Question 1

A, B, C, D and E appeared in the same examination. A gets more marks than B but fewer marks than C. D gets fewer marks than E but more marks than A. If C gets fewer marks than D, then who among A, B, C, D and E obtains the highest marks?

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Introduction / Context: This comparison problem involves ranking five students by their marks using given inequalities. Each statement compares two or three students, and you must combine these inequalities to obtain a complete order from lowest to highest marks. Once that order is known, identifying the highest scorer is straightforward. These types of questions develop comfort with inequality chaining and relational reasoning. Given Data / Assumptions: A scores more marks than B but fewer marks than C, so B < A < C. D scores fewer marks than E but more marks than A, so A < D < E. We are additionally told that C scores fewer marks than D, so C < D. We assume all marks are different and can be arranged in a strict order. Concept / Approach: The idea is to combine the inequalities step by step. Starting from B < A < C, and A < D < E, we can place A in a chain where B is below and C is above. Then we insert D and E accordingly. The extra condition C < D tells us how C and D compare, allowing us to fit all five students into a single sequence. The person at the top of this sequence has the highest marks. Step-by-Step Solution: From “A gets more marks than B but fewer than C”, we write B < A < C. From “D gets fewer marks than E but more than A”, we write A < D < E. Combine these two chains initially as B < A < C and A < D < E. At this stage, the relative ordering of C and D is not fixed. We are then told that “C gets fewer marks than D”, which is C < D. Now we can merge everything: B is below A, A is below C, C is below D, and D is below E. Thus the full order from lowest to highest is B < A < C < D < E. From this chain, E is clearly at the top, so E obtains the highest marks. Verification / Alternative check: We can verify by assigning sample numerical scores that respect the inequalities. For example, take B = 10, A = 20, C = 30. Then choose D = 40 and E = 50. These values satisfy B < A < C, A < D < E, and C < D. With these values, E clearly has the highest marks. Any other choice of numbers respecting the same inequality structure still places E at the top, confirming that E must be the highest scorer. Why Other Options Are Wrong: C cannot be the highest because C is explicitly less than D, and D is less than E. D cannot be the highest because D is still less than E. A is less than C and D and therefore cannot be highest. B is even lower, as B is less than A. Only E stands higher than everyone else in the combined chain. Common Pitfalls: A frequent error is to overlook the additional condition C < D and conclude that C is highest based only on the first comparison B < A < C. Another pitfall is to mix up “less than” and “more than” when translating the verbal statements into inequalities. Writing each inequality separately and then merging them carefully helps avoid confusion. Final Answer: The student who obtains the highest marks among A, B, C, D and E is E.

Question 2

In the English alphabet, which letter is 13th from the right end when you count from Z backwards towards A?

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Introduction / Context: This question tests your understanding of positions of letters in the English alphabet when counting from the right end, that is from Z towards A. You must find which letter lies at a specific position from the right. Such alphabet position questions are common in reasoning sections and are straightforward if you know basic positional relationships. Given Data / Assumptions: The English alphabet in order from left to right is A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z. The 1st letter from the left is A and the 26th is Z. We want the 13th letter from the right end, that is counting from Z backwards towards A. Concept / Approach: There are two ways to handle this. One is to count directly from Z backwards, which is simple because 13 is not a large number. The other is to use a positional relation: the k-th letter from the right is the (27 - k)-th letter from the left, since there are 26 letters in total. Using this formula turns a “from the right” position into a more familiar “from the left” position. Step-by-Step Solution: Let us use the relation method. If a letter is k-th from the right in a 26 letter alphabet, then its position from the left is 27 - k. Here k = 13. So the position from the left is 27 - 13 = 14. Now list or recall the alphabet sequence up to the 14th letter: A(1), B(2), C(3), D(4), E(5), F(6), G(7), H(8), I(9), J(10), K(11), L(12), M(13), N(14). The 14th letter from the left is N. Therefore, the 13th letter from the right is N. Verification / Alternative check: As a direct check, we can count backwards from Z. From the right: Z(1), Y(2), X(3), W(4), V(5), U(6), T(7), S(8), R(9), Q(10), P(11), O(12), N(13). We again land on N as the 13th letter from the right. Both methods agree, confirming that N is the correct answer. Why Other Options Are Wrong: L is the 12th letter from the left, so from the right that would correspond to another position. M is 13th from the left, not 14th. O and P are 15th and 16th from the left respectively. None of these correspond to the 13th position from the right according to the relation 27 - k. Only N satisfies the required position. Common Pitfalls: A common mistake is to confuse “13th from right” with “13th from left” or to forget the 27 - k relation. Some candidates also miscount when listing the alphabet in their mind. Writing down at least part of the sequence A to Z and marking positions is a good way to avoid these errors, especially under exam pressure. Final Answer: The letter that is 13th from the right end in the English alphabet is N.

Question 3

In a row of books, a book of English is 16th from the left end. A book of Mathematics is 12th from the right end. The Mathematics book is 6th to the right of the English book. How many books are there in the row in total?

Accepted Answer

Introduction / Context: This is another rank and position problem with two specific books in a row. You are given each book’s position from one end and the relative separation between them. Using this information, you must find the total number of books in the row. These questions practice moving between left side positions, right side positions and total counts using standard relationships. Given Data / Assumptions: The English book is 16th from the left end of the row. The Mathematics book is 12th from the right end of the row. The Mathematics book is 6th to the right of the English book. All books are arranged in a straight row with no gaps in between. Concept / Approach: First, use the relative information that the Mathematics book is 6th to the right of the English book to determine its position from the left. Then, use the relation between left and right positions for a known total N: if an item is at position L from the left and R from the right, then the total number of items is N = L + R - 1. Substituting the known left and right positions of the Mathematics book into this formula gives the total number of books. Step-by-Step Solution: Let the position of the English book from the left be E = 16. The Mathematics book is 6th to the right of the English book. So its position from the left, call it M, is M = 16 + 6 = 22. We are told that the Mathematics book is also 12th from the right end. Let the total number of books be N. For the Mathematics book, we then have left position L = 22 and right position R = 12. Use the formula N = L + R - 1. Substitute L = 22 and R = 12 to get N = 22 + 12 - 1. Compute: 22 + 12 = 34, and 34 - 1 = 33. Therefore, there are 33 books in the row. Verification / Alternative check: Check consistency by recomputing positions. If N = 33, a book at position 22 from the left has position from the right equal to 33 - 22 + 1 = 12, which matches the given position of the Mathematics book from the right. Also, the English book at position 16 and the Mathematics book at 22 are separated by 6 positions when counting to the right, since 22 - 16 = 6. This confirms that N = 33 satisfies all given conditions. Why Other Options Are Wrong: If N were 32 or 34, a book at position 22 from the left would not be 12th from the right. For N = 32, the right position would be 32 - 22 + 1 = 11. For N = 34, it would be 34 - 22 + 1 = 13. Similar contradictions arise for 31 or 30. Only N = 33 maintains both the 22nd position from the left and the 12th from the right for the Mathematics book while preserving the separation of 6 positions to the right of the English book. Common Pitfalls: A common error is to misinterpret “6th to the right” and use 5 instead of 6 when adding, or to forget the -1 term in the formula N = L + R - 1. Some candidates also confuse the positions of the two books and mistakenly use the English book’s right position, which is not given. Working step by step, and clearly labeling positions, helps avoid these mistakes. Final Answer: The total number of books in the row is 33.

Question 4

Hitesh, Sunny, Vicky, Nitin and Bharat are arranged in order of decreasing height from the top, so that the tallest is at the top and the shortest is at the bottom. Hitesh is in the third position from the top. Bharat is somewhere between Nitin and …

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Introduction / Context: This is a height comparison and ordering problem involving five friends. They are arranged from top to bottom in order of decreasing height, meaning the tallest stands at the top and the shortest at the bottom. Using a few relative placement clues, you must find who is at the top and therefore has the maximum height. These questions train your ability to build and interpret ordered sequences from partial information. Given Data / Assumptions: The friends are Hitesh, Sunny, Vicky, Nitin and Bharat. They are arranged from top to bottom in decreasing order of height: position 1 is tallest, position 5 is shortest. Hitesh is at the third position from the top. Bharat is between Nitin and Hitesh in this order. Nitin is not at the bottom position. We need to identify who has the maximum height, that is who stands at the top. Concept / Approach: Since positions are fixed from 1 (top) to 5 (bottom), we place Hitesh at position 3. Bharat must be between Nitin and Hitesh, which means in the vertical order either Nitin is above Bharat and Bharat is above Hitesh, or Hitesh is above Bharat and Bharat is above Nitin. These two possibilities give us two different patterns for Nitin and Bharat. We then apply the constraint that Nitin is not at the bottom to eliminate the invalid pattern. Once that is done, the remaining two friends, Sunny and Vicky, must occupy the remaining positions, and we can see who ends up at the top. Step-by-Step Solution: Label the positions from top to bottom as 1, 2, 3, 4 and 5, with 1 being the tallest. Hitesh is at position 3 by the given condition. Bharat is between Nitin and Hitesh. In a vertical ordering from top to bottom, this can happen in two ways: (a) Nitin above Bharat above Hitesh, giving Nitin, Bharat, Hitesh in that order. (b) Hitesh above Bharat above Nitin, giving Hitesh, Bharat, Nitin in that order. Consider case (a). With Hitesh fixed at position 3, Bharat must be at position 2 and Nitin at position 1 for the order Nitin (1), Bharat (2), Hitesh (3). In this case, Nitin is at position 1 and is clearly not at the bottom, satisfying the condition that Nitin is not at the bottom. Sunny and Vicky would then occupy positions 4 and 5 in some order. Consider case (b). With Hitesh at position 3, Bharat must be at position 4 and Nitin at position 5 for the order Hitesh (3), Bharat (4), Nitin (5). This places Nitin at the bottom, which contradicts the statement that Nitin is not at the bottom. Therefore case (b) is impossible, and case (a) must be correct. In this valid case, Nitin stands at position 1 and is therefore the tallest. Verification / Alternative check: We can verify the arrangement in case (a). Place Nitin at 1, Bharat at 2 and Hitesh at 3. This automatically satisfies that Bharat is between Nitin and Hitesh. With Sunny and Vicky at positions 4 and 5 in any order, Nitin is not at the bottom, which matches the given condition. No other pattern for placing Nitin and Bharat with Hitesh at 3 respects both the “between” condition and the restriction on Nitin. Thus Nitin must be at the top and is tallest. Why Other Options Are Wrong: Hitesh cannot be tallest because he is fixed at the third position. Bharat cannot be tallest because in the valid arrangement he is at position 2, below Nitin. Sunny and Vicky must occupy positions 4 and 5, which are lower than position 1 and therefore correspond to shorter heights. None of these friends can exceed Nitin’s position in height. Common Pitfalls: A common mistake is to assume that Hitesh being in the middle automatically makes him the tallest or shortest, which is incorrect. Another pitfall is to misinterpret “between Nitin and Hitesh” and place Bharat at a corner or outside the correct segment. Some candidates also ignore the condition that Nitin is not at the bottom, allowing an invalid arrangement. Carefully testing each possible order and checking all conditions avoids these errors. Final Answer: The person who has the maximum height among the five friends is Nitin.

Question 5

In a group of five buildings named Pearl Towers, Sky Towers, Unity Towers, Cyber Towers and Indus Towers, Pearl Towers is taller than Sky Towers but shorter than Unity Towers. Unity Towers and Cyber Towers are of the same height, and Pearl Towers is…

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Introduction / Context: This verbal reasoning question tests your ability to compare and order items by height using a set of relational statements. Such ranking and ordering problems are very common in competitive exams and help to check whether you can convert English sentences into a clear logical order. Given Data / Assumptions: Buildings: Pearl Towers (P), Sky Towers (S), Unity Towers (U), Cyber Towers (C), Indus Towers (I). P is taller than S. P is shorter than U. U and C are of the same height. P is shorter than I. No two different buildings, except Unity and Cyber, are of the same height. Concept / Approach: We will use inequality type relations (taller/shorter) to place each building in increasing order of height. Once we know the smallest (shortest) building, we can easily identify the second shortest by looking at the next item in the ordered list. Step-by-Step Solution: Step 1: From “Pearl Towers is taller than Sky Towers”, we write S < P in terms of height. Step 2: From “Pearl Towers is shorter than Unity Towers”, we get P < U. Step 3: From “Unity Towers and Cyber Towers are of same height”, we note U = C. Step 4: From “Pearl Towers is shorter than Indus Towers”, we get P < I. Step 5: Combine all relations around Pearl Towers: S < P < U, S < P < C, and S < P < I. Step 6: Clearly, Sky Towers is shorter than Pearl Towers, and no other building is given as shorter than Sky Towers. So, Sky Towers is the shortest. Step 7: Buildings Unity, Cyber and Indus are all taller than Pearl Towers, so they must stand above Pearl Towers in the height order. Step 8: Therefore, after the shortest (Sky Towers), the next taller building must be Pearl Towers, independent of the exact order among Unity, Cyber and Indus. Verification / Alternative check: Even if Indus Towers is the tallest or Unity and Cyber are placed anywhere above Pearl Towers, the only strict information about the lower end is that S is below P and all others are above P. So the relative positions of U, C and I do not affect which building is the second shortest. Why Other Options Are Wrong: Sky Towers: It is the shortest, not the second shortest, because it is explicitly shorter than Pearl Towers and no building is said to be shorter than Sky Towers. Indus Towers: It is taller than Pearl Towers, so it cannot be second from the bottom. Unity Towers: Unity is taller than Pearl Towers, so it must be above Pearl Towers in the order. Cyber Towers: Cyber Towers has the same height as Unity Towers, which is taller than Pearl Towers, so it is not among the two shortest buildings. Common Pitfalls: Many learners overthink the exact order between Unity, Cyber and Indus even though it is not required. The question only asks for the second shortest, so you only need to focus on the lower end of the order, not the whole ranking. Another common mistake is to think that if we do not know the entire order uniquely, we cannot answer the question, which is not true here. Final Answer: Thus, the second shortest building in the group is Pearl Towers.

Question 6

In a class, Gowtham ranks eighteenth from the top. You are given additional information about the total number of students or about another student's position. Based on the given statements, what is Gowtham's rank when counted from the last in the c…

Accepted Answer

Introduction / Context: This is a classic data sufficiency problem from verbal reasoning and aptitude. You are not asked to compute the numerical answer directly at first; instead, you must judge whether the given statements provide enough information to determine Gowtham's rank from the last. Understanding how to relate ranks from the top and from the bottom is the key idea here. Given Data / Assumptions: Gowtham ranks 18th from the top in his class. Statement I: There are 47 students in the class. Statement II: Jagan ranks 10th from the top and 38th from the last in the same class. All ranks are unique and there are no ties. Concept / Approach: When a student is r-th from the top in a class of N students, the rank from the bottom is given by: rank from last = N - r + 1 In data sufficiency questions, we check each statement alone and then together, deciding if they are individually or jointly sufficient to obtain Gowtham's rank from the last. Step-by-Step Solution: Step 1: Using Statement I alone: total students N = 47, Gowtham's rank from top r = 18. Step 2: Apply the formula: rank from last = 47 - 18 + 1 = 30. Step 3: Therefore, Statement I alone is sufficient to find Gowtham's rank from the bottom. Step 4: Now test Statement II alone. Jagan is 10th from the top and 38th from the last. Step 5: For Jagan, total students N = 10 + 38 - 1 = 47. This gives the total class strength again. Step 6: We still have the information from the question stem that Gowtham is 18th from the top, and we now know N = 47 from Statement II. Step 7: Using the same formula, rank from last for Gowtham = 47 - 18 + 1 = 30. Step 8: Thus Statement II alone is also sufficient to give the required rank from the last. Verification / Alternative check: We can confirm that both statements independently fix the total number of students as 47. Once N is known, the conversion between top rank and bottom rank is straightforward and unique, so there is no ambiguity about Gowtham's rank from the last. Why Other Options Are Wrong: Statement I alone is sufficient: This is true, but the option ignores the fact that Statement II alone is also sufficient, so it is incomplete. Both the statements together are needed: This is incorrect because each statement independently gives N = 47, so they are not required together. Statement II alone is sufficient: This is again partially correct but fails to recognize that Statement I alone is also sufficient. Neither I nor II is sufficient: Clearly wrong because each statement leads to a definite answer. Common Pitfalls: Students often think they must use both statements simply because both are provided. In data sufficiency questions, you must test each statement separately before considering them together. Another mistake is forgetting the formula linking top and bottom ranks, which can lead to arithmetic errors or the belief that the information is insufficient when it actually is enough. Final Answer: Therefore, either Statement I or Statement II alone is sufficient to determine Gowtham's rank from the last.

Question 7

In a row of buses, the Panjab bus stands at the 19th position from the right end. The Raftaar bus is 23 places to the left of the Panjab bus and is exactly at the centre of the row. How many buses are standing strictly between the Raftaar bus and th…

Accepted Answer

Introduction / Context: This is a typical ranking and arrangement question involving positions of buses in a single row. The goal is to translate the verbal description into positions counted from one end, find the total number of buses and then compute how many buses lie between two specific positions in the row. Given Data / Assumptions: Panjab bus is 19th from the right end. Raftaar bus is 23 places to the left of the Panjab bus. Raftaar bus is exactly at the centre of the row. All buses are arranged in a straight line, and positions are counted in whole numbers. Concept / Approach: We use two key ideas: Relationship between rank from left and rank from right when total number of items is known. The central position in a row of N buses (where N is odd) is (N + 1) / 2 from either end. We form equations using the information about the centre and the relative distances between the buses to find the total number of buses and then count the buses between two positions. Step-by-Step Solution: Step 1: Let the total number of buses be N. Step 2: Panjab is 19th from the right. From the left, its position = N - 19 + 1 = N - 18. Step 3: Raftaar is 23 places to the left of Panjab, so Raftaar's position from the left = (N - 18) - 23 = N - 41. Step 4: We are told that the Raftaar bus is exactly at the centre of the row. For N buses, the centre position is (N + 1) / 2 from the left. Step 5: Equate these: N - 41 = (N + 1) / 2. Step 6: Multiply by 2: 2N - 82 = N + 1, which gives N = 83. Step 7: The central position from the left is (83 + 1) / 2 = 42, so Raftaar's position from the left is 42. Step 8: The leftmost bus is at position 1. Buses strictly between position 1 and position 42 are from position 2 to position 41. Step 9: Count of buses between them = 41 - 2 + 1 = 40. Verification / Alternative check: We can quickly confirm the values: Panjab from left = N - 18 = 83 - 18 = 65. Distance between Raftaar (42) and Panjab (65) is 23 places, which matches the question. This confirms that our interpretation and calculations are consistent. Why Other Options Are Wrong: 44, 42, 46, 38: All these alternatives correspond to different assumed totals of buses or incorrect counting of buses between two positions. They arise if someone mistakenly includes one of the endpoints or miscomputes the central position. Common Pitfalls: A frequent mistake is to misinterpret “between” and accidentally include one or both endpoint positions in the count. Another error is forgetting to adjust the formula N - rank from right + 1 when converting to rank from the left. Finally, some test takers incorrectly assume an even number of buses, which would not allow a single exact middle bus as described in the problem. Final Answer: The number of buses between Raftaar and the bus at the left end is 40.

Question 8

In a row of boys, Punit occupies the 33rd position from the left end and Ankit occupies the 25th position from the right end. After they interchange their positions in the same row, Punit is now 45th from the left. Based on this information, how man…

Accepted Answer

Introduction / Context: This problem is a standard example of rank and order reasoning. Two boys exchange positions in a row, and you must determine the total number of boys. The key idea is to use the relationship between rank from the left, rank from the right and the total number of boys in the line. Given Data / Assumptions: Before interchange, Punit is 33rd from the left end. Before interchange, Ankit is 25th from the right end. After interchange, Punit becomes 45th from the left end. All boys remain in a single straight row, and no one leaves or joins the row. Concept / Approach: If there are N boys: Rank from right = N - (rank from left) + 1. When two boys interchange positions, each takes the other's original position. We will express the positions of Punit and Ankit in terms of N and then use the new rank after interchange to find N. Step-by-Step Solution: Step 1: Let total number of boys be N. Step 2: Initially, Punit is 33rd from the left; his position from the right would be N - 33 + 1 = N - 32. Step 3: Initially, Ankit is 25th from the right; his position from the left is N - 25 + 1 = N - 24. Step 4: When they interchange positions, Punit takes Ankit's former place. So, after interchange, Punit should be at position N - 24 from the left. Step 5: The question tells us that, after interchange, Punit is actually 45th from the left. Step 6: Therefore, we equate N - 24 = 45. Step 7: Solve for N: N = 45 + 24 = 69. Step 8: Hence, there are 69 boys in the row. Verification / Alternative check: We can verify by computing Ankit's new rank. Before interchange, Ankit was N - 24 from left, which is 69 - 24 = 45. After interchange, Ankit goes to Punit's old position, which is 33rd from the left. From the right, this becomes 69 - 33 + 1 = 37. All positions are consistent, confirming N = 69. Why Other Options Are Wrong: 70, 71, 74, 68: Each of these alternatives would break the equality N - 24 = 45 or would make the new ranks inconsistent. For example, if N were 70, then N - 24 = 46, which does not equal the given final rank 45 from the left. Common Pitfalls: A common mistake is to mix up which position is being swapped. Remember that after the interchange, each boy takes the other's original seat. Another frequent error is forgetting to add 1 when converting ranks from the right to ranks from the left or vice versa, which leads to off-by-one errors and wrong totals. Final Answer: The total number of boys standing in the row is 69.

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