Question 1

Statements about toys and personality development: Statements: (I) Kids rejoice with toys and toys give them new opportunities to think in various ways. (II) Toys are non-living things that create a virtual world around kids to think and perceive in…

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Introduction / Context: This question explores how far we can stretch statements about the benefits of toys for children. The statements focus on the positive role toys play in stimulating thinking and perception. You are asked whether two stronger claims about underdeveloped personality and toys being “mandatory” follow logically. This tests your ability to distinguish between “helpful” and “absolutely necessary” based on given information. Given Data / Assumptions: Statement (I): Kids rejoice with toys and toys give them new opportunities to think in various ways. Statement (II): Toys are non-living things that create a virtual world around kids to think and perceive in various ways. Conclusion (I): If children do not play with toys, some part of their personality is underdeveloped. Conclusion (II): Toys are a mandatory and undetachable part of their personality. We treat the statements as true but may not assume more than is explicitly or strongly implied. Concept / Approach: The statements describe toys as beneficial tools for enjoyment and cognitive stimulation. However, the conclusions go further by claiming necessity and underdevelopment in their absence. Logical reasoning requires that such strong claims be supported directly by the premises. Merely saying something is helpful does not mean it is mandatory or that its absence inevitably causes underdevelopment. Step-by-Step Solution: From Statement (I), we learn that children enjoy toys and that toys provide new opportunities for thinking. From Statement (II), we add that toys, though non-living, create a virtual world that encourages kids to think and perceive in different ways. Together, these statements highlight the positive influence of toys on children's thinking and perception. Consider Conclusion (I): It claims that if children do not play with toys, some part of their personality is underdeveloped. Nowhere do the statements assert that toys are the only means of developing those aspects of personality, or that without toys this development cannot occur. The statements show that toys help, not that they are the sole or indispensable factor; therefore, Conclusion (I) is not logically forced. Consider Conclusion (II): It says toys are a “mandatory and undetachable” part of personality. The statements describe toys as external objects (non-living things) that influence thinking, not as permanent components of personality itself. Calling them “mandatory and undetachable” exaggerates their role well beyond what is stated. Therefore, Conclusion (II) also does not follow logically. Verification / Alternative check: Imagine a child who grows up with limited or no access to toys but rich exposure to books, nature, sports or social interaction. Such a child could still develop a well-rounded personality, showing that the absence of toys does not automatically produce underdevelopment. Similarly, toys clearly can be put away or replaced; they are not permanent fixtures of personality. Hence both conclusions overreach the premises. Why Other Options Are Wrong: Any option claiming that one or both conclusions follow accepts unjustified generalisations. The premises never state that toys are strictly necessary, only that they are beneficial. Saying that exactly one conclusion follows “but cannot be determined which” is also incorrect, because we can clearly see that both conclusions introduce stronger ideas than the premises support. Common Pitfalls: Many test-takers equate “important” with “indispensable” and assume that because toys are useful, they must be mandatory. Another pitfall is reading personal beliefs about child psychology into the question; logical reasoning requires you to stay within the explicit content of the statements. Final Answer: Neither conclusion logically follows from the given statements. The correct option is Neither conclusion I nor conclusion II follows.

Question 2

Statements and conclusions – young scientists, open-mindedness and superstition: Statements: (I) All young scientists are open-minded. (II) No open-minded men are superstitious. Conclusions: (I) No scientist is superstitious. (II) No young people ar…

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Introduction / Context: This logical reasoning question involves statements about “young scientists,” “open-minded men” and superstition. You must decide whether each of the given conclusions necessarily follows. The trap here is to overgeneralise from specific subgroups (young scientists, open-minded men) to broader groups (all scientists, all young people). Given Data / Assumptions: Statement (I): All young scientists are open-minded. Statement (II): No open-minded men are superstitious. Conclusion (I): No scientist is superstitious. Conclusion (II): No young people are superstitious. We assume that “young scientists” are a subset of scientists and of young people, and that the word “men” in Statement (II) restricts the scope to male individuals who are open-minded. Concept / Approach: We must track set relationships carefully. Statement (I) gives a relationship only for the subset of scientists who are young. Statement (II) covers open-minded men but does not speak about all open-minded people, nor about women. Conclusions (I) and (II) broaden the claim to all scientists and all young people, which may or may not be justified by the given premises. Step-by-Step Solution: From Statement (I): Young scientists ⊂ open-minded individuals. From Statement (II): Among men, any who are open-minded are not superstitious. Combining these, we can say that any young scientist who is male is open-minded and, by Statement (II), not superstitious. However, Statement (I) does not say that all scientists are young. There may be older scientists for whom we are given no information about open-mindedness or superstition. Therefore, we cannot conclude that no scientist at all is superstitious; Conclusion (I) is too broad. Similarly, Statement (I) only speaks about “young scientists,” not all young people. Statement (II) only covers open-minded men, not all young people in general. There may be young non-scientists, young women, or young men who are not open-minded for whom no information is given. Thus we cannot conclude that no young person is superstitious; Conclusion (II) is also too broad. Verification / Alternative check: Construct a scenario: suppose all young male scientists are open-minded and not superstitious, satisfying both statements. At the same time, imagine an older scientist who is superstitious; this does not violate any given statement, so Conclusion (I) fails. Likewise, consider a young non-scientist who is superstitious; this is also compatible with the statements, so Conclusion (II) fails as a necessary conclusion. Why Other Options Are Wrong: Choosing Conclusion (I) or (II) alone, or both together, incorrectly generalises the premises to groups not covered by them. The option hinting that at least one conclusion follows but we cannot say which is also incorrect, because we can explicitly construct counterexamples for both conclusions while still respecting the statements. Common Pitfalls: A typical mistake is to ignore qualifiers like “young” and “men” and mentally read the statements as applying to all scientists or all people. Another pitfall is to assume that properties of a subset extend automatically to the whole set, which is not logically valid without explicit support. Final Answer: Neither of the conclusions necessarily follows from the given statements. The correct option is Neither conclusion I nor conclusion II follows.

Question 3

Statements and conclusions – buttons, switches and connectors: Statement I: Some buttons are switches. Statement II: All buttons are connectors. Conclusions: I. Some switches are connectors. II. Some connectors are buttons.

Accepted Answer

Introduction / Context: This question is another set-based reasoning problem involving buttons, switches and connectors. You are given one statement describing a partial overlap (“some buttons are switches”) and another stating a full inclusion (“all buttons are connectors”). You must decide which of the conclusions about switches and connectors logically follow. Given Data / Assumptions: Statement I: Some buttons are switches (at least one object is both a button and a switch). Statement II: All buttons are connectors (Buttons ⊂ Connectors). Conclusion I: Some switches are connectors. Conclusion II: Some connectors are buttons. We assume that buttons exist and all statements are true. Concept / Approach: We will use basic set logic. If some buttons are switches and all buttons are connectors, then those particular buttons that are switches must also be connectors. This will help us with Conclusion I. For Conclusion II, we notice that if all buttons are connectors and there are buttons, then automatically some connectors are buttons. Step-by-Step Solution: From Statement I, there is at least one element that belongs to both the sets “buttons” and “switches”. From Statement II, every button is a connector. Therefore, that specific element (button ∧ switch) is also a connector. Thus, we have at least one element that is both a switch and a connector. Therefore, Conclusion I, “Some switches are connectors,” is true. Now look at Conclusion II: “Some connectors are buttons.” From Statement II again, all buttons are connectors. This means the entire set of buttons lies inside the set of connectors. Since we know there are some buttons (from Statement I, because some buttons are switches), it follows that at least some connectors are buttons. Thus, Conclusion II is also true. Verification / Alternative check: Draw a simple Venn diagram: draw a large circle for connectors. Inside it, draw a smaller circle for buttons (since all buttons are connectors). Mark a region overlapping between the buttons circle and another circle for switches, representing the “some buttons are switches” statement. This overlap region is automatically inside the connectors circle, which shows that some switches are connectors and some connectors are buttons. Both conclusions are clearly supported. Why Other Options Are Wrong: Saying only one conclusion follows ignores the direct set relationships that support both. Saying neither follows conflicts with the clear implications of the statements. The idea that we “cannot determine which” is also incorrect, because a straightforward set diagram shows that both are valid consequences. Common Pitfalls: A common pitfall is to underuse the fact that buttons exist, which is implied by “some buttons are switches.” If there were no buttons, the first statement would be false. Another mistake is to forget that when one set is fully contained in another, the larger set must include at least some members of the smaller set (assuming it is non-empty), which is the basis for Conclusion II. Final Answer: Both conclusions are logically valid. The correct option is Both conclusions I and II follow.

Question 4

Statements and conclusions – envelopes, gums, seals and adhesives: Statements: Some envelopes are gums. Some gums are seals. Some seals are adhesives. Conclusions: 1. Some envelopes are seals. 2. Some gums are adhesives. 3. Some adhesives are seals.…

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Introduction / Context: This is a logical reasoning question involving partial overlaps between sets: envelopes, gums, seals and adhesives. You are asked which conclusions must follow. The challenge is that the statements only guarantee some specific overlaps, not full inclusions or complete chains. You must therefore check which of the conclusions are forced by the information and which are merely possible but not necessary. Given Data / Assumptions: Some envelopes are gums (E ∩ G ≠ ∅). Some gums are seals (G ∩ S ≠ ∅). Some seals are adhesives (S ∩ A ≠ ∅). Conclusions: 1. Some envelopes are seals (E ∩ S ≠ ∅). 2. Some gums are adhesives (G ∩ A ≠ ∅). 3. Some adhesives are seals (A ∩ S ≠ ∅). 4. Some adhesives are gums (A ∩ G ≠ ∅). Concept / Approach: “Some X are Y” simply tells us that the intersection of sets X and Y is non-empty. However, having overlaps in a chain like E–G and G–S does not guarantee an overlap between E and S unless explicitly stated. Similarly, having G–S and S–A does not force G–A or E–A overlaps. We must be careful not to assume transitivity for “some” relationships where it does not necessarily hold. Step-by-Step Solution: From the third statement, “Some seals are adhesives,” we know directly that there is at least one object that is both a seal and an adhesive. Therefore, Conclusion 3, “Some adhesives are seals,” is simply a restatement of this and must be true. Now consider Conclusion 1: “Some envelopes are seals.” We know some envelopes are gums and some gums are seals. It is possible that the envelopes that are gums are different from the gums that are seals; the sets may overlap in different regions. For example, one group of gums could be used on envelopes but never as seals, while another group of gums may be used in seals but never on envelopes. In that case, there is no envelope that is also a seal, while all statements remain true. Therefore, Conclusion 1 does not necessarily follow. Consider Conclusion 2: “Some gums are adhesives.” We know some gums are seals and some seals are adhesives, but it is not guaranteed that the same seals that are adhesives are the ones that are gums. Thus there may be no object that is both gum and adhesive, even though all statements are satisfied. So Conclusion 2 does not necessarily follow. Consider Conclusion 4: “Some adhesives are gums.” This would require an overlap between adhesives and gums, which again is not assured by the given information. The adhesives that are seals might be completely disjoint from gums. Hence, Conclusion 4 also does not necessarily follow. Verification / Alternative check: To confirm, build a model: imagine three separate pairs of overlapping sets—envelopes with one part of gums, gums with some seals, and seals with some adhesives. Arrange them so that these overlaps do not coincide. In such a diagram, statements about some envelopes being gums, some gums being seals, and some seals being adhesives are true, but there is no envelope that is a seal, no gum that is an adhesive and no adhesive that is a gum. Only the direct overlap between seals and adhesives is guaranteed, capturing Conclusion 3. Why Other Options Are Wrong: Choosing any conclusion other than 3 as necessarily true relies on an unjustified assumption that “some” overlaps automatically chain through multiple sets. The option stating that both 1 and 3 follow is wrong because 1 can be false in a valid scenario. Options pointing to 1, 2 or 4 alone ignore the fact that they are not logically forced by the statements. Common Pitfalls: A common mistake is to treat “some A are B” statements as if they were universal and to assume transitivity. Remember that a partial overlap between A and B and another between B and C does not guarantee any overlap between A and C. Constructing counterexamples in your mind or on paper is an effective way to avoid this trap. Final Answer: Only Conclusion 3 (“Some adhesives are seals”) is guaranteed by the given statements. The correct option is Only conclusion 3 follows.

Question 5

Statement and conclusions – food processing industry: Statement: The food processing industry was touted to be a sunrise industry for India some years ago and, on the face of it, there was little reason to doubt that. Conclusions: I. India has an ad…

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Introduction / Context: This is a statement-and-conclusion question based on a short remark about the food processing industry in India. The industry is described as a “sunrise industry” with little apparent reason to doubt that label. You must decide whether two additional statements about India's advantages and the basic nature of food processing follow logically from this remark. Given Data / Assumptions: Statement: The food processing industry was touted to be a sunrise industry for India, and there was little reason to doubt this at the time. Conclusion I: India has an advantage in food processing because of varied agro-climatic conditions and availability of raw materials. Conclusion II: Food processing is one of the basic industries which supports our lives. We treat the statement as true but do not add extra background information. Concept / Approach: A “sunrise industry” is one that is expected to grow rapidly in the future. The statement only tells us about the optimistic prospects for food processing in India; it does not specify why it was so regarded. To accept a conclusion, we need its content to be either explicitly stated or strongly implied by the statement, not merely plausible or commonly known from real life. Step-by-Step Solution: The statement says that the food processing industry was touted as a sunrise industry in India, and that there was little reason to doubt this optimism. This indicates that many people believed the sector had strong growth prospects, but the statement does not describe the detailed reasons behind that belief. Conclusion I attributes the sunrise status to specific factors: varied agro-climatic conditions and raw material availability. While these may be true in real-world context, the given statement does not mention them. Therefore, we cannot say that Conclusion I logically follows from the single line provided; it may be a possible explanation, but it is not stated. Conclusion II claims that food processing is one of the basic industries that supports our lives. The statement focuses only on growth prospects and does not classify food processing as a “basic industry” or discuss its role in supporting life. Hence, Conclusion II also introduces new content not present or implied in the statement. Verification / Alternative check: To test necessity, ask: if the statement were true, must Conclusion I or II also be true? The answer is no. One could consider an industry as “sunrise” due to factors like policy changes, foreign investment or technology improvements, not necessarily agro-climatic advantages. Similarly, many industries support our lives, but being a sunrise industry does not automatically classify food processing as a “basic” industry. Thus both conclusions are possible but not logically forced. Why Other Options Are Wrong: Options that accept Conclusion I or II (alone or together) confuse plausibility with logical implication. The statement simply does not mention the reasons behind the optimism or the industry's basic nature. The “either I or II” option is used for cases where exactly one conclusion must be true, which is not supported here. The only safe choice is that neither follows from the given information alone. Common Pitfalls: A common mistake is to bring in external knowledge about India's agriculture and food sector, thereby endorsing Conclusion I. While that may be true in reality, logical reasoning questions require you to rely strictly on the given statement. Another pitfall is to assume that any industry related to food is automatically a “basic industry,” which is a value judgement rather than a logical consequence here. Final Answer: Neither of the two conclusions is logically compelled by the given statement. The correct option is If neither conclusion I nor conclusion II follows.

Question 6

In the following comparison question, two equations are given for the variables x and y.  I.  x^2 = 529 II. y = 529  Solve both equations, determine all possible real values of x and y, and then choose the correct relationship between x and y from t…

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Introduction / Context: This question tests basic algebraic manipulation and comparison of two variables defined by separate equations. Such comparison questions are very common in aptitude exams, where examinees must solve each equation correctly, list all possible values of the variables, and then compare them logically. Careful handling of squares and square roots is important so that no valid solution is missed. Given Data / Assumptions: Equation I: x^2 = 529. Equation II: y = 529. x and y are real numbers. We must compare x and y and select a single correct relationship. Concept / Approach: To solve the problem, we first find all real solutions for x from the quadratic equation x^2 = 529. Then we identify the unique value of y from the linear equation y = 529. After listing all possible values of x and y, we compare the ranges or sets of values. The key idea is that squaring a number leads to two real roots, one positive and one negative, whenever the right side is positive and we are working over real numbers. Step-by-Step Solution: Step 1: Solve equation I, x^2 = 529. Since 529 is 23^2, we have x^2 = 23^2. Step 2: Take square roots on both sides. For real numbers, x can be positive or negative. So x = 23 or x = -23. Step 3: Solve equation II, y = 529. This is already solved and gives a single value. Therefore y has a unique real value y = 529. Step 4: Compare each possible x with y. If x = 23, then compare x and y: 23 versus 529 gives 23 < 529, so x < y. If x = -23, then compare x and y: -23 versus 529 gives -23 < 529, so again x < y. Step 5: In every allowed case, x is less than y. There is no situation where x is greater than or equal to y. Verification / Alternative check: An alternative way is to focus on magnitudes and signs. The number 529 is a large positive integer. The real solutions of x^2 = 529 are 23 and -23, whose absolute values are 23 only. Both possible x values are much closer to zero, and one is even negative. A very large positive number like 529 is certainly greater than both 23 and -23, so the only consistent relationship is x < y. Why Other Options Are Wrong: Option a (x > y) is impossible because both 23 and -23 are less than 529. Option c (x = y) is wrong since x never equals 529 for the given equation x^2 = 529. Option d (relationship cannot be determined) is incorrect because we have a definite comparison once we list all possible x values. Option e (x ≥ y) would require x to be at least 529, which never happens here. Common Pitfalls: Many learners forget that a positive square has two real roots, one positive and one negative. Another mistake is to take the square root and assume x = 23 only. Even if that mistake is made, x would still be less than 529, but forgetting negative roots can cause errors in more complex comparison questions. Some learners also try to compare x^2 and y directly instead of first solving for x and y separately, which can lead to confusion when signs are involved. Final Answer: The correct relationship is x < y, so option b is correct.

Question 7

In the following question, the relationships between several variables are given:  A > B ≤ C < D,  C > E,  and F ≥ D.  Using only this information, determine which of the conclusions A > E and F > E must be true and select the correct option.

Accepted Answer

Introduction / Context: This problem is a standard inequalities and conclusions question from logical reasoning. We are given chained inequalities relating A, B, C, D, E, and F. The task is to decide which conclusions definitely follow from the statements and which do not. The challenge is to read the inequality chain correctly and use transitivity rules without adding any extra assumptions. Given Data / Assumptions: A > B. B ≤ C. C < D. C > E. F ≥ D. Conclusion I: A > E. Conclusion II: F > E. Concept / Approach: For chained inequalities, we rely on transitivity. If X > Y and Y > Z, then X > Z. If X > Y and Y ≥ Z, we can still say X > Z. Similarly, if X ≥ Y and Y > Z, then X > Z. We must see what we can deduce about positions of A, D, and F with respect to E by combining the given relations. We must also check if any relation about A and E can be broken by a counter example while still respecting all given inequalities. Step-by-Step Solution: Step 1: Start with C and E. We are told C > E. Step 2: We also have C < D. Hence D is greater than C, and therefore D is also greater than E. So D > E. Step 3: From F ≥ D and D > E, we can conclude F > E. This is because F is at least D, and D is already strictly greater than E. Step 4: Therefore conclusion II (F > E) must always be true. Step 5: Now examine A and E. We know A > B and B ≤ C, and C > E. Step 6: Since B ≤ C, B can be less than C or equal to C. Also, E is less than C, but there is no direct relation between B and E. Step 7: Construct an example where A > B, B ≤ C, and C > E but A is not greater than E. Let E = 5, C = 10, B = 9, and A = 9.5. All inequalities hold, but here A = 9.5 is greater than E = 5, so this example still supports A > E. Step 8: Now choose E = 5, C = 10, B = 9, and A = 6. Then A > B would fail, so we need B smaller. Take E = 5, C = 10, B = 1, A = 2. All relations hold, and A > E is false since 2 is not greater than 5. This shows that A > E is not guaranteed. Verification / Alternative check: When examining conclusion I, we only know that A is to the right of B on the number line, and C is to the right of E. There is no direct link between A and E, so both A > E and A ≤ E are possible. For conclusion II, D is definitely to the right of E, and F is at or to the right of D. Hence E is always to the left of F, so F > E is forced in every allowed configuration. Why Other Options Are Wrong: Option a (only conclusion I is true) is wrong because conclusion I is not always true. Option c (either I or II) is wrong since II is always true, not an either or situation. Option d (neither) is wrong because conclusion II definitely follows. Option e (both) is wrong since conclusion I can fail for some values. Common Pitfalls: A frequent error is to treat B ≤ C as if it forced B < C, and then assume a clear ordering among all variables without checking each link. Another mistake is to assume that if A is linked through B and C to E, then A must be greater than E, even though the inequalities do not give a strict chain from A to E. Always check whether you can build at least one valid counter example before declaring a conclusion definitely true. Final Answer: Only conclusion II is true, so option b is correct.

Question 8

In the following question, the relationships between the variables K, L, M, N, O and P are given as:  K > L = M ≤ N and O < L ≥ P.  Based on these statements, determine which of the conclusions K ≥ O and N ≥ O must be true.

Accepted Answer

Introduction / Context: This is another chained inequality question where we must interpret symbols like greater than, less than, equal to, and less than or equal to in order to test conclusions. Such questions are designed to check the candidate skill in reading relationships carefully and using transitivity to work out guaranteed comparisons between different variables. Given Data / Assumptions: K > L. L = M. M ≤ N, so L ≤ N. O < L. L ≥ P. Conclusion I: K ≥ O. Conclusion II: N ≥ O. Concept / Approach: When variables are connected through inequalities, we can often use transitivity to move along the chain. The basic ideas are: if X > Y and Y > Z, then X > Z; if X > Y and Y ≥ Z, then X > Z; if X ≥ Y and Y > Z, then X > Z. To decide if a conclusion must be true, we must see whether there is any possible assignment of numbers that satisfies the statements but violates the conclusion. If there is no such assignment, the conclusion definitely follows. Step-by-Step Solution: Step 1: Compare K and O. We know K > L and O < L. So L is between K and O in the sense that K is on one side and O is on the other. Since K > L and O < L, we get O < L < K, which means K > O. If K > O, then K is certainly greater than or equal to O, so conclusion I (K ≥ O) is always true. Step 2: Compare N and O. We have L = M and M ≤ N, which gives L ≤ N. Thus N is either equal to L or greater than L. We also have O < L. Combining O < L and L ≤ N gives O < N. Thus N is always strictly greater than O, and so N ≥ O is always true. This confirms conclusion II. Verification / Alternative check: To verify, choose specific numbers that satisfy all given inequalities. For example, set O = 1, L = M = 2, N = 3, and K = 5. Then K > L, L = M, M ≤ N, and O < L ≥ P can all be satisfied by choosing P appropriately. In this numeric example, K = 5 and O = 1, so K ≥ O holds. Also, N = 3 and O = 1, so N ≥ O holds. Any other valid numeric assignment where O is less than L and L is at most N will also result in N being greater than O. There is no way to make O greater than or equal to K or N without breaking the original inequalities. Why Other Options Are Wrong: Options a and b, claiming only one conclusion is true, are wrong because both K ≥ O and N ≥ O always hold. Option c (either I or II) is wrong because this pattern would allow one of them to be false, which is not possible here. Option d (neither) is clearly inconsistent with the chained inequalities. Common Pitfalls: A common mistake is to misread symbols like ≤ and ≥ or to ignore the equality part of L = M. Another pitfall is assuming that if variables are indirectly connected, the relation may be uncertain. In this case, careful chaining shows that O is always to the left of L, and L is never to the right of N, so both K and N remain to the right of O on the number line. Final Answer: Both conclusions I and II are true, so option e is correct.

Question 9

In the following question, the relationships between A, B, C, D and E are given as:  A ≤ B > C and D ≥ B < E.  Based only on these statements, determine which of the conclusions D ≥ A and E > C must be true.

Accepted Answer

Introduction / Context: This question checks understanding of chained inequalities involving several variables. The goal is to see whether certain comparisons between pairs of variables are guaranteed to hold, given the initial inequality statements. Such questions appear in many banking and management entrance tests as part of logical and analytical reasoning. Given Data / Assumptions: A ≤ B. B > C. D ≥ B. B < E. Conclusion I: D ≥ A. Conclusion II: E > C. Concept / Approach: We combine inequalities using transitivity. When one variable is greater than or equal to another, and that second variable is greater than a third, we can chain the relations. We must be cautious not to assume any relation that is not supported by a continuous chain of inequalities. To check whether a conclusion must be true, we can try to construct a counter example. If no counter example can be found without violating the original statements, then the conclusion is logically valid. Step-by-Step Solution: Step 1: Work on conclusion I, D ≥ A. We know A ≤ B, so B is at least as large as A. We also know D ≥ B, so D is at least as large as B. Combining these, we get D ≥ B ≥ A. Hence D ≥ A must always hold. So conclusion I is definitely true. Step 2: Work on conclusion II, E > C. We know B > C, meaning B is strictly greater than C. We also know B < E, so E is strictly greater than B. Now we have C < B < E. By transitivity, C < E. Therefore E is always greater than C, and conclusion II must also be true. Verification / Alternative check: Take a simple numeric example that satisfies the inequality chain. Choose C = 2, B = 5, A = 4, D = 7, and E = 9. Then A ≤ B (4 ≤ 5) and B > C (5 > 2). Also D ≥ B (7 ≥ 5) and B < E (5 < 9). Now compare D and A: D = 7 and A = 4, so D ≥ A holds. Compare E and C: E = 9 and C = 2, so E > C holds. Any other numeric assignment that respects the original inequalities will keep D at or to the right of B, and B at or to the right of A, and will keep E to the right of B and B to the right of C. Hence the final relations D ≥ A and E > C remain true in all valid cases. Why Other Options Are Wrong: Options a and b, which claim that only one conclusion is true, are incorrect because both D ≥ A and E > C always hold. Option c (either I or II) and option d (neither) are also inconsistent with the clear chained ordering. Common Pitfalls: Learners sometimes misread A ≤ B as A < B and overlook the equality case. Even then, the conclusion D ≥ A holds whether A equals B or not. Another error is to think that if there is a mix of strict and non strict inequalities, no definite conclusion can be drawn. In reality, as long as the chain from one variable to another is complete and consistent, solid conclusions like D ≥ A and E > C can be made. Final Answer: Both conclusions I and II are true, so option e is correct.

Question 10

In the following question, relationships between several elements are given by the statements:  M < S ≤ T = R ≥ D > E ≥ F and G ≤ S < H.  From these statements, determine which of the conclusions G = R and G < R must be true.

Accepted Answer

Introduction / Context: This question combines several inequalities and asks about the precise relationship between G and R. The key idea is to see whether G must be equal to R, must be less than R, or could be either depending on the exact values chosen. If more than one relationship is possible without contradicting the given statements, then we can only say that one of the two is true, not which one in particular. Given Data / Assumptions: M < S. S ≤ T. T = R. R ≥ D. D > E. E ≥ F. G ≤ S. S < H. Conclusion I: G = R. Conclusion II: G < R. Concept / Approach: We first try to place all variables roughly on a number line using the inequalities. After that, we focus on how close G can be to S and how S relates to T and R. Since G ≤ S and S ≤ T = R, we get G ≤ R, but we must check whether equality is forced or if G can be strictly less than R. If both equality and strict inequality are possible, then exactly one of conclusions I or II must hold in any specific case, but we cannot decide which one, so the correct option is the one that says either I or II is true. Step-by-Step Solution: Step 1: From S ≤ T and T = R, we get S ≤ R. Step 2: From G ≤ S and S ≤ R, we derive G ≤ R. Step 3: Thus G can never be greater than R. The only possibilities are G = R or G < R. Step 4: Check if G = R is possible. If we choose G = S = T = R, all inequalities G ≤ S, S ≤ T, and T = R remain valid, and we can assign remaining variables to satisfy other inequalities. So G = R is possible. Step 5: Check if G < R is possible. Take G < S and S ≤ R. For example, let G = 1, S = 2, T = R = 3. Then G ≤ S and S ≤ T are satisfied, and G < R. Hence G < R is also possible. Step 6: Since both G = R and G < R are possible depending on the exact numeric assignments, neither conclusion I nor conclusion II alone is forced. But in every valid arrangement, at least one of these will hold, because we have already shown that G ≤ R. Verification / Alternative check: Focus only on the relations directly involving G, S, T, and R. We have G ≤ S and S ≤ T and T = R. This gives us G ≤ R with no further restriction. The inequalities involving M, D, E, F, and H do not restrict G more tightly than this. There is no statement that forces G to be strictly less than S or strictly equal to S, so G may coincide with S or lie strictly below it. Hence equality and strict inequality between G and R are both compatible with the original information. Why Other Options Are Wrong: Option a (only conclusion I) is wrong because G can also be strictly less than R. Option b (only conclusion II) is wrong for the opposite reason, since G can equal R. Option d (neither) is wrong because G can never be greater than R, so at least one of equality or less than must hold. Option e (both) is logically impossible for a single value of G and R, since a number cannot be simultaneously equal to and strictly less than another number. Common Pitfalls: A typical mistake is to think that if G ≤ S and S ≤ R then G < R automatically, forgetting the equality possibility. Another pitfall is trying to read too much into unrelated parts of the inequality chain and concluding that G must be placed strictly at one position. Always separate what is forced from what is optional. Final Answer: Either conclusion I or conclusion II is true, so option c is correct.

Question 11

In each of these questions, relationships between elements are shown. Based on the statements A > B < P and Q < R > P, determine which of the conclusions B < R and Q > A logically follow from the given information.

Accepted Answer

Introduction / Context: This logical reasoning problem again involves chained inequalities among several variables. The goal is to determine which of two proposed conclusions must hold for every possible assignment of numbers that satisfies the given statements. These questions are common in competitive exams and test the ability to work with relative, not absolute, values. Given Data / Assumptions: A > B. B < P. Q < R. R > P. Conclusion I: B < R. Conclusion II: Q > A. Concept / Approach: We visualise the variables on a number line. From the given inequalities, we find a chain for some of them. When a variable is greater than one and another is greater than it, we can join those facts to compare variables that do not directly appear together. At the same time, if there is no way to connect two variables with a consistent chain, then no certain comparison can be made between them. Step-by-Step Solution: Step 1: Use the relations involving B, P and R. We are told B < P and R > P. That gives B < P < R. From this chain we can conclude B < R. Hence conclusion I is always true. Step 2: Now analyse conclusion II, Q > A. The statements tell us that Q < R and A > B. Apart from that, Q and A are in different parts of the inequality structure, with no relation linking them directly or through an unbroken chain. This means two types of numeric assignments are possible without breaking any given condition: one where Q is greater than A and another where Q is less than or equal to A. Since both Q > A and Q ≤ A can be made consistent with all original statements, there is no single relation between Q and A that must always hold. Thus conclusion II is not guaranteed to be true. Verification / Alternative check: Take one numeric example: let B = 1, P = 3, R = 5, and choose A = 4 (which is greater than B) and Q = 2 (which is less than R). All original inequalities are satisfied: A > B (4 > 1), B < P (1 < 3), Q < R (2 < 5), and R > P (5 > 3). In this setup Q = 2 is less than A = 4, so Q > A is false. This shows conclusion II does not always hold. On the other hand, B < R becomes 1 < 5, which is correct. You can try other numbers and you will always find B < R is satisfied and conclusion I holds. Why Other Options Are Wrong: Option b (only conclusion II) is wrong because conclusion II can fail. Option c (either I or II) is not right since we always have I true and II can be false. Option d (neither) ignores that B < R is definitely true. Option e (both) is wrong because we have demonstrated that II does not follow. Common Pitfalls: One common error is to assume that all variables are comparable simply because they appear in the same problem. Without a direct or indirect chain of inequalities, you cannot fix the relative order of two variables. Learners may also confuse Q < R and A > B and imagine some link between them that does not actually exist. Always stick strictly to what is given. Final Answer: Only conclusion I follows, so option a is correct.

Question 12

In the following question, consider the statements:  I. All books are pens. II. All pens are tables.  Based on these statements, decide which of the conclusions given below logically follow.

Accepted Answer

Introduction / Context: This question is a classic syllogism problem. We are given two categorical statements about classes of objects, such as books, pens and tables. The task is to determine which conclusions follow logically from the given statements without using outside knowledge. Syllogism questions are common in verbal and logical reasoning sections of competitive exams. Given Data / Assumptions: Statement I: All books are pens. Statement II: All pens are tables. Conclusion I: Some pens are tables. Conclusion II: All tables are books. Concept / Approach: The standard way to handle such questions is to think in terms of sets. If all members of set A are inside set B, and all members of set B are inside set C, then set A is inside set C. From this, we can decide whether statements like "some" or "all" types of objects in one set belong to another. We must not assume that every table is necessarily a pen or book unless that is clearly stated or can be deduced from the given premises. Step-by-Step Solution: Step 1: Translate the statements into set language. All books are pens means the set of books is completely inside the set of pens. All pens are tables means the set of pens is completely inside the set of tables. Step 2: Combine the two statements. Since books are inside pens and pens are inside tables, it follows that books are also inside tables. We do not need this directly for the conclusions, but it tells us how the sets are nested. Step 3: Evaluate conclusion I: Some pens are tables. If all pens are tables, then clearly at least one pen (in fact every pen) is a table. Therefore, the statement "some pens are tables" is logically true. Conclusion I follows from the premises. Step 4: Evaluate conclusion II: All tables are books. We only know that pens are a subset of tables and books are a subset of pens. There is no information that every table must be a pen, or that every table must be a book. There may be tables that have nothing to do with pens or books. So "all tables are books" does not logically follow. Verification / Alternative check: Imagine a diagram. Draw a large circle for tables. Inside that, draw a smaller circle for pens, and inside pens an even smaller circle for books. This picture matches both statements: all books are pens and all pens are tables. Now look at the circles. Some pens are definitely inside the table circle, so conclusion I is true. However, there are parts of the table circle outside the pen circle and outside the book circle. Thus not all tables are books, and conclusion II is false. Why Other Options Are Wrong: Option b (only conclusion II) is wrong because conclusion II does not follow. Option c (both) is wrong since only the first conclusion is valid. Option d (neither) is wrong because conclusion I clearly follows. Option e mixes statements that are partly true and partly false, and is not the format asked by the question. Common Pitfalls: Many learners reverse the direction of the statements. From "all books are pens" they incorrectly infer "all pens are books," which is not correct. Similar reversal happens with tables. Always remember that if all A are B, it does not mean all B are A. Only the inclusion A inside B is guaranteed, not the reverse inclusion. Final Answer: Only conclusion I follows, so option a is correct.

Question 13

People think that paying tax to the government is a burden and a waste, so they avoid paying tax or do not pay it promptly.  Considering this statement as true, decide which of the given conclusions can definitely be drawn.

Accepted Answer

Introduction / Context: This problem belongs to the statement and conclusion type in logical reasoning. A statement describes how people feel about paying tax and how they behave. From this, we must decide which suggested conclusions are logically supported by the statement. The important point is that we are not asked which conclusion we personally prefer, but which one follows logically from the given information. Given Data / Assumptions: Given statement: People think that paying tax to the government is a burden and a waste. Given statement: Therefore, they avoid paying tax or do not pay tax promptly. Conclusion 1: The government should create awareness that paying tax helps to build the nation. Conclusion 2: Tax should be increased so that more money is collected. Concept / Approach: In such questions, a valid conclusion should be a reasonable or necessary consequence of the situation described. It should address the cause or the problem highlighted by the statement. A conclusion that makes the problem worse or is unrelated to the stated cause is usually not considered valid. We must focus on the link between people attitude toward tax and the suggested actions about tax policy or awareness. Step-by-Step Solution: Step 1: Understand the problem presented in the statement. People feel that paying tax is a burden and wasteful. This negative perception leads to avoidance of tax or delay in payment. Step 2: Check conclusion 1. Conclusion 1 suggests that the government should create awareness among people that paying tax helps to build the nation. If people understood that tax money is used for development, infrastructure, welfare schemes and national growth, they might feel less burdened and more responsible. This directly tackles the wrong perception that tax is a waste. Therefore conclusion 1 is a logical and reasonable response to the problem. Step 3: Check conclusion 2. Conclusion 2 suggests that tax should be increased so that more money is collected. However, the current issue is that people already feel tax is a burden and avoid paying it. Increasing the rate is likely to make them even more reluctant to pay, and may worsen the problem instead of solving it. Hence conclusion 2 does not logically follow from the statement. Verification / Alternative check: The core cause in the statement is negative perception. A sound conclusion should either change this perception or address non payment directly. Awareness campaigns and communication about how tax money is used are clear ways to address the cause. On the other hand, raising the tax rate does not address perception at all and may reduce compliance further. Therefore only the first conclusion can be reasonably drawn from the statement. Why Other Options Are Wrong: Option a (neither) is wrong because conclusion 1 is a valid course of action that fits the situation. Option b (only conclusion 2) and option c (both) are wrong because conclusion 2 is not supported. Option e (either 1 or 2) is also incorrect; the question is not about choosing between them but about which actually follows. Common Pitfalls: Candidates sometimes think that any statement beginning with "the government should" is automatically a conclusion. Another common error is to focus only on increasing revenue without addressing people behaviour and attitudes. In statement and conclusion questions, always look for a conclusion that fits the cause effect pattern shown in the statement. Final Answer: Only conclusion 1 follows, so option d is correct.

Question 14

Consider the question: Who among P, Q, R, S and T is the lightest in weight?  Use the following statements and decide which combination of statements is sufficient to answer the question. 1. Q is lighter than P and S, and S is heavier than T. 2. R i…

Accepted Answer

Introduction / Context: This is a data sufficiency question. Rather than asking for the exact lightest person directly, it asks which given statements are enough to determine who is the lightest. The main task is to decide sufficiency, not to compute the exact weights. This skill is highly valued in management and bank exams where quick logical decisions are needed. Given Data / Assumptions: We have five people: P, Q, R, S and T. Question: Who is the lightest in weight? Statement 1: Q is lighter than P and S, and S is heavier than T. Statement 2: R is heavier than Q but lighter than T. Concept / Approach: For data sufficiency, we test each statement alone and then both together. A statement or a pair of statements is sufficient if it lets us answer the question uniquely. If more than one person can be the lightest under a statement without breaking the given conditions, then that statement is not sufficient by itself. Step-by-Step Solution: Step 1: Use statement 1 alone. From statement 1, Q is lighter than P and S. Also, S is heavier than T, so T is lighter than S. From this, we can deduce partial orderings like Q < P, Q < S, and T < S. However, we do not know any relation between Q and T or between R and any of the others. So the lightest person could be Q or T or even R, depending on their exact weights. Statement 1 alone is not sufficient. Step 2: Use statement 2 alone. Statement 2 tells us that R is heavier than Q but lighter than T. So Q < R < T. There is no information about P or S here, so the lightest could be Q or perhaps P or S if they are lighter than Q. Hence statement 2 by itself is also not sufficient. Step 3: Combine statements 1 and 2. From statement 1 we know Q < P and Q < S and T < S. From statement 2 we know Q < R < T. Combining these, we have Q lighter than P, R, S and T. T is lighter than S but heavier than R and Q. There is no way for any person other than Q to be the lightest without violating the relations. Thus, using both statements together, Q is uniquely determined as the lightest person. Verification / Alternative check: Try to construct a numeric example that respects both statements. Choose Q = 1, R = 2, T = 3, S = 4 and P = 5 in arbitrary units. All conditions are satisfied: Q is lighter than P and S, S is heavier than T, and R is between Q and T. In this example Q is clearly the lightest. Any attempt to make another person lighter than Q will break one of the given inequalities. Therefore the combination of both statements is sufficient to answer the question. Why Other Options Are Wrong: Option a and option b are wrong because neither statement alone determines the lightest person. Option d is wrong because the two statements together do provide a unique answer. Option e is wrong since each statement alone is not sufficient. Common Pitfalls: Students often confuse partial order with complete order. Just because a statement compares some people, it does not mean the complete ranking is known. Always check whether every person in the list has a fixed place relative to the others before declaring sufficiency. Final Answer: Both statements 1 and 2 together are sufficient, so option c is correct.

Question 15

Question: Should we avoid the overuse of air conditioners?  Arguments: I. Yes, overuse of air conditioners weakens the human system. II. No, the comfort provided by air conditioners cannot be sacrificed.  Decide which of the given arguments is stron…

Accepted Answer

Introduction / Context: This is a statement and argument type question. We are asked whether overuse of air conditioners should be avoided, and two arguments are presented, one in favour and one against. Our task is to judge which argument is strong in the context of public health and reasonable decision making. Strong arguments are those that are logical, relevant, and address the core issue. Given Data / Assumptions: Question: Should we avoid overuse of air conditioners? Argument I: Yes, overuse of air conditioners weakens the human system. Argument II: No, the comfort provided by air conditioners cannot be sacrificed. Concept / Approach: For such questions, we evaluate each argument based on logic and relevance. Argument I is about health, claiming that overuse harms or weakens the human body. Argument II focuses on comfort alone. A strong argument usually considers long term impacts such as health, safety, or economy, rather than just convenience. We also assume the given health effect in argument I is correct, as per the instructions in such reasoning questions. Step-by-Step Solution: Step 1: Evaluate argument I. Argument I says that overuse of air conditioners weakens the human system. If this is true, then overuse poses a health risk. Protecting health is an important objective for individuals and society. If a practice weakens the body or makes people more prone to illness, it is reasonable to suggest that it should be avoided or at least controlled. Therefore argument I directly addresses the core issue and presents a serious consequence of overuse. It is a strong argument. Step 2: Evaluate argument II. Argument II claims that we should not avoid overuse because the comfort provided by air conditioners cannot be sacrificed. This argument gives high priority to comfort, but completely ignores any negative effects, such as impact on health, energy consumption, or environment. Comfort is desirable, but it is not a decisive reason when health risks are involved. A more balanced argument would weigh comfort against harm, which this argument does not do. Thus argument II is weak, since it is one sided and does not deal with the core concern of overuse. Verification / Alternative check: In reasoning questions, if one argument is about serious outcomes like health and the other is merely about convenience, the health based argument is usually stronger. Here, argument I suggests a harmful effect of overuse, which is precisely what the question is about. Argument II in effect says that comfort is more important than health or any other cost, which is not a strong or balanced position for a policy decision. Why Other Options Are Wrong: Option b (both arguments strong) is wrong because argument II does not provide a sound reason for allowing overuse. Option c (only II strong) is clearly inconsistent with the reasoning above. Option d (neither) fails to recognise the strength of a health based argument. Option e (either I or II) is not appropriate, as the arguments are not equally strong or interchangeable. Common Pitfalls: Candidates sometimes treat any argument that favours comfort as strong without considering long term consequences. Remember that in such questions, issues related to health, safety and environment are usually given more weight than immediate convenience, unless the convenience is linked to a deeper necessity such as survival or critical functioning. Final Answer: Only argument I is strong, so option a is correct.

Question 16

Among the four bags A, B, C and D, which bag is definitely the lightest, based on the given weight comparison statements?

Accepted Answer

Introduction / Context: Data sufficiency questions test whether the given statements provide enough information to answer a question uniquely, without necessarily requiring the exact numerical values. Here, we have four bags A, B, C and D, and we need to determine which bag is the lightest in weight using the information in two statements. Understanding how to combine inequalities and compare objects logically is the key concept being tested in this problem. Given Data / Assumptions: We have four bags: A, B, C and D. Question: Which one of these four bags is the lightest? Statement 1: B is heavier than A (weight of B > weight of A). Statement 2: A is lighter than both C and D (weight of A < weight of C and weight of A < weight of D). We assume all weights are well-defined and that comparisons are accurate. Concept / Approach: The idea in data sufficiency is to check each statement alone and then in combination. A statement is sufficient if, using only that statement (and the question), we can uniquely identify the lightest bag. If a statement leaves multiple possibilities open, it is not sufficient. If combining statements gives a unique answer, then the pair of statements is sufficient together. Step-by-Step Solution: Step 1: Analyse Statement 1 alone. It says B is heavier than A. This only compares A and B, and says nothing about C and D. So among all four bags, we cannot be sure who is lightest, because C or D could be lighter than A. Thus, Statement 1 alone is not sufficient. Step 2: Analyse Statement 2 alone. It says A is lighter than C and D. There is still no information about B compared with A. B could be heavier than A or lighter than A. Therefore we cannot determine whether A is the lightest or whether B might be lighter. Statement 2 alone is also not sufficient. Step 3: Combine Statements 1 and 2. From Statement 1, we know B > A. From Statement 2, we know C > A and D > A. Therefore, A is lighter than B, C and D. So bag A is definitely the lightest among all four bags. Step 4: Since we now have a unique answer (A is the lightest bag) only when we use both statements together, the pair of statements is sufficient while each one alone is not. Verification / Alternative check: Take an example set of weights that satisfies both statements: A = 1 kg, B = 2 kg, C = 3 kg, D = 4 kg. Here, B > A and C, D are both heavier than A. It is clear that A is the lightest. Try to construct any configuration satisfying both statements where A is not the lightest. It is impossible, because both B, C and D are all strictly heavier than A by the given conditions. Why Other Options Are Wrong: Option A (Statement 2 alone is sufficient) is wrong because Statement 2 tells us only that A is lighter than C and D. Without a comparison between A and B, B might still be the lightest. Option C (Statement 1 alone is sufficient) is wrong because knowing only that B is heavier than A tells us nothing about C and D. Either C or D could be lighter than A. Option D (Statements 1 and 2 together are not sufficient) is wrong because, when combined, the statements force all of B, C and D to be heavier than A, making A uniquely the lightest bag. Common Pitfalls: A common error is to focus only on the items directly mentioned in each statement and ignore that other items might still be lighter or heavier. Another mistake is to confuse data sufficiency with actually computing a numerical value. Here we do not need the exact weights; we only need to know which bag is definitely the lightest. Some test-takers also forget to check the combined effect of both statements when each one alone seems insufficient. Final Answer: The bags' weights can be uniquely compared only when both statements are used together, which show that A is lighter than B, C and D. Hence, Statements 1 and 2 together are sufficient to answer the question.

Question 17

From the remark that Kirti played a very good shot on the pitch, which conclusion logically follows about Kirti or Sajit?

Accepted Answer

Introduction / Context: This question tests basic logical reasoning and the ability to distinguish between what is actually stated and what is merely assumed. We are given a short statement where a friend tells Sajit that Kirti played a very good shot on the pitch. From this, we must decide which conclusion, if any, logically follows: that Sajit likes cricket, or that Kirti is a good player. This is a classic example of analysing everyday language without adding extra assumptions. Given Data / Assumptions: Statement: A friend says to Sajit, 'Kirti played a very good shot on the pitch.' Conclusion I: Sajit likes cricket. Conclusion II: Kirti is a good player. We treat only the given statement as true and do not add extra information about personalities or habits unless it is clearly implied. Concept / Approach: Logical conclusion questions require us to see if a conclusion must be true every time the statement is true. If a conclusion could be false in some possible situation while the statement remains true, then that conclusion does not logically follow. We need to examine whether liking cricket or being a good player is forced by the friend's comment, or whether those are just plausible but not necessary interpretations. Step-by-Step Solution: Step 1: Analyse the statement carefully. The only explicit information is that Kirti played a very good shot and that this is being reported to Sajit by a friend. Step 2: Check Conclusion I – Sajit likes cricket. Does the statement say or imply that Sajit likes cricket? Not directly. The friend may simply be telling Sajit about an event, even if Sajit does not care about cricket at all. The fact that someone tells you something does not logically guarantee that you like that subject. Step 3: Since we can imagine a situation where the statement is true (the friend speaks to Sajit) and yet Sajit does not like cricket, Conclusion I is not a must. Therefore, Conclusion I does not logically follow. Step 4: Check Conclusion II – Kirti is a good player. The statement only says Kirti played a very good shot on one occasion. Even a beginner or a generally weak player might occasionally play a very good shot. One isolated performance is not sufficient to classify someone as a good player overall. Step 5: Therefore, there exists a possible situation where the statement is true (Kirti hits one good shot) and Kirti is still not generally a good player. Hence, Conclusion II also does not logically follow. Verification / Alternative check: Imagine Kirti is a novice who usually misses the ball but once connects and plays a beautiful shot. The friend truthfully says, 'Kirti played a very good shot.' Yet this does not make Kirti a consistently good player. Similarly, Sajit might dislike cricket but the friend still mentions the incident casually. So the statement can be true regardless of Sajit's interest in cricket. Why Other Options Are Wrong: Option A (Conclusion I alone follows) is wrong because liking cricket is never stated or compelled by the sentence. Option B (Conclusion II alone follows) is wrong because one good shot does not logically prove that Kirti is a generally good player. Option D (Both conclusions follow) is wrong because neither conclusion is guaranteed by the given statement. Common Pitfalls: Students often confuse 'plausible' with 'logically certain'. It may be reasonable to suspect that Sajit likes cricket or that Kirti is good, but the question asks what must follow. Another pitfall is reading additional information into the sentence, such as assuming the friend would only speak about cricket to a cricket lover, which is not necessarily true. Final Answer: Since neither Sajit's liking of cricket nor Kirti's overall skill level is guaranteed by the given remark, neither conclusion I nor conclusion II logically follows from the statement.

Question 18

Given that all notebooks are diaries and all books are notebooks, which of the conclusions about diaries and books must logically follow?

Accepted Answer

Introduction / Context: This is a standard syllogism question involving three categories: books, notebooks and diaries. We are given two premises and must decide which conclusions are logically forced by these premises. Such questions test your understanding of subset relationships and how to translate verbal statements like 'All X are Y' into logical diagrams or set relations. Given Data / Assumptions: Statement I: All notebooks are diaries. Statement II: All books are notebooks. Conclusion I: All diaries are books. Conclusion II: All books are diaries. We assume there is at least one book and one notebook, unless otherwise contradicted, in line with typical exam conventions. Concept / Approach: When we read 'All books are notebooks', it means the set of books is fully contained in the set of notebooks. Similarly, 'All notebooks are diaries' means the notebooks set is contained in the diaries set. Combining these tells us how books relate to diaries. But we must be careful not to mistakenly reverse the direction of these subset relationships. The direction 'All X are Y' does not mean 'All Y are X'. Step-by-Step Solution: Step 1: Represent the statements as set relations. Let B be the set of all books, N be the set of all notebooks and D be the set of all diaries. Step 2: 'All books are notebooks' translates to B ⊆ N (every book is a notebook). Step 3: 'All notebooks are diaries' translates to N ⊆ D (every notebook is a diary). Step 4: Combine the two subset relations. If B ⊆ N and N ⊆ D, then B ⊆ D. In words, all books are notebooks and all notebooks are diaries, so all books are diaries. Step 5: Analyse Conclusion II: 'All books are diaries.' This is exactly the relation B ⊆ D, which we just derived. Therefore, Conclusion II definitely follows from the given statements. Step 6: Analyse Conclusion I: 'All diaries are books.' This would mean D ⊆ B. But we only know that B ⊆ N and N ⊆ D, which together give B ⊆ D. There is no information that every diary must also be a notebook or a book. There could be diaries that are not notebooks or books at all, for example, personal diaries that are not notebooks. Step 7: Because we can imagine diaries that are not books, while still keeping the original statements true, Conclusion I does not logically follow. Verification / Alternative check: Example: Suppose there are 10 diaries, out of which 4 are notebooks, and all 4 notebooks are also books. Then, 'All notebooks are diaries' and 'All books are notebooks' are both true. Still, there are 6 diaries which are not books. So 'All diaries are books' is false, but 'All books are diaries' is true. Why Other Options Are Wrong: Option A (Only conclusion I follows) is wrong because Conclusion I does not necessarily hold; we have no evidence that every diary is a book. Option C (Both conclusions follow) is wrong because Conclusion I fails in many possible situations. Option D (Neither conclusion follows) is wrong because we clearly established that all books are diaries (Conclusion II) based on transitivity of subsets. Common Pitfalls: A very common error is to treat 'All X are Y' as if it were 'All Y are X', which is logically incorrect. This is reversing the subset relation. Another pitfall is ignoring transitivity: if each book is a notebook and each notebook is a diary, then each book automatically becomes a diary. Final Answer: Only the statement that all books are diaries is forced by the given information. Hence, Only conclusion II follows.

Question 19

From Nita's remark that Limay's new watch is awesome and her question about where it was bought, what can we logically conclude?

Accepted Answer

Introduction / Context: This verbal reasoning question is about interpreting an everyday conversation and seeing what logically follows from it. Nita sees Limay's new watch and says, 'Oh, that's so awesome. Where did you buy it from?' We must decide whether it logically follows that the watch is attractive and that Nita wants to know where to buy a similar watch. The focus is on reasonable and direct implications of the words spoken, not on far-fetched possibilities. Given Data / Assumptions: Statement: Looking at Limay's new watch, Nita comments, 'Oh, that's so awesome. Where did you buy it from?' Conclusion I: Limay's watch is attractive. Conclusion II: Nita wants to know where to buy a similar watch from. We assume normal conversational meaning of the words 'awesome' and the question about the place of purchase. Concept / Approach: We need to determine which conclusions are directly supported by the statement. In such questions, a conclusion follows when it is a natural and necessary reading of the statement, not when it is merely a remote or forced interpretation. Expressions of admiration and questions about purchase location typically carry clear implications about liking the item and interest in where it was bought. Step-by-Step Solution: Step 1: Interpret Nita's word 'awesome'. In everyday language, calling something awesome is clearly a strong compliment. It implies that she finds the watch very impressive or attractive. Step 2: Therefore, it is fully justified to conclude that Limay's watch is attractive. So Conclusion I is a direct and logical consequence of the statement. Step 3: Now consider Nita's follow-up question: 'Where did you buy it from?' Typically, when someone admires an object and then asks where it was bought, they want this information because they are interested in buying a similar item for themselves or for someone else. Step 4: The question about the place of purchase is not random. It strongly indicates that Nita wants to know how to obtain the same or a similar watch. Thus, Conclusion II is also logically supported by the statement. Step 5: Therefore, both conclusions are reasonable and directly follow from the given statement under normal conversational interpretation. Verification / Alternative check: It is hard to imagine a normal context where Nita calls the watch 'awesome' but does not actually find it attractive. The word itself is a strong positive evaluation. Similarly, it is rare for someone to ask 'Where did you buy it from?' without any interest in the place of purchase. This question practically implies curiosity about the shop or brand so that one can potentially buy it. Why Other Options Are Wrong: Option B (Conclusion II alone follows) is wrong because it ignores the clear implication that 'awesome' means the watch is attractive, so Conclusion I must also follow. Option C (Neither conclusion follows) is wrong because it denies both obvious implications of admiration and inquiry about purchase location. Option D (Conclusion I alone follows) is wrong because asking where it was bought strongly supports Conclusion II as well. Common Pitfalls: A common mistake is to be over-cautious and reject reasonable conclusions by insisting on only literal meanings, ignoring normal conversational context. Another pitfall is to treat logical reasoning questions as if nothing beyond the exact words can ever be inferred, which is not how such verbal inference questions are designed. Final Answer: Since Nita's comment shows that she finds the watch impressive and her question indicates interest in where to purchase such a watch, both Conclusion I and Conclusion II logically follow.

Question 20

L, M, N, O and P stand in a circle facing the centre. Using the given statements about who is next to whom, who is standing to the right of L?

Accepted Answer

Introduction / Context: This is a circular arrangement and data sufficiency problem. Five people L, M, N, O and P are standing in a circle facing the centre. We need to identify who is standing to the right of L, using the given statements about which people stand next to each other and on which side. The core concepts here are circular seating, 'right of' in a circle, and checking whether a set of statements is enough to uniquely determine the answer. Given Data / Assumptions: People: L, M, N, O, P. They are standing in a circle, facing the centre. Question: Who is standing immediately to the right of L? Statement 1: Next to L are P and M. (So L has P on one side and M on the other, but we do not yet know which is on the right and which is on the left.) Statement 2: O is standing to the right of P. Statement 3: O is standing to the left of N. All face the centre, so 'right' means the neighbour on the clockwise side when we look at them from above, using the common convention in such problems. Concept / Approach: We must check the sufficiency of statements. A statement (or combination of statements) is sufficient if it leads to a unique answer for who is to the right of L, without any ambiguity. We should test: Statement 1 alone, Statement 2 alone, and then Statements 1 and 2 together. Statement 3 is additional information but, given the options, the critical test is whether Statements 1 and 2 together can fix the person to L's right. Step-by-Step Solution: Step 1: Use Statement 1 alone: 'Next to L are P and M.' This tells us L's two neighbours are P and M, but does not specify which one is on the right side. So L could have P on the right and M on the left, or M on the right and P on the left. Hence, Statement 1 alone is not sufficient. Step 2: Use Statement 2 alone: 'O is standing to the right of P.' This gives information only about P and O. It does not involve L at all, so we cannot know who stands to the right of L. Therefore, Statement 2 alone is also not sufficient. Step 3: Combine Statement 1 and Statement 2. From Statement 1, we know L is between P and M. From Statement 2, O is to the right of P. Because they form a circle facing the centre, consistent arrangements that satisfy both statements can be constructed. When all valid arrangements satisfying both Statement 1 and Statement 2 are examined, L always has the same person to the right. Step 4: In all consistent arrangements, P ends up on the right side of L and M on the left side of L. Hence, combining Statement 1 and Statement 2 uniquely fixes that P is to the right of L. Step 5: Statement 3, 'O is standing to the left of N', further restricts positions of O and N but does not change the fact already determined from Statements 1 and 2: P is to the right of L. Thus, Statements 1 and 2 are already sufficient. Verification / Alternative check: Try constructing different circular orders satisfying Statement 1 and Statement 2. You will see that although the entire circle can be rotated, the relative positions force P to be on L's right in every valid arrangement. Because the rotation of the whole circle does not change who is to the immediate right of L, the answer remains uniquely determined: P is to L's right. Why Other Options Are Wrong: Option A (Statement 1 and 2 are not sufficient) is wrong because, as shown, together they uniquely determine that P is to the right of L. Option C (The statements are insufficient) suggests that even with all the available statements we cannot decide, but we actually can: P is always to the right of L when the conditions are satisfied. Option D (Statement 1 alone is sufficient) is wrong because Statement 1 alone leaves ambiguity: P could be either right or left of L. Common Pitfalls: A common mistake is to forget that neighbours in a circle can be permuted in more than one way if side information (left/right) is missing. Another error is not considering all distinct circular arrangements or misinterpreting 'right of' for people facing the centre. Final Answer: Since only the combination of Statement 1 and Statement 2 allows us to uniquely determine who stands to the right of L, Statements 1 and 2 together are sufficient.

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