoons are blue” is discussed in this context, spoons exist. Concept / Approach: The key ideas are: some cups are plates, no plate is a spoon, and all spoons are blue. From these, we can deduce information about cups that are plates and about blue objects that come from the spoons group. For each conclusion, we should either derive it directly or construct a counterexample that satisfies all statements but makes the conclusion false. Conclusions that survive this scrutiny are the ones that logically follow. Step-by-Step Solution: Step 1: From statement (I), there exists at least one object that is both a cup and a plate.Step 2: From statement (III), no plate is a spoon. Therefore, any object that is a plate cannot be a spoon.Step 3: Combine steps 1 and 2. The object that is both a cup and a plate is not a spoon, because all plates are not spoons. Hence at least one cup is not a spoon. This directly supports conclusion (I): “Some cups are not spoon.”Step 4: Examine conclusion (II): “Some plates are not blue.” We know only that no plate is a spoon and all spoons are blue. Plates could still be blue items that are not spoons. The statements do not say that plates are never blue. It is possible that every plate is blue but none is a spoon. Therefore we cannot guarantee that some plates are not blue, so conclusion (II) does not necessarily follow.Step 5: Examine conclusion (III): “Some cups are not blue.” Again, nothing in the statements restricts cups from being blue or not blue. Some cups that are plates might be blue or not blue, and cups that are not plates are completely unconstrained by the statements. It is possible that, in one valid scenario, every cup is blue. Since we can construct such a case, conclusion (III) does not logically follow.Step 6: Examine conclusion (IV): “Some blue are not plates.” From statement (II), all spoons are blue, and from statement (III), no plate is a spoon. This implies that spoons are blue objects that cannot be plates. Under the usual exam assumption that spoons actually exist, at least one spoon exists, which is blue and not a plate. Hence there is at least one blue object that is not a plate. Conclusion (IV) therefore follows. Verification / Alternative check: We can verify with a concrete model. Suppose there is one object that is both a cup and a plate, and that object is blue. Also suppose there is at least one spoon that is blue and not a plate. Further, let all plates be blue, and let all remaining cups be blue as well. In this model, all three statements hold: some cups are plates, all spoons are blue, and no plates are spoons. Check the conclusions: there is a cup that is a plate and not a spoon, so conclusion (I) holds. There is no plate that is not blue, so conclusion (II) fails. There is no cup that is not blue, so conclusion (III) fails. There is at least one spoon that is blue and not a plate, so conclusion (IV) holds. Thus only conclusions (I) and (IV) are forced by the statements. Why Other Options Are Wrong: Option A includes conclusion (III), but we have shown that it can be false in a valid arrangement. Option B and option C both include conclusion (II), which is not compelled because plates may all be blue. Option D, which claims that only conclusions (I) and (IV) follow, matches the analysis. There is no option that lists just conclusion (I), so we must rely on the careful reasoning that shows (IV) is also valid. Common Pitfalls: One common mistake is to assume that if all spoons are blue, then blue objects must be spoons, which reverses the logic. Another typical error is to think that if some cups are plates and no plates are spoons, then those cups are automatically not blue, which is not supported by the statements. Always distinguish between being restricted from being a spoon and being restricted from being blue, as they are different properties here. Final Answer: Hence, the correct decision is that only conclusions (I) and (IV) follow from the given statements.

Question 4

In this reasoning question, two statements relate clocks, watches, and alarms, followed by two conclusions. Accept the statements as true even if they do not reflect real world categories, and decide which conclusion logically follows. Statement 1: …

Accepted Answer

Introduction / Context: This is a straightforward syllogism problem about clocks, watches, and alarms. The statements describe subset relationships between clocks and watches and a partial overlap between clocks and alarms. Your goal is to determine whether each proposed conclusion necessarily follows from these relations when the statements are treated as completely true. Given Data / Assumptions: Statement 1: All clocks are watches. Statement 2: Some clocks are alarm. Conclusion I: Some alarms are watches. Conclusion II: All watches are alarm. We accept that there is at least one clock, because “some clocks are alarm” asserts existence. Concept / Approach: When we say “All clocks are watches,” we mean that the set of clocks is entirely contained within the set of watches. The second statement, “Some clocks are alarm,” means there exists at least one object that is both a clock and an alarm. By combining these facts, we can identify at least one object that is at the same time a clock, a watch, and an alarm. This clearly supports a “some” type conclusion. However, we must be careful not to overgeneralize this to “all watches.” Step-by-Step Solution: Step 1: Draw a large set for watches.Step 2: Place the clocks set entirely inside the watches set because all clocks are watches.Step 3: Represent alarms as another set that intersects the clocks set in at least one region because some clocks are alarm.Step 4: Consider conclusion I: “Some alarms are watches.” The clocks that are alarms are also watches because all clocks are watches. Therefore, at least one object that is an alarm is also a watch. So conclusion I definitely follows.Step 5: Consider conclusion II: “All watches are alarm.” This would require the entire set of watches to be inside the set of alarms. However, the statements only guarantee that some clocks (a subset of watches) are alarms. Other watches, which are not clocks, are unconstrained relative to alarms and can be non alarm watches. Hence conclusion II is not forced by the statements. Verification / Alternative check: We can verify the logic with a numerical example. Suppose there are 10 watches. Among them, 4 are clocks and 6 are wristwatches without any clock label. Out of the 4 clocks, 2 are alarms. So “All clocks are watches” holds, since all 4 clocks are among the 10 watches. “Some clocks are alarm” also holds, because 2 clocks are alarms. However, not all 10 watches are alarms; the 6 wristwatches are not alarms. In this example, conclusion I is true because those 2 alarm clocks are both alarms and watches. Conclusion II is false because many watches are not alarms. Since the statements are satisfied while conclusion II fails, conclusion II cannot be accepted as a necessary logical outcome. Why Other Options Are Wrong: Option B claims that only conclusion II follows, but we have just constructed a scenario where conclusion II is false. Option C says both conclusions follow, which again is contradicted by the counterexample. Option D claims that neither conclusion follows, ignoring the clear reasoning that some alarms are necessarily watches. Only option A, which accepts conclusion I and rejects conclusion II, is compatible with proper logical reasoning. Common Pitfalls: Students sometimes misinterpret “All clocks are watches” as “All watches are clocks,” reversing the subset relationship. This leads to the mistaken belief that if some clocks are alarms, then all watches must be alarms. Always remember that “All A are B” does not mean “All B are A.” Another pitfall is neglecting the existence information in “some” statements, which is crucial to support conclusion I. Final Answer: Thus, the logically correct result is that only conclusion I follows from the given statements.

Question 5

In this statement and conclusion reasoning question, two statements connect squares, rectangles, and triangles. Accept the statements as true even if they contradict actual geometry, then examine the conclusions and decide which of them logically fo…

Accepted Answer

Introduction / Context: This question is a logic puzzle that uses the familiar shapes squares, rectangles, and triangles in an abstract way. Even though the statements conflict with actual geometry, you must treat them as logically true for the purpose of the problem. Your task is to judge whether either of the two conclusions logically follows from these artificial relations. Given Data / Assumptions: Statement 1: No squares are rectangles. Statement 2: All rectangles are triangles. Conclusion I: Some triangles are squares. Conclusion II: Some triangles are rectangles. We focus on logical structure, not real geometric facts. Concept / Approach: The first statement says that the sets “squares” and “rectangles” are completely disjoint. The second statement says that the set of rectangles is fully contained within the set of triangles. Thus any rectangle is automatically a triangle. For the conclusions, we must see whether any intersection between triangles and squares is forced and whether we can guarantee the existence of at least one triangle that is a rectangle. Step-by-Step Solution: Step 1: Draw a large set representing triangles.Step 2: Place the rectangles set completely inside the triangles set, because all rectangles are triangles.Step 3: Place the squares set completely outside the rectangles set, because no square is a rectangle as per statement 1.Step 4: Evaluate conclusion I: “Some triangles are squares.” This requires at least one object that is both triangle and square. However, the statements do not link squares directly to triangles. Squares may or may not belong to the triangle set. It is logically possible to draw the squares set entirely outside the triangles set, making their intersection empty, while both statements remain true. Therefore conclusion I does not necessarily follow.Step 5: Evaluate conclusion II: “Some triangles are rectangles.” Statement 2, “All rectangles are triangles,” means every rectangle is also a triangle. Under typical exam conventions, we consider that rectangles exist. If at least one rectangle exists, then that rectangle is both a rectangle and a triangle, so some triangles are rectangles. Hence conclusion II follows in that standard interpretation. Verification / Alternative check: Symbolically, statement 2 can be written as rectangle implies triangle. If there exists at least one rectangle, call it r, then r is a rectangle and therefore r is a triangle. This directly satisfies conclusion II that some triangles are rectangles. Statement 1, that no square is a rectangle, does not prevent squares from being triangles or non triangles; it only says they cannot be rectangles. Since nothing forces squares to be triangles, we cannot accept conclusion I as a necessary outcome. Why Other Options Are Wrong: Option A claims that only conclusion I follows, but we have seen that squares might be placed completely outside the triangle set without violating the statements. Option C claims that both conclusions follow, which is too strong because conclusion I is not guaranteed. Option D says that neither conclusion follows, which ignores the direct implication contained in statement 2 when we assume the existence of rectangles. Only option B, which accepts conclusion II alone, is consistent with the usual reasoning conventions used in such exam questions. Common Pitfalls: One common mistake is to be influenced by real geometry, where every square is also a rectangle. Here, the question explicitly defines a different abstract relationship. Another mistake is to overlook the existence implied by the presence of a set like rectangles in such questions. While strict symbolic logic can treat a universal statement as vacuously true even for an empty set, exam questions of this type normally assume that the mentioned categories are non empty unless stated otherwise. Final Answer: Therefore, under the stated assumptions, only conclusion II follows from the given statements.

Question 6

In this logical reasoning question, two categorical statements are given followed by two conclusions I and II. You must treat the statements as logically true, even if they appear to contradict common real world facts, and then decide which conclusi…

Accepted Answer

Introduction / Context: This problem is a classic example of a syllogism based on categorical statements. We are given two statements about the relationship between bikes, two wheelers, and wheels, and then we are asked to judge which conclusion follows logically. The key idea is to ignore real world knowledge and work only with the abstract logic of sets. Visualizing the sets as circles in a Venn diagram is very helpful for such questions. Given Data / Assumptions: - Statement I: No bikes are two wheelers, so the set of bikes and the set of two wheelers are completely disjoint. - Statement II: All wheels are bikes, so the set of wheels lies entirely inside the set of bikes. - Conclusions compare the sets wheels and two wheelers using the information from the two statements. Concept / Approach: We interpret the statements in terms of set relationships. "No A are B" means A and B do not overlap at all. "All A are B" means the entire set A lies inside set B. If a third set is inside one of these sets, its relationship with the other set can be derived by transitivity of inclusion or exclusion. We then test each conclusion separately and see whether it must be true in every possible diagram that satisfies the two given statements. Step-by-Step Solution: Step 1: Represent bikes as set B, two wheelers as set T, and wheels as set W. Step 2: From Statement I, no bikes are two wheelers, so B and T do not intersect. Symbolically, B ∩ T = empty set. Step 3: From Statement II, all wheels are bikes, so W lies completely inside B. Symbolically, W ⊆ B. Step 4: Since W ⊆ B and B has no common part with T, anything inside W also cannot be in T. That means W and T are also disjoint. Step 5: Therefore, it is true that no two wheelers are wheels, so Conclusion I follows. Step 6: For Conclusion II, "All wheels are two wheelers" would require W ⊆ T, but we just deduced that W and T are disjoint, so this cannot be true in any valid diagram. Verification / Alternative check: Draw one circle for bikes and place wheels completely inside it. Draw another separate circle for two wheelers with no overlap with bikes. You will see that no element can belong to both wheels and two wheelers, so Conclusion I holds. At the same time, it is impossible that all wheels are two wheelers, which invalidates Conclusion II. Why Other Options Are Wrong: Option B claims that only Conclusion II follows, which is false because we have shown Conclusion II contradicts the diagram. Option C claims both conclusions follow, but Conclusion II does not follow. Option D says neither conclusion follows, but Conclusion I clearly follows. Option E talks of an either or situation, which is also incorrect because only Conclusion I logically follows from the given statements. Common Pitfalls: A common mistake is to rely on real world knowledge, such as the fact that in reality bikes are two wheelers. The question explicitly instructs you to ignore real world facts and trust only the given statements. Another common error is to think that if all wheels are bikes and bikes are two wheelers in real life, then both conclusions might follow. The correct approach is purely logical and set based, not factual. Final Answer: The correct option is Only conclusion I follows, because "No two wheelers are wheels" must be true, while "All wheels are two wheelers" is logically impossible under the given statements.

Question 7

In this aptitude based question, you are given two mathematical inequalities involving surds and are asked to identify which of the statements is true. You must compare the values of 2 times square root of 3 and 3 times square root of 2, and also co…

Accepted Answer

Introduction / Context: This question checks your understanding of how to compare expressions containing square roots, also called surds. Instead of approximating the values with decimals, you are expected to manipulate the expressions algebraically. Both statements involve positive quantities, so squaring is a safe and powerful method to compare their magnitudes. Mastering such comparisons is very useful in many competitive exams where calculators are not allowed. Given Data / Assumptions: - Statement I: 2 times square root of 3 is greater than 3 times square root of 2 (written as 2√3 > 3√2). - Statement II: 4 times square root of 2 is greater than 2 times square root of 8 (written as 4√2 > 2√8). - All roots are positive real numbers, and usual rules of arithmetic apply. Concept / Approach: To compare expressions like a√b and c√d, you can either square both sides or simplify the surds so that they share a common base. Squaring is valid when both sides are non negative, because if x and y are non negative, then x > y is equivalent to x^2 > y^2. For the second statement, simplifying √8 using factorization is efficient, because 8 can be written as 4 times 2 and the square root of 4 is easy to handle. Step-by-Step Solution: Step 1: Consider Statement I, 2√3 and 3√2. Both are positive, so square both expressions. Step 2: (2√3)^2 = 4 * 3 = 12. Step 3: (3√2)^2 = 9 * 2 = 18. Step 4: Since 12 is less than 18, we have 2√3 < 3√2, which means Statement I is false. Step 5: Now consider Statement II, 4√2 and 2√8. First simplify √8. Step 6: 8 = 4 * 2, so √8 = √4 * √2 = 2√2. Step 7: Substitute this back: 2√8 = 2 * 2√2 = 4√2. Step 8: Therefore 4√2 and 2√8 are exactly equal, not greater than or less than each other, so Statement II is also false. Verification / Alternative check: You can also approximate numerically to confirm. Square root of 2 is about 1.414 and square root of 3 is about 1.732. Then 2√3 is roughly 3.464 and 3√2 is roughly 4.242, so the first inequality is incorrect. For the second, once we see both sides simplify to 4√2, equality is obvious, so the strict greater than sign cannot be correct. Why Other Options Are Wrong: Option A claims only Statement I is true, which is incorrect because we just showed 2√3 is less than 3√2. Option B claims only Statement II is true, but Statement II leads to equality, not a strict inequality. Option D says both statements are true, which contradicts the analysis. Option E suggests both statements are equal, which misinterprets the situation because the first statement compares two different values and the second compares two equal values, and both comparisons are false as written. Common Pitfalls: Many students forget that they must be careful when squaring inequalities and must check that all quantities involved are non negative, which they are in this case. Another common error is to assume √8 is 8^(1/2) and then miscalculate it directly without factorizing. Memorizing that 8 = 4 * 2 and that √4 = 2 makes such problems much easier. Final Answer: The correct option is Neither I nor II, because both statements are false when the surds are compared correctly.

Question 8

In this statement and conclusion question about the Indian economy, two factual statements are given followed by two conclusions I and II. You must treat the statements as true and decide which conclusions logically follow from them.  Statement I: T…

Accepted Answer

Introduction / Context: This question is based on interpretation of economic statements and drawing logical conclusions about employment. You are told that the gross domestic product of India is growing at a reasonable rate, but job creation is not keeping pace, and that more than 20 million young Indians enter the workforce every year. You must reason about population and job demand using these facts and decide which conclusions are justified. Given Data / Assumptions: - Statement I: India's GDP is growing reasonably, but new jobs are not being created at the same pace as overall economic growth. - Statement II: Each year, more than 20 million young Indians join the workforce and start seeking jobs. - Conclusion I: The increase in population, at least in terms of new job seekers, is more than the rate of job creation. - Conclusion II: The job market has a smaller supply of jobs and a very large demand from job seekers. Concept / Approach: In statement and conclusion questions, we focus on what must logically follow, not on what might be true by outside knowledge. Here, we compare inflow of job seekers with the pace of job creation. If every year huge numbers of workers enter the job market, and the job creation rate is slower than that inflow, we can infer that demand for jobs exceeds the supply of jobs. We also interpret population increase, in the context of the question, as the increase in the number of people who are ready to work. Step-by-Step Solution: Step 1: From Statement I, we know that economic growth is reasonable but job creation lags behind. This implies that jobs are not being created fast enough compared to some relevant benchmark. Step 2: From Statement II, we know that every year more than 20 million young people join the workforce, which means that there is a very large and continuous inflow of job seekers. Step 3: Combine both statements. If a very large number of new workers appear each year and job creation is not growing at the same pace, the number of job seekers must grow faster than the number of available jobs. Step 4: Therefore, the population of job seekers, or the relevant part of population, increases faster than job creation. This supports Conclusion I. Step 5: The same reasoning shows that demand for jobs (job seekers) is very high, while the supply of jobs is relatively limited. This is exactly what Conclusion II states, so Conclusion II also follows. Verification / Alternative check: Imagine a simple model where every year 20 million new job seekers enter, but only, for example, 10 million new jobs are added. Over time, the backlog of job seekers will grow. The question does not specify exact numbers, but the phrase "not picking up the similar pace" implies job creation is slower than the growth of the workforce. This validates both conclusions as natural and necessary interpretations of the data provided. Why Other Options Are Wrong: Option A says only Conclusion II follows, but we have seen that Conclusion I is also supported because the increase in workforce outstrips job creation. Option C says neither conclusion follows, which ignores the clear mismatch between job inflow and job creation. Option D says only Conclusion I follows, but that would ignore the direct implication about demand and supply of jobs which is clearly captured by Conclusion II. Option E says they are only possible but not certain, but the wording of the statements makes the imbalance in job market quite explicit, so both conclusions do follow logically. Common Pitfalls: A typical mistake is to confuse economic growth rate with job growth rate. The question clearly separates them and states that job creation is slower. Another error is to think that population growth must refer to the entire population, including children and elderly, but within the context of employment, the relevant population is the working age group entering the workforce. Using this focused interpretation helps answer correctly. Final Answer: The correct option is Conclusion I and II both follow, because the statements together show that workforce growth exceeds job creation and that demand for jobs is much higher than the supply of jobs.

Question 9

In this syllogism based logical reasoning question, two statements about matchboxes, lighters, and fire are given, followed by two conclusions I and II. You must assume the statements are logically true, even if they do not match real world facts, a…

Accepted Answer

Introduction / Context: This question tests basic understanding of categorical logic using the standard structure of statements and conclusions. We are given relationships between three sets: matchboxes, lighters, and fire. The task is to see what must be true based only on the given statements. Such questions are often solved using Venn diagrams that represent each category as a circle and then checking whether a conclusion always holds. Given Data / Assumptions: - Statement I: All matchboxes are lighters, so the set of matchboxes lies completely inside the set of lighters. - Statement II: Some fire is made using matchboxes, meaning there is at least one case that belongs to both the set fire and the set matchboxes. - From Statement I and II combined, that same element of matchboxes and fire must also belong to lighters. - Conclusion I says that no lighters are related to fire, and Conclusion II says that all fire is caused by lighters. Concept / Approach: Translate the statements into set language. "All matchboxes are lighters" means matchbox set is a subset of lighter set. "Some fire are matchboxes" means the intersection of fire and matchbox sets is non empty. Using these relationships, we can infer how fire and lighters are connected. Then we check each conclusion: a universal negative like "no lighters are fire" and a universal positive like "all fire are lighters" must be tested against all possible configurations that satisfy the statements. Step-by-Step Solution: Step 1: Let M represent matchboxes, L represent lighters, and F represent fire. Step 2: From Statement I, M ⊆ L. This means that every matchbox is also a lighter. Step 3: From Statement II, some F are M, which means there exists at least one element that is both in F and in M. Symbolically, F ∩ M is non empty. Step 4: Because M is a subset of L, any element that is in M must also be in L. Therefore, the element that lies in F ∩ M also lies in L. Step 5: This means that there is at least one element that belongs to both fire and lighters, so the sets F and L do intersect. Step 6: Conclusion I says "No lighters are fire," which would mean F ∩ L is empty. This contradicts Step 5, so Conclusion I is false. Step 7: For Conclusion II, "All fire are lighters" would mean F ⊆ L. However, we only know that some fire comes from matchboxes and therefore from lighters. There could be other sources of fire that are not lighters at all, so we cannot say that all fire is within the set of lighters. Verification / Alternative check: If you draw a Venn diagram, place M entirely inside L and then mark some overlap between M and F. It is clear from the picture that L and F must intersect at least where M lies. This refutes Conclusion I. At the same time, nothing forces the rest of F to lie inside L, so F could extend outside L, which refutes Conclusion II as a universal statement. Why Other Options Are Wrong: Option A says only Conclusion I follows, but we have shown that Conclusion I is contradicted by the diagram. Option B says only Conclusion II follows, but there is no guarantee that every fire event comes through a lighter. Option C claims both follow, which is impossible given the direct contradiction. Option E suggests an exclusive or, but neither conclusion follows, so it is also incorrect. Common Pitfalls: A tricky point is that students sometimes confuse "some" with "all." Knowing that some fire events involve lighters does not imply every fire involves lighters. Another common error is to misinterpret the universal negative "no lighters are fire" when we clearly have an example where fire, matchbox, and lighter overlap. Always check for the existence of at least one element in the intersection when evaluating such conclusions. Final Answer: The correct option is Neither conclusion I nor conclusion II follows, because the statements guarantee that some fire involves lighters, but they neither support a universal negative nor a universal positive relationship between fire and lighters.

Question 10

In this logical reasoning problem, two statements about drinks, food, and eatables are given. You must treat the statements as true and decide which of the two conclusions logically follows.  Statement 1: All drinks are food. Statement 2: No eatable…

Accepted Answer

Introduction / Context: This is a typical syllogism question involving three categories: drinks, food, and eatables. You are given two categorical statements that describe how these sets are related. The task is to test each conclusion against all possible Venn diagrams that satisfy the statements and identify which conclusions must be true. The key is to remember that we cannot assume any relationship that is not explicitly forced by the statements. Given Data / Assumptions: - Statement 1: All drinks are food, which means the set of drinks lies entirely inside the set of food. - Statement 2: No eatables are drinks, which means the sets eatables and drinks are completely disjoint. - Conclusion I: Some food are eatables, claiming there is overlap between food and eatables. - Conclusion II: Some eatables are food, which is essentially the same overlap stated from the eatables side. Concept / Approach: In set notation, "All drinks are food" is represented as D ⊆ F, and "No eatables are drinks" is E ∩ D = empty set. The conclusions both assert that E ∩ F is non empty. To see whether this must be true, we check if the given statements force any overlap between eatables and food. If we can construct at least one valid diagram where eatables and food do not overlap, then the conclusions are not logically guaranteed to follow. Step-by-Step Solution: Step 1: Draw a large circle for food, labeled F. Step 2: Draw a smaller circle for drinks, labeled D, completely inside the food circle to represent D ⊆ F. Step 3: Now add the set eatables, labeled E, such that it has no overlap with drinks, because Statement 2 says E ∩ D = empty set. Step 4: Nothing in the statements forces E to overlap with F. E could be drawn completely outside F, or it could partly overlap F, and both possibilities would satisfy the statements. Step 5: Since there is at least one valid configuration where E and F do not intersect at all, the statement "Some food are eatables" in Conclusion I is not necessarily true. Step 6: By the same reasoning, "Some eatables are food" in Conclusion II is also not guaranteed because the overlap between E and F is not forced by the given information. Verification / Alternative check: To verify, construct two diagrams. In Diagram A, let E partially overlap F and avoid D. In this case both conclusions are true. In Diagram B, place E entirely outside of F and still avoid D. Here both conclusions are false, but both diagrams satisfy the original two statements. Because the conclusions are not true in every valid diagram, they do not logically follow. Why Other Options Are Wrong: Options A and B each assume that one of the conclusions is forced by the statements, but as shown, we can create a diagram where there is no overlap between food and eatables, which makes both conclusions false in that scenario. Option C, which says both follow, is even stronger and therefore cannot be correct. Option E suggests that exactly one of the two must follow, but we have seen that in some configurations neither follows, so this is also incorrect. Common Pitfalls: A common misconception is to assume that "eatables" is simply another word for "food" and to merge the sets in your mind. In logical reasoning, however, each term represents a separate set unless explicitly equated by a statement. You must not import real world meanings that are not backed by the given statements. Always rely purely on the logical structure and the constraints they impose on the Venn diagram. Final Answer: The correct option is Neither I nor II follows, because nothing in the statements forces any overlap between food and eatables, so both conclusions are not logically guaranteed.

Question 11

In this logical reasoning question, two statements describe the relationship between books, diaries, and paper. You must treat the statements as true and decide which of the conclusions I and II logically follows.  Statement 1: Some books are diarie…

Accepted Answer

Introduction / Context: This question is another example of a categorical syllogism involving three sets: books, diaries, and paper. By interpreting the statements in terms of set relationships, we can see what must be true about diaries and paper. The problem checks whether you can distinguish between a conclusion that is logically forced and a conclusion that is only partially supported or completely unsupported. Given Data / Assumptions: - Statement 1: Some books are diaries. This means there is at least one element that belongs to both the set of books and the set of diaries. - Statement 2: All books are paper. This means the set of books lies entirely inside the set of paper. - Conclusion I: All diaries are paper, which claims every diary belongs to the set of paper. - Conclusion II: Some paper are diaries, which claims that there is at least one element common to the sets paper and diaries. Concept / Approach: We use basic set logic. If some books are diaries and all books are paper, the part of books that overlaps diaries must also belong to paper. From this, we can infer that at least one diary is paper. However, to say that all diaries are paper, we would need additional information that every diary is also a book or is otherwise linked to paper, which we do not have. The key is to move carefully from "some" relationships to "all" relationships only when fully justified. Step-by-Step Solution: Step 1: Let B represent books, D represent diaries, and P represent paper. Step 2: From Statement 1, we know that B ∩ D is non empty. There exists at least one element that is both a book and a diary. Step 3: From Statement 2, we know B ⊆ P. Every book is paper. Step 4: The element that lies in B ∩ D must also lie in P because it is a book and all books are paper. Step 5: Therefore, there exists at least one element that belongs to both P and D. This proves that some paper are diaries, so Conclusion II is true. Step 6: However, we have no information about diaries that are not books. Diaries could include many items that are not books at all, and we do not know whether such diaries are made of paper or not. Step 7: Since only some diaries are books and thus paper, we cannot infer that all diaries are paper. Therefore, Conclusion I does not follow. Verification / Alternative check: Visualize this with a Venn diagram. Draw P as a large circle, B inside P, and D overlapping B only partially. The overlapping part shows diaries that are also books and therefore paper. The remaining part of D could lie outside P, representing diaries that are not paper. Such a diagram satisfies both statements but makes Conclusion I false while keeping Conclusion II true, confirming our analysis. Why Other Options Are Wrong: Option A says only Conclusion I follows, but we just saw Conclusion I is not forced by the statements. Option C says both conclusions follow, which is too strong because Conclusion I does not necessarily hold. Option D says neither follows, but Conclusion II clearly does follow from the overlap. Option E claims that exactly one follows without specifying, but the correct specific combination is that only Conclusion II follows, which is captured by Option B. Common Pitfalls: A frequent mistake is to jump from "some books are diaries" and "all books are paper" directly to "all diaries are paper," which is an over generalization. The word "some" is crucial. It indicates that only a part of diaries is guaranteed to be books and therefore paper, not the entire set of diaries. Always treat "some" as at least one but not necessarily all. Final Answer: The correct option is Only conclusion II follows, because we can be sure that some paper are diaries, but we cannot claim that every diary is made of paper based on the given statements.

Question 12

In this statement and conclusion question about retail shops and customer behaviour, two statements are given. You must treat the statements as true and decide which of the conclusions I and II logically follow from them.  Statement I: Retail shops …

Accepted Answer

Introduction / Context: This question tests your ability to draw logical conclusions from a small business oriented scenario. You are told that retail shops care about retaining potential buyers and that a fixed percentage of customers are lost due to products being out of stock. Based on this, you must decide whether specific reasons for stockouts can be inferred and whether retailers desire maximum conversion of visitors into buyers. Given Data / Assumptions: - Statement I: Retail shops want to retain potential buyers, which indicates a general desire to convert visitors into paying customers and reduce lost sales. - Statement II: Ten percent of customers are lost because certain products are out of stock. - Conclusion I: Customers fail to find their size or preferred colour and therefore leave without buying anything. - Conclusion II: Retailers want as many people as possible who enter the shop to end up purchasing something, so they seek maximum conversion of footfall into sales. Concept / Approach: We must distinguish between what is definitely implied by a statement and what is just one possible explanation. Statement II mentions out of stock products but does not specify whether the problem is size, colour, or some other attribute. Therefore, any conclusion that specifies a particular type of stock problem goes beyond the data. Meanwhile, Statement I directly supports the idea that retailers want higher conversion of visitors into buyers, which is essentially what Conclusion II states. Step-by-Step Solution: Step 1: Interpret Statement I. If retail shops want to retain potential buyers, they want visitors who enter the shop to stay and eventually purchase instead of leaving without buying. Step 2: This desire to retain potential buyers is the same as wanting a high conversion rate from footfall to sales, which is the core idea of Conclusion II. Step 3: Interpret Statement II. Ten percent of customers are lost due to out of stock products. This tells us that some items that customers want are not available, but it does not specify exactly what aspect is missing. Step 4: Conclusion I specifies that customers do not find their size or preferred colour. However, Statement II only says that products are out of stock, which can be due to many reasons, such as the entire item being unavailable, wrong model, or even a discontinued product. Step 5: Because Statement II does not restrict the unavailability to size or colour alone, Conclusion I is only one possible explanation, not a logically necessary conclusion. Step 6: On the other hand, Conclusion II is a direct restatement of the motivation in Statement I. If shops want to retain potential buyers, they naturally want maximum footfall to convert into purchases. Verification / Alternative check: Consider whether it is possible that customers are lost due to out of stock products of a different nature, such as lack of a particular brand or model, rather than size or colour. This is clearly possible and still consistent with Statement II, which shows that Conclusion I is not forced. However, it is hard to imagine a shop that wants to retain potential buyers but does not want maximum conversion of visitors into purchasers, so Conclusion II is strongly supported by the basic business logic expressed in Statement I. Why Other Options Are Wrong: Option B says both conclusions follow, but Conclusion I adds specific details not given in the statements. Option C says neither follows, ignoring the direct link between Statement I and Conclusion II. Option D says only Conclusion I follows, which is incorrect because Conclusion I relies on an extra assumption. Option E is incorrect because Conclusion II is very clearly supported, so it is not doubtful at all. Common Pitfalls: A common mistake is to treat a likely explanation as a logically certain conclusion. Exam questions of this type require conclusions that are necessarily true, not just plausible. Always ask yourself whether you can construct a scenario that satisfies the statements but makes the proposed conclusion false. If you can, then the conclusion does not follow logically. Final Answer: The correct option is Only conclusion II follows, because it directly reflects the intention of retail shops to convert as many visitors as possible into buyers, while Conclusion I adds unnecessary and unsupported details about size and colour.

Question 13

In this statement and conclusion question about school children and handwriting, two statements are given about when children start using pens and why ink pens are prescribed. You must treat these statements as true and decide which conclusions logi…

Accepted Answer

Introduction / Context: This question focuses on reasoning from everyday school related statements about when children start using pens and why schools recommend ink pens. You must analyze which conclusions are justified by the information. One conclusion is about the capability of children up to fifth standard, and the other is about the benefits of ink pens for handwriting and comfort. Given Data / Assumptions: - Statement I: Children start writing with a pen in sixth standard according to school practice. - Statement II: Most schools prescribe ink pens for children because ink pens maintain handwriting quality and provide comfort to the child while writing. - Conclusion I: Children up to fifth standard are completely unable to use a pen on their own. - Conclusion II: Ink pens provide a proper flow of ink on paper and make it easier to put words on paper with less effort. Concept / Approach: We must identify what is explicitly stated versus what is an overreach. Starting to use a pen in sixth standard is a matter of school policy or practice and does not tell us that students earlier are incapable of using pens. On the other hand, the second statement directly links ink pens with better handwriting and comfort, which implies smooth flow and less effort. We base our evaluation of the conclusions strictly on these logical implications. Step-by-Step Solution: Step 1: Interpret Statement I as a policy decision. Schools decide that children will officially start writing with pens in sixth standard. Step 2: This decision does not state anything about the physical or mental capability of children in fifth standard or lower. It only tells us what is allowed or prescribed at school. Step 3: Therefore, saying that children are completely unable to use pens before sixth standard, as in Conclusion I, is an unjustified extrapolation. Many children could possibly use pens earlier, but the school may not allow it. Step 4: Now interpret Statement II, which says ink pens are prescribed because they maintain handwriting and comfort. Comfort in writing usually comes from smooth ink flow and reduced pressure on the pen, which in turn makes writing easier. Step 5: Conclusion II rephrases this idea by stating that ink pens maintain a proper flow of ink and reduce effort to put words on paper. This is in line with the reason given in Statement II and can be accepted as a logical elaboration. Step 6: Thus, only Conclusion II is a valid interpretation that follows from the given statements, while Conclusion I introduces an absolute claim about inability that is not supported. Verification / Alternative check: Imagine a school where pencils are used until fifth standard even though children are capable of using pens earlier. The policy exists for clarity or neatness, not because of inability. Such a scenario satisfies Statement I but makes Conclusion I false. However, in any scenario where ink pens are prescribed for handwriting and comfort, it remains reasonable that the ink flow is smoother and that writing requires less effort, so Conclusion II continues to hold as a logical restatement of the reason behind the prescription. Why Other Options Are Wrong: Option B says both conclusions follow, which is incorrect because Conclusion I clearly does not. Option C claims neither conclusion follows and ignores the link between Statement II and Conclusion II. Option D says only Conclusion I follows, which reverses the correct evaluation. Option E is not precise enough; the exact correct choice is that only Conclusion II follows, which is captured by Option A. Common Pitfalls: Students sometimes read policy statements as if they were statements about ability. Just because a school permits or forbids something at a certain class level does not imply that students are incapable before that level. Another pitfall is to ignore the cause and effect relation in Statement II and treat it as a mere formality, when it actually explains why ink pens are preferred, which directly supports Conclusion II. Final Answer: The correct option is Only conclusion II follows, because the benefit of ink pens for smooth writing and comfort is directly supported by the given statements, while the claim about inability before sixth standard is not.

Question 14

In this logical reasoning question, two statements describe the relationship between bolts, nails, and screws. You must regard the statements as true and determine which of the conclusions I and II logically follow.  Statement I: All bolts are nails…

Accepted Answer

Introduction / Context: This question involves three related objects from the hardware domain: bolts, nails, and screws. Although they are familiar physical items, you must ignore real world details and focus purely on the logical relationships described by the statements. The goal is to check whether the conclusions about all nails and all screws are justified by the given information. Given Data / Assumptions: - Statement I: All bolts are nails, so the set of bolts lies entirely inside the set of nails. - Statement II: Some screws are bolts, meaning at least one element is both a screw and a bolt. - Conclusion I: All nails are screws, which claims the entire nail set is inside the screw set. - Conclusion II: All screws are nails, which claims the entire screw set is inside the nail set. Concept / Approach: Use set notation and Venn diagrams. Let B represent bolts, N represent nails, and S represent screws. From Statement I we get B ⊆ N. From Statement II we know S ∩ B is non empty. That means there are some screws that belong to N by virtue of being bolts. However, having some overlap is very different from saying that all elements of one set are inside another. We carefully test both universal conclusions against this structure. Step-by-Step Solution: Step 1: From B ⊆ N, every bolt is a nail. So if an object is in set B, it is automatically in set N. Step 2: From S ∩ B being non empty, some screws are bolts. These particular screws are in both S and B. Step 3: Since all bolts are nails, these screws that are bolts must also belong to N. So some screws are nails. Step 4: However, nothing is said about screws that are not bolts. There could be many screws that are outside B and therefore might or might not be nails. Step 5: Because we do not know whether every nail is a screw, the statement "All nails are screws" in Conclusion I is not forced by the information. Nails could include many items that are not screws. Step 6: Similarly, we do not know whether every screw is inside N. We only know about some screws that are bolts, but other screws could be outside both B and N. Thus, we cannot conclude that "All screws are nails" as claimed in Conclusion II. Verification / Alternative check: Draw N as a large circle. Inside N draw a smaller circle B for bolts. Now draw S so that it intersects B in at least one region but extends outside N as well. This satisfies both statements because some screws are bolts and all bolts are nails. In this picture, clearly not all nails are screws and not all screws are nails, which shows that both conclusions are false in at least one valid configuration. Why Other Options Are Wrong: Option A assumes that all nails are screws, which is not supported. Option B assumes all screws are nails, which again is not supported. Option C claims both conclusions follow, which is stronger and therefore even further from the truth. Option E suggests that some screws are nails, which is true, but it does not match the exact requirement of the question, which focuses only on the given conclusions I and II. The correct answer must address those specific conclusions. Common Pitfalls: A common error is to overlook the word "some" in Statement II and mentally replace it with "all." This leads to the mistaken impression that all screws are bolts, and thus all screws are nails. Another trap is to read too much symmetry into the sets and assume that because one set is inside another, the reverse might also hold. Always treat "all," "some," and "no" very carefully, as they carry precise logical meaning. Final Answer: The correct option is Neither conclusion I nor conclusion II follows, because the statements only guarantee that some screws are nails through bolts, and nothing more general is logically forced.

Question 15

In this logical reasoning question involving money, two statements relate notes, coins, and currency. You must regard the statements as true and decide which of the conclusions I and II logically follow.  Statement I: Some notes are coins. Statement…

Accepted Answer

Introduction / Context: This problem uses familiar money related terms to frame a categorical logic question, but as always, you must ignore real world banking details and focus purely on the logical structure. There are three sets: notes, coins, and currency. The statements describe how notes relate to coins and currency, and the conclusions propose possible relationships between coins and currency. Your goal is to see what must be true in every scenario that satisfies the statements. Given Data / Assumptions: - Statement I: Some notes are coins, meaning there is at least one item that is both a note and a coin. - Statement II: All notes are currency, meaning the set of notes lies entirely inside the set of currency. - Conclusion I: No coins are currency, which states that coins and currency are completely disjoint sets. - Conclusion II: Some currency are coins, which claims that there is at least one element common to both currency and coins. Concept / Approach: We translate everything into set relationships. Let N be the set of notes, C be the set of coins, and R be the set of currency. Statement I gives N ∩ C is non empty. Statement II gives N ⊆ R. From these, we can deduce information about the intersection of C and R. Then we check if each conclusion is logically consistent with these relations. A conclusion is valid only if it holds in every possible configuration that respects the given statements. Step-by-Step Solution: Step 1: Because some notes are coins, there exists at least one element x such that x ∈ N and x ∈ C. Step 2: Since all notes are currency, if an element is in N, then it must also be in R. So x ∈ N implies x ∈ R. Step 3: Therefore, x belongs to N, C, and R simultaneously. Hence x is in C ∩ R, which proves that the intersection of coins and currency is non empty. Step 4: This directly supports Conclusion II, which states that some currency are coins. Step 5: Conclusion I says that no coins are currency, meaning C ∩ R is empty. However, we have just shown that at least one element belongs to both sets. Step 6: Therefore Conclusion I contradicts the information in the statements and cannot be true in any configuration that satisfies them. Verification / Alternative check: Draw a circle N for notes inside a larger circle R for currency. Then mark a region where N overlaps with another circle C for coins. That overlapping region is notes that are also coins and therefore also currency. In this diagram, C and R clearly intersect, which makes Conclusion II true. But you cannot draw any valid diagram satisfying both statements where C and R do not intersect, so Conclusion I must always be false. Why Other Options Are Wrong: Option A chooses Conclusion I, which we have shown contradicts the statements. Option C says both conclusions follow, but they are mutually inconsistent because one says no intersection and the other says some intersection. Option D says neither follows, which ignores the firm deduction that some currency must be coins. Option E is incorrect because coins and currency are not independent; they definitely intersect due to the overlapping notes. Common Pitfalls: Some students are misled by the everyday idea that notes and coins are separate forms of money and may think of them as disjoint. However, the question explicitly tells you that some notes are coins, so you must abandon real life intuition. Always work from the statements themselves, and remember that "some" indicates at least one common element in the intersection. Final Answer: The correct option is Only conclusion II follows, because the statements guarantee that some currency items are also coins, while the claim that no coins are currency directly contradicts the given information.

Question 16

In this statement and conclusion question about dawn, day, and night, two statements are given. You must take the statements as true and decide which of the conclusions I and II logically follow.  Statement 1: All dawn is day. Statement 2: No day is…

Accepted Answer

Introduction / Context: This question uses everyday time related words dawn, day, and night in a purely logical setting. The aim is to determine which conclusions about their relationships must follow from the given statements. Even though you might have intuitive ideas about how dawn, day, and night relate in real life, you must base your reasoning strictly on the logical content of the statements. Given Data / Assumptions: - Statement 1: All dawn is day, meaning the set representing dawn lies entirely inside the set representing day. - Statement 2: No day is night, meaning the sets day and night are completely disjoint. - Conclusion I: No night is day, which is the converse of Statement 2 but logically equivalent in this context. - Conclusion II: Some dawn is night, claiming that dawn and night have at least one common element. Concept / Approach: We treat the terms as sets: Dd for dawn, D for day, and N for night. From Statement 1 we get Dd ⊆ D. From Statement 2 we get D ∩ N = empty set. Two things follow: anything that is dawn is also day, and nothing that is day can be night. We then check each conclusion. Conclusion I restates the non overlap between day and night from the perspective of night, while Conclusion II claims an overlap between dawn and night that appears to contradict the earlier information. Step-by-Step Solution: Step 1: Because all dawn is day, if an element belongs to Dd, it automatically belongs to D. Step 2: Statement 2 says that no element can belong to both D and N. So D and N are disjoint sets. Step 3: Conclusion I, "No night is day," is a symmetric restatement of Statement 2. If no day is night, then no night is day because the intersection of D and N is empty from both sides. Step 4: Therefore, Conclusion I follows directly and is logically valid. Step 5: Now check Conclusion II, "Some dawn is night." Any dawn element is also in D because Dd ⊆ D. Step 6: Since D and N have no common element, it is impossible for a dawn element, which is within D, to also be in N. Step 7: Therefore, the intersection of dawn and night must be empty, and Conclusion II is false. Verification / Alternative check: Draw D as a large circle, N as another circle that does not overlap D at all, and Dd as a smaller circle entirely inside D. Because D and N do not intersect, no part of Dd can intersect N. This diagram clearly supports Conclusion I and directly contradicts Conclusion II. There is no way to draw the sets differently without breaking the original statements, which confirms our evaluation. Why Other Options Are Wrong: Option B says only Conclusion II follows, but Conclusion II cannot possibly be true given that day and night do not overlap. Option C claims both conclusions follow, which would require dawn to overlap night even though dawn is inside day and day does not intersect night. Option D says neither follows, which ignores the fact that Conclusion I is logically equivalent to Statement 2. Option E suggests a mutually exclusive situation where exactly one of the two follows but does not identify which; the precise correct option is that only Conclusion I follows, which is given by Option A. Common Pitfalls: One common mistake is to rely too much on real life images of dawn being a transition between night and day, and then assume some overlap with night. However, the statements in this problem define dawn as completely contained within day, and they separate day entirely from night. Logical questions often redefine familiar words in ways that do not match real life, so always follow the given statements, not your intuition. Final Answer: The correct option is Only conclusion I follows, because "No night is day" is logically equivalent to "No day is night," while any overlap between dawn and night is directly ruled out by the given statements.

Question 17

In this statement and conclusion question, two statements describe the relationship among games, sports, and exercise. You must treat the statements as true and decide which of the conclusions I and II logically follow.  Statement I: Some games are …

Accepted Answer

Introduction / Context: This is another categorical reasoning question with three sets: games, sports, and exercise. The statements talk about some overlap between games and sports and a complete separation between games and exercise. The conclusions attempt to connect sports to exercise. Your task is to see whether such connections are logically required by the given information. Given Data / Assumptions: - Statement I: Some games are sports, meaning there is at least one activity that is both a game and a sport. - Statement II: No exercise is a game, meaning sets exercise and games do not overlap. - Conclusion I: All sports are exercise, claiming that sports set lies inside exercise set. - Conclusion II: Some exercise are sports, claiming there is at least one element common to exercise and sports. Concept / Approach: Let G represent games, S represent sports, and E represent exercise. We know that the intersection G ∩ S is non empty, and that E ∩ G is empty. However, no statement links sports directly to exercise. The question is whether, despite this lack of direct connection, either of the conclusions is forced. In set theory terms, we must decide if S ⊆ E is required or if E ∩ S is required to be non empty, given only the two statements. Step-by-Step Solution: Step 1: Since some games are sports, draw a Venn diagram where G and S intersect in at least one region. Step 2: Since no exercise is a game, draw E as a set that does not intersect G at all. Step 3: Note that there is no restriction on how E relates to S, except that E cannot intersect any part of S that lies within G, because that part also belongs to G and E is disjoint from G. Step 4: To test Conclusion I, "All sports are exercise," we would need every element of S to be inside E. However, nothing in the statements imposes this requirement. Step 5: In fact, we already know that at least some S elements lie within G because G ∩ S is non empty. Those elements cannot be in E since E does not intersect G, so S cannot be fully contained in E. Step 6: Therefore, Conclusion I is false because some sports that are also games cannot be exercises. Step 7: For Conclusion II, "Some exercise are sports," we would need E ∩ S to be non empty. But this is also not forced. We could draw E completely outside S and G, creating a valid diagram where exercise has no overlap with sports at all. Step 8: Since the statements allow both overlap and no overlap between E and S, we cannot say that some exercise must be sports. Verification / Alternative check: Construct two diagrams that satisfy the statements. In Diagram A, let some sports be games, and let exercise lie completely outside both games and sports. In this case, both conclusions about exercise and sports are false. In Diagram B, let exercise overlap with a part of sports that does not overlap games. Here Conclusion II becomes true, but Conclusion I is still false. The fact that different diagrams lead to different truth values for Conclusion II shows that it is not logically forced by the statements. Why Other Options Are Wrong: Option A assumes all sports are exercise, which conflicts with the existence of sports that are also games and cannot be exercises. Option B assumes some exercise are sports, which is not guaranteed. Option C claims both conclusions follow, which is even further from the truth. Option E introduces an additional claim about sports being neither games nor exercise, which may or may not be true and is not asked in the question. Common Pitfalls: Students often mistakenly assume that sports must automatically count as exercise and that exercise must have some relation to sports. However, logical reasoning questions treat these as abstract sets with no inherent real world overlap unless explicitly stated. Always base your reasoning solely on the given statements and what they force in the Venn diagram, not on common sense about physical activities. Final Answer: The correct option is Neither conclusion I nor conclusion II follows, because the statements do not establish any necessary relationship between sports and exercise beyond the restriction involving games.

Question 18

In this statement and conclusion question about determination and goal setting, two statements are given. You must treat them as true and decide which of the conclusions I and II logically follow.  Statement I: Determination is the key to success. I…

Accepted Answer

Introduction / Context: This problem explores logical reasoning in the context of motivation, determination, and planning. Two statements describe the power of determination and the importance of prioritizing goals. You must use these statements to judge whether the given conclusions about success with multiple goals are logically supported. Given Data / Assumptions: - Statement I: Determination is the key to success, and if a person firmly decides to achieve a goal, no one can stop that person from achieving it. - Statement II: Prioritizing different determined goals is an important part of decision making. - Conclusion I: If someone aims for three goals, energy will be divided so much that success becomes impossible. - Conclusion II: Making a prior plan for those three goals can help the person move closer to all of them. Concept / Approach: The first statement emphasizes that determination leads to success, not failure. The second statement emphasizes planning and prioritization. A conclusion that directly denies the possibility of success when multiple goals exist clashes with the basic spirit of Statement I. On the other hand, a conclusion that highlights the usefulness of planning for multiple goals fits naturally with Statement II. Step-by-Step Solution: Step 1: From Statement I, if a person is determined about a goal, that determination acts as a strong driving force towards success. Step 2: Statement I does not say that determination becomes ineffective when there is more than one goal; it only states that determination is key for success with goals in general. Step 3: Statement II explains that when there are many goals, prioritization and planning become important decision making tools. Step 4: Conclusion I states that if a person works toward three goals, energy is divided into three parts and success can never be achieved. Step 5: This directly contradicts Statement I, which says that determination can overcome obstacles and lead to success. There is no mention that multiple goals automatically make success impossible. Step 6: Therefore, Conclusion I does not follow; it is more pessimistic than the statements support. Step 7: Conclusion II says that making a prior plan for three goals can help the person move closer to all of them. This is consistent with Statement II, which stresses the importance of prioritizing and planning for determined goals. Step 8: Planning and prioritization are natural strategies to manage multiple goals, so Conclusion II is a reasonable and logical outcome of the given statements. Verification / Alternative check: Consider a person with three goals, each approached with strong determination. According to Statement I, determination is key to success; there is no restriction on the number of goals. Now add Statement II, which suggests prioritizing and planning. Combining both, we expect that with determination plus proper planning, the person can progress significantly on all three goals. This supports Conclusion II. However, claiming that success is impossible simply because energy is divided ignores the positive role of determination and planning described in the statements. Why Other Options Are Wrong: Option B says both conclusions follow, but Conclusion I clearly conflicts with the idea that determination leads to success. Option C says neither follows, which wrongly rejects Conclusion II even though it is directly supported by the emphasis on prioritizing goals. Option D chooses only Conclusion I, ignoring that this conclusion is contrary to the text. Option E suggests that Conclusion II is not logically forced, but it naturally flows from the combination of determination and planning highlighted in the statements. Common Pitfalls: One common error is to interpret multiple goals as inherently negative, leading to assumptions that energy gets diluted and success becomes impossible. While this may be a personal belief, the statements in the problem emphasize determination and effective planning, not failure. Always align your conclusions with the tone and content of the given statements rather than personal opinions about having many goals. Final Answer: The correct option is Only conclusion II follows, because effective planning and prioritization of multiple determined goals are directly supported, while an absolute claim of failure is not.

Question 19

In this statement and conclusion question about children playing outdoors, two statements are given. You must treat the statements as true and decide which of the conclusions I and II logically follow from them.  Statement I: Children play in the pl…

Accepted Answer

Introduction / Context: This problem discusses children playing in the playground and the impact of play on problem solving and decision making. Although the subject is familiar and most people have opinions about it, you must focus strictly on what the statements say and avoid inserting extra assumptions. The conclusions make broader claims about overall development and the need for balancing play and study, which may or may not be logically supported. Given Data / Assumptions: - Statement I: Children play in the playground, a simple factual description of activity. - Statement II: Playing in the playground gives children a different approach to problem solving and decision making, indicating a specific cognitive benefit of play. - Conclusion I: Outdoor play is very necessary for the overall development of a child, which is a strong, general statement about overall development. - Conclusion II: There should be a balance between playing and studying, which introduces the idea of balancing two activities even though study has not been mentioned in the statements. Concept / Approach: The key is to distinguish between what is explicitly stated and what is simply desirable or reasonable as advice. Statement II links outdoor play to certain mental skills, but it does not claim that this is the only or strictly necessary way to achieve overall development. Nor do the statements introduce any idea of studying or balancing time between play and study. Therefore, we must be careful not to turn reasonable sounding advice into logical conclusions. Step-by-Step Solution: Step 1: From Statement II, we learn that playing in the playground helps children develop a different approach to problem solving and decision making. Step 2: This suggests that play is beneficial for some aspects of mental development, but it does not say that play is the only way or that it is strictly necessary. Step 3: Conclusion I claims that playing outdoors is very necessary for overall development. Overall development includes emotional, social, physical, academic, and other aspects that are not mentioned in the statements. The statements give evidence of benefit in one particular area, not overall development. Step 4: Therefore, we cannot conclude from the given information that outdoor play is very necessary for overall development, only that it helps with certain cognitive skills. Step 5: Conclusion II introduces the idea that there should be a balance between playing and studying. However, the statements never mention studying or any conflict between play and study time. Step 6: While it may be good advice in real life, this balance is not logically derived from the two statements, which speak only about play and its benefits. Step 7: Because neither conclusion is strictly forced by the statements, neither can be said to logically follow in the strict sense required by such questions. Verification / Alternative check: Imagine a situation where children play in the playground and gain problem solving skills as described, but also receive strong development in other areas through different activities. In this case, outdoor play is beneficial but might not be strictly necessary for overall development. Also imagine that the school schedule already provides playtime and study time without any discussion of balance in the statements. These scenarios show that the conclusions introduce new ideas that are not compelled by the statements. Why Other Options Are Wrong: Option A states that only Conclusion II follows, but study and balance are not mentioned in any statement, so this cannot be logically concluded. Option B claims both conclusions follow, which is even stronger and clearly not justified. Option D says only Conclusion I follows, but the statement about necessary overall development goes far beyond the specific cognitive benefits described. Option E suggests Conclusion I is better, but the question requires strict logical following, not subjective preference. Common Pitfalls: A frequent mistake is to treat these questions as if they ask for good advice rather than strict logical implications. Many test takers agree that play is important and that a balance of play and study is healthy, so they mark the conclusions as if they were opinion questions. However, logical reasoning questions demand that the conclusion must be necessarily true whenever the statements are true, which is not the case here. Final Answer: The correct option is Neither I nor II follow, because the statements describe specific benefits of play but do not support strong claims about overall development or the need for a balance between play and study.

Question 20

In this very simple statement and conclusion question involving inequalities, two statements about numbers are given. You must consider the statements as true and decide which of the conclusions I and II logically follow.  Statement I: 1 < 2. Statem…

Accepted Answer

Introduction / Context: This question is designed to test fundamental understanding of inequalities and the transitive property of order among real numbers. The statements given are basic and obviously true for the natural numbers 1, 2, and 3. Your job is to decide which of the conclusions must follow logically from these statements. Given Data / Assumptions: - Statement I: 1 is less than 2 (1 < 2). - Statement II: 2 is less than 3 (2 < 3). - Conclusion I: 1 is less than 3 (1 < 3). - Conclusion II: 2 is less than 3 (2 < 3). Concept / Approach: The key mathematical property here is transitivity of inequality for real numbers. For any three real numbers a, b, and c, if a < b and b < c, then it logically follows that a < c. Additionally, any statement that is identical to one of the given statements is trivially valid as a conclusion. We apply these simple ideas directly to the numbers 1, 2, and 3. Step-by-Step Solution: Step 1: From Statement I, we know that 1 is strictly less than 2. Step 2: From Statement II, we know that 2 is strictly less than 3. Step 3: Using the transitive property of inequalities, if 1 < 2 and 2 < 3, then 1 must be less than 3. Symbolically, we have 1 < 3. Step 4: This directly supports Conclusion I, which states 1 < 3. Step 5: Conclusion II simply restates Statement II, that 2 < 3, which is already given as true. Step 6: Therefore, both conclusions are logically valid consequences of the given statements. Verification / Alternative check: You can verify numerically with the standard ordering of natural numbers. On the number line, 1 is to the left of 2, and 2 is to the left of 3. This means 1 is to the left of 3 as well, confirming 1 < 3. Furthermore, since Statement II is assumed true, there is no doubt about 2 < 3. No other arrangement of 1, 2, and 3 can satisfy the original statements while making either conclusion false. Why Other Options Are Wrong: Option A says only Conclusion I follows, but Conclusion II is simply the same as Statement II and must be true as well. Option B says only Conclusion II follows, ignoring the clear transitive relation. Option C says neither follows, which contradicts both basic arithmetic and the given statements. Option E restricts validity to a transitive conclusion, but the question includes an explicit conclusion that restates a given statement; that is also valid. Common Pitfalls: Because the question is very simple, the main risk is overthinking. Some test takers might suspect a trick and doubt whether an already given statement can be treated as a valid conclusion. Remember that if the question asks which conclusions follow from the statements, any conclusion that is identical to a statement must also follow, since the statements are assumed true. Final Answer: The correct option is Both I and II follows, because 1 < 3 follows by transitivity, and 2 < 3 is explicitly given in the statements.

Statement and Conclusion Questions