Question 1

Different-subject ranks – Sairam is 23rd from the top in Mathematics and 27th from the bottom in Physics. How many students are there in the class?

Accepted Answer

Introduction / Context:The formula N = top + bottom − 1 works only for the same arrangement. If the two ranks come from different subjects (i.e., different orderings), you cannot combine them to get class size.Given Data / Assumptions:Maths rank: 23rd from top.Physics rank: 27th from bottom.No linkage is given between the two subject-wise orderings.Concept / Approach:Because orderings differ across subjects, “23rd from top” in Maths does not correspond to a fixed bottom-rank complement in Physics. The two values cannot be summed.Step-by-Step Solution:We lack a single, consistent lineup relating both ranks. Therefore, N is undetermined.Verification / Alternative check:Construct counterexamples with the same class size but different Physics ordering; you can realize many possible N values consistent with the stated ranks.Why Other Options Are Wrong:Any fixed number presumes one ordering, which is not provided.Common Pitfalls:Blindly applying N = L + R − 1 across different subjects.Final Answer:Data inadequate

Question 2

Row swap & total – Dilip is 10th from the left; Jagdish is 20th from the right. They swap places and Jagdish becomes 23rd from the right. How many students are in the row?

Accepted Answer

Introduction / Context:When a person’s position is known from one side after a swap, combine left and right ranks for that same final position to compute total N via N = L + R − 1.Given Data / Assumptions:Dilip (before swap): 10th from left.Jagdish (before swap): 20th from right.After swapping, Jagdish is at Dilip’s old seat and is 23rd from right.Concept / Approach:After swap, Jagdish’s left rank equals Dilip’s original left rank (=10). Combine with his new right rank (=23).Step-by-Step Solution:N = left + right − 1 = 10 + 23 − 1 = 32.Verification / Alternative check:Check complements: In a row of 32, 10th from left corresponds to 23rd from right (since 32 − 10 + 1 = 23). Consistent.Why Other Options Are Wrong:33/42/44 violate the complement formula for the observed final ranks.Common Pitfalls:Using Jagdish’s original right rank (20) instead of his final right rank (23) in the formula.Final Answer:32

Question 3

Row swap using one given side – Jaya is 12th from the left; Rekha is 20th from the right. After swapping, Jaya becomes 22nd from the left. How many students are there?

Accepted Answer

Introduction / Context:When a student moves to the other’s seat and we know the new left rank, we can back out the total using the other seat’s original right rank.Given Data / Assumptions:Jaya: 12th from left initially.Rekha: 20th from right initially.After swapping, Jaya is 22nd from left (so she is at Rekha’s old seat).Concept / Approach:Rekha’s old seat had right rank 20 → its left rank is L = N − 20 + 1. After swap, Jaya’s left rank at that seat is 22. Hence N − 20 + 1 = 22.Step-by-Step Solution:N − 19 = 22 ⇒ N = 41.Verification / Alternative check:In a row of 41, 20th from right maps to 22nd from left (41 − 22 + 1 = 20). Consistent.Why Other Options Are Wrong:30/31/34 fail the left/right complement relation implied by the final 22nd position.Common Pitfalls:Forgetting the “+1” when converting right rank to left rank.Final Answer:41

Question 4

Pass–fail ratio with partial ranks – Among passed students: Neeta is 22nd from top; Kalyan is 5 ranks below Neeta and 34th from the bottom. The class pass:fail ratio is 4:1. How many students are in the class?

Accepted Answer

Introduction / Context:This combines two-sided rank within the passed subgroup with an overall pass:fail ratio to determine total class size.Given Data / Assumptions:Neeta (passed) = 22nd from top.Kalyan is 5 ranks below Neeta → 27th from top among passed.Kalyan is 34th from bottom among passed.Pass : Fail = 4 : 1.Concept / Approach:First, compute the number of passed students (P) using Kalyan’s two-sided rank: P = 27 + 34 − 1. Then use the given ratio to get total N.Step-by-Step Solution:P = 27 + 34 − 1 = 60.Pass:Fail = 4:1 → P = 4k ⇒ 60 = 4k ⇒ k = 15.Total N = 5k = 75.Verification / Alternative check:Failed students = N − P = 75 − 60 = 15, matching the 4:1 ratio.Why Other Options Are Wrong:60 is the passed count, not total; 90 contradicts the computed ratio; “Data inadequate” is incorrect because the subgroup data suffices.Common Pitfalls:Using Neeta’s rank to compute P; forgetting to subtract one in two-sided ranks.Final Answer:75

Question 5

Workday deduction with holidays – Seema took leave after 21 Oct and before 27 Oct. Rita took leave on 23 Oct but Seema was present that day. 24 Oct was a public holiday and 26 Oct was Sunday. On which day did Seema take leave?

Accepted Answer

Introduction / Context:We narrow a leave window using attendance information and non-working days. “Leave” is taken on working days, so public holidays and Sundays are typically excluded.Given Data / Assumptions:Seema’s leave: after 21st and before 27th → {22,23,24,25,26}.Seema was present on 23rd (Rita’s leave day) → remove 23.24th is a public holiday → generally not a leave day.26th is Sunday → not a working day.Concept / Approach:Eliminate non-working days and known present days from the allowable window. Remaining feasible working days are the answer.Step-by-Step Solution:Start set: {22,23,24,25,26}.Remove 23 (present), 24 (holiday), 26 (Sunday).Remaining: {22, 25}.Verification / Alternative check:Both 22 and 25 lie strictly between 21 and 27, and neither conflicts with given facts.Why Other Options Are Wrong:Only 22 or only 25 is too specific; the data allow both.Common Pitfalls:Keeping 24 (holiday) or 26 (Sunday) as potential leave days.Final Answer:22nd or 25th October

Question 6

Relative weights with an unknown – Among P, Q, R, S, T (all distinct weights): R is heavier than S but lighter than T; P is lighter than S. Who is the heaviest?

Accepted Answer

Introduction / Context:We have partial inequalities that rank some people but leave one (Q) unconstrained relative to the current maximum. The heaviest could be the known top of the chain or an unconstrained outlier.Given Data / Assumptions:T > R > S.S > P (so T > R > S > P).No relation given for Q vs anyone.Concept / Approach:From the chain, T is above R, S, P. However, Q could be heavier than T or lighter than anyone; nothing excludes Q being the heaviest.Step-by-Step Solution:Chain without Q: T > R > S > P.Insert Q: no constraints → Q can be anywhere.Verification / Alternative check:Construct two scenarios: (i) Q very light → T is heaviest; (ii) Q very heavy → Q is heaviest. Both satisfy all given constraints.Why Other Options Are Wrong:“T” alone ignores the possibility Q > T; “Q” alone ignores T’s current lead without a contrary statement; “Data inadequate” is less precise than the correct disjunction acknowledging both possibilities.Common Pitfalls:Assuming “no info on Q” implies average or middle placement; it does not.Final Answer:Either T or Q

Question 7

Who has the least money? – Four persons A, B, C, D with conditions: (i) A + B = C + D; (ii) B + D > A + C; (iii) A > B.

Accepted Answer

Introduction / Context:We use sum equalities/inequalities to compare individuals. With A+B = C+D and B+D > A+C, we can deduce pairwise relations and identify the least amount.Given Data / Assumptions:a + b = c + d.b + d > a + c.a > b.Concept / Approach:From the equality, express c in terms of a, b, d, then apply the inequality to compare d and a; finally, use c = a + b − d to rank c against b.Step-by-Step Solution:From a + b = c + d ⇒ c = a + b − d.From b + d > a + c and substituting c, we get b + d > a + (a + b − d) = 2a + b − d ⇒ 2d > 2a ⇒ d > a.Since a > b (given) and d > a, we compare c to b: c = a + b − d < a + b − a = b.Therefore, c is the least.Verification / Alternative check:Choose numbers satisfying d > a > b and set c = a + b − d; c will fall below b while equality (i) and inequality (ii) hold.Why Other Options Are Wrong:A and D are both greater than C by the deductions; B is greater than C because c < b.Common Pitfalls:Attempting to add/subtract the two original statements directly without substitution; missing the consequence d > a.Final Answer:C

Question 8

Height ordering – Priya taller than Tiya and shorter than Siya; Riya shorter than Siya but taller than Priya; Riya taller than Diya, who is shorter than Tiya. Arrange in descending height.

Accepted Answer

Introduction / Context:Turn comparative statements into a strict order from tallest to shortest (descending). Ensure all pairwise relations are satisfied.Given Data / Assumptions:Tiya < Priya < Siya.Priya < Riya < Siya.Diya < Tiya.Concept / Approach:Combine the chains. From both, Siya is at the top. Riya is below Siya but above Priya. Priya is above Tiya, and Tiya is above Diya.Step-by-Step Solution:Top: Siya.Next: Riya (since Siya > Riya > Priya).Then: Priya (Priya > Tiya).Then: Tiya (Tiya > Diya).Last: Diya.Verification / Alternative check:Check each original statement against the final sequence; all are satisfied.Why Other Options Are Wrong:They violate at least one given comparison (e.g., putting Priya above Siya).Common Pitfalls:Confusing “shorter than” direction; forgetting Diya is below Tiya.Final Answer:Siya - Riya - Priya - Tiya - Diya

Question 9

Ranking test – family ages ordering: Seema's younger brother Sohan is older than Seeta. Sweta is younger than Deepti but older than Seema. From these facts, who is the eldest among Deepti, Sweta, Seema, Sohan, and Seeta?

Accepted Answer

Introduction / Context:This is a classic ranking/ordering puzzle involving relative ages. We must translate comparative statements into an ordered chain and identify the oldest (maximum) element.Given Data / Assumptions:Sohan is Seema's younger brother ⇒ Sohan is younger than Seema.Sohan is older than Seeta ⇒ Sohan > Seeta.Sweta is younger than Deepti but older than Seema ⇒ Deepti > Sweta > Seema.All people are distinct individuals; ages are comparable (no ties stated).Concept / Approach:Convert each comparison into a chain and then merge the chains carefully. The symbol “>” means “older than.”Step-by-Step Solution:From “younger brother”: Seema > Sohan.Given Sohan > Seeta ⇒ Seema > Sohan > Seeta.From “Sweta younger than Deepti but older than Seema”: Deepti > Sweta > Seema.Merge: Deepti > Sweta > Seema > Sohan > Seeta.Verification / Alternative check:Every statement is satisfied by the merged chain: Sohan younger than Seema, yet older than Seeta; Sweta between Deepti and Seema; Deepti above all those three. No conflicts appear.Why Other Options Are Wrong:Seema is below Sweta; Sweta is below Deepti; Seeta is second youngest. Hence none of them is the eldest.Common Pitfalls:Forgetting “younger brother” implies strict order, not equality; or reversing “older than/younger than.”Final Answer:Deepti

Question 10

Ranking test – convert right-rank to left-rank: Rashmi is 14th from the right end in a row of 40 girls. What is Rashmi's position from the left end?

Accepted Answer

Introduction / Context:Left/right rank conversions rely on a single identity relating total count and positions from either end. This problem checks that formula and careful substitution.Given Data / Assumptions:Total girls N = 40.Rashmi's rank from the right = 14.All are in a single straight line; no gaps/duplicates.Concept / Approach:Use the conversion: position_from_left = N − position_from_right + 1. This counts how many stand before her from the left side.Step-by-Step Solution:position_from_left = 40 − 14 + 1= 26 + 1= 27.Verification / Alternative check:If she is 14th from the right, there are 13 to her right and therefore 40 − 13 − 1 = 26 to her left; counting Rashmi gives 27th from left—consistent.Why Other Options Are Wrong:Values like 25th or 26th come from forgetting the “+1” term; “21th” miscalculates the gap.Common Pitfalls:Dropping the “+1,” or confusing direction (left vs right) especially under time pressure.Final Answer:27th

Question 11

Ranking test – total strength from top and bottom ranks: Kavi ranked 9th from the top and 38th from the bottom in a class. How many students are there in the class in total?

Accepted Answer

Introduction / Context:When one student’s rank from the top and from the bottom are both known, the class size is computed by summing those ranks and subtracting one (to avoid double-counting the same student).Given Data / Assumptions:Kavi's top-rank = 9.Kavi's bottom-rank = 38.Concept / Approach:The formula is: class_size N = top_rank + bottom_rank − 1.Step-by-Step Solution:N = 9 + 38 − 1 = 46.Verification / Alternative check:Imagine 8 students above and 37 below Kavi: 8 + 1 + 37 = 46, confirming the identity.Why Other Options Are Wrong:45 or 44 result from forgetting to include Kavi correctly or misapplying the −1 adjustment.Common Pitfalls:Adding ranks without subtracting 1, which double-counts Kavi.Final Answer:46

Question 12

Ranking test – totals of two separate rows: Row–1: Jeevan is 7th from the start and 11th from the end. Row–2: Vikas is 10th from the start and 12th from the end. How many boys are there in both rows together?

Accepted Answer

Introduction / Context:Each row's total can be found from a single student’s top and bottom ranks using the same identity as earlier; then we add the two row totals.Given Data / Assumptions:Row–1 (Jeevan): top 7th, bottom 11th.Row–2 (Vikas): top 10th, bottom 12th.Concept / Approach:For each row: N = top_rank + bottom_rank − 1. Sum both Ns.Step-by-Step Solution:Row–1 total = 7 + 11 − 1 = 17.Row–2 total = 10 + 12 − 1 = 21.Combined = 17 + 21 = 38.Verification / Alternative check:The counts are independent across rows; nothing in the statement suggests shared students.Why Other Options Are Wrong:40 and 32 arise from arithmetic slips; “Cannot be determined” is incorrect because each row’s total is uniquely determined.Common Pitfalls:Missing the −1 in each row; adding ranks and subtracting −1 only once.Final Answer:38

Question 13

Ranking test – shift and convert ends: 37 boys stand in a row facing the building. Ashwini is 15th from the left end. He moves six places to the right. What is his new position from the right end?

Accepted Answer

Introduction / Context:We perform an intra-row shift (left-to-right) and then convert left-rank to right-rank using the standard identity. Facing direction is uniform, so “left/right” are consistent.Given Data / Assumptions:Total N = 37.Initial left-rank = 15.Shift right by 6 positions ⇒ new left-rank = 21.Concept / Approach:After the shift, compute new right-rank via: position_from_right = N − position_from_left + 1.Step-by-Step Solution:New left-rank = 15 + 6 = 21.Right-rank = 37 − 21 + 1 = 17.Verification / Alternative check:Counting to the right of the new position: there are 16 persons (ranks 22 to 37), so Ashwini is 17th from the right—consistent with the formula.Why Other Options Are Wrong:16th/18th/20th/21st do not match 17 obtained from the identity and direct counting. Hence, among the given choices, the only accurate selection is “None of these.”Common Pitfalls:Forgetting the +1 term; misapplying shift direction; assuming facing reverses left/right (it does not change within a single row).Final Answer:None of these

Question 14

Ranking test – swap and deduce total: In a row of girls, Kamya is 5th from the left and Preeti is 6th from the right. When they exchange positions, Kamya becomes 13th from the left. What is Preeti's position from the right after the exchange?

Accepted Answer

Introduction / Context:Swapping people in fixed seats preserves the seats’ absolute indices. A post-swap rank lets us deduce total N, then convert to the requested rank.Given Data / Assumptions:Before swap: Kamya = 5th from left; Preeti = 6th from right.After swap: Kamya = 13th from left (so she sits in Preeti’s former seat).Concept / Approach:Preeti’s original seat is 13th from left and also 6th from right. Thus N − 13 + 1 = 6, giving N. After swap, Preeti moves to Kamya’s former seat (5th from left), so we convert to right-rank.Step-by-Step Solution:N − 13 + 1 = 6 ⇒ N = 18.Preeti's new right-rank = 18 − 5 + 1 = 14.Verification / Alternative check:Check consistency: a seat 13th from left is indeed 6th from right when N = 18 (since 18 − 13 + 1 = 6).Why Other Options Are Wrong:7th/11th/18th correspond to incorrect N or to converting the wrong seat.Common Pitfalls:Using persons’ ranks post-swap as if they were seat indices pre-swap; forgetting the +1 term in conversions.Final Answer:14th

Question 15

Ranking test – left/right conversion with an offset: In a row of 25 children, Nayan is 14th from the right end. Arun stands 3 places to the left of Nayan. What is Arun's position from the left end?

Accepted Answer

Introduction / Context:We first convert Nayan’s right-rank to a left-rank, then adjust for Arun being 3 to the left (which reduces the left-rank by 3), and finally confirm boundaries.Given Data / Assumptions:N = 25 children in a single row.Nayan: 14th from right.Arun is 3 places to the left of Nayan.Concept / Approach:Use left-rank = N − right-rank + 1, then subtract 3 for the leftward shift to find Arun’s left-rank.Step-by-Step Solution:Nayan left-rank = 25 − 14 + 1 = 12.Arun left-rank = 12 − 3 = 9.Verification / Alternative check:Arun is indeed further left (smaller left-rank) than Nayan; 9 is within 1…25, so it’s feasible.Why Other Options Are Wrong:7th/8th/10th reflect miscounting the 3-position offset or left/right conversion.Common Pitfalls:Adding 3 instead of subtracting when moving left on left-ranks; dropping the +1 in the initial conversion.Final Answer:9th

Question 16

Ranking test – same person counted from both ends: A line of girls is formed. One girl is 19th when counted from both the left end and the right end. How many girls are there in the line?

Accepted Answer

Introduction / Context:If a specific person's rank from both ends is known and it is the same person (not two different), the total equals the sum minus one—because the person is counted in both ranks.Given Data / Assumptions:The same girl is 19th from left and 19th from right.No ties; single-file line.Concept / Approach:Use N = left_rank + right_rank − 1 = 19 + 19 − 1.Step-by-Step Solution:N = 19 + 19 − 1 = 37.Verification / Alternative check:There are 18 girls to her left and 18 to her right; adding her makes 37 total.Why Other Options Are Wrong:38 or 39 double-count the middle girl; 27 is unrelated to the identity.Common Pitfalls:Forgetting to subtract 1 when combining top/bottom ranks of the same person.Final Answer:37

Question 17

Ranking test – rank from the end: Surbhi ranks 18th in a class of 49 students (from the top). What is Surbhi’s rank from the last?

Accepted Answer

Introduction / Context:The position from the last (bottom-rank) is computed by subtracting the top-rank from the class size and then adding one—mirroring left/right conversions in rows.Given Data / Assumptions:Class size N = 49.Surbhi's top-rank = 18.Concept / Approach:Use bottom_rank = N − top_rank + 1.Step-by-Step Solution:bottom_rank = 49 − 18 + 1 = 32.Verification / Alternative check:If 17 students are ahead of Surbhi and 31 are behind, then from the last she is 32nd—consistent.Why Other Options Are Wrong:31 or 35 arise from dropping/adding the “+1,” not from the correct identity.Common Pitfalls:Confusing “from last” with “number behind.” Rank includes the student, so we add one.Final Answer:32

Question 18

Ranking test – integrate overall rank with gender-wise ranks: There are 35 students in a class. Suman ranks third among the girls in the class. Amit ranks fifth among the boys. Suman is one rank below Amit in the overall class ranking (no ties). Wha…

Accepted Answer

Introduction / Context:This problem combines category ranks (within boys/girls) with overall ranks. The key idea is to account for how many boys and girls appear ahead before a given student and to relate two consecutive overall ranks.Given Data / Assumptions:Total students = 35 (exact total is not directly needed).Amit is 5th among boys ⇒ exactly 4 boys are ahead of Amit.Suman is 3rd among girls ⇒ exactly 2 girls are ahead of Suman.Suman’s overall rank is one position below Amit’s overall rank (consecutive), and there are no ties.Concept / Approach:Let Amit’s overall rank be k. Then Suman’s overall rank is k + 1. Among the k people ahead of Suman, there must be (i) the 4 boys ahead of Amit, (ii) Amit himself (a boy), and (iii) the 2 girls ahead of Suman. That totals 7 people.Step-by-Step Solution:Number ahead of Suman = k = 4 (boys) + 1 (Amit) + 2 (girls) = 7.Hence k = 7 ⇒ Amit’s overall rank = 7th.Verification / Alternative check:Then Suman is 8th overall, which is consistent with being just below Amit. The composition (boys/girls) ahead fits the category ranks precisely.Why Other Options Are Wrong:5th or 8th contradict the category counts and the “just below” constraint; “Cannot be determined” is incorrect because the data uniquely fix k.Common Pitfalls:Forgetting to include Amit in the count of people ahead of Suman; or mixing up category ranks with overall ranks.Final Answer:7th

Question 19

Ranking in a row (facing North): Ritesh is 12th from the left end. Sudhir is 22nd from the right end and sits 4 positions to the right of Ritesh. Find the total number of children in the row.

Accepted Answer

Introduction / Context:This is a classic single-row ranking problem. Two positions are given from opposite ends, and a relative offset between the two people is also provided. We need to convert between left-rank and right-rank to compute the total strength of the row.Given Data / Assumptions:Row faces North (orientation does not affect left/right counting, but confirms standard convention).Ritesh is 12th from the left.Sudhir is 22nd from the right.Sudhir is 4th to the right of Ritesh (i.e., Sudhir's left-rank = Ritesh's left-rank + 4).Concept / Approach:Use the identity: right_rank = N − left_rank + 1, where N is the total. Express Sudhir's left-rank from the relative information, then equate it to the formula derived from his right-rank to solve for N.Step-by-Step Solution:1) Ritesh's left-rank L(R) = 12.2) Sudhir is 4 to the right of Ritesh ⇒ L(S) = 12 + 4 = 16.3) Sudhir's right-rank is 22 ⇒ 22 = N − L(S) + 1 = N − 16 + 1 = N − 15.4) Hence N = 22 + 15 = 37.Verification / Alternative check:Convert Sudhir's left-rank back to right with N = 37: right = 37 − 16 + 1 = 22, matching the given.Why Other Options Are Wrong:34, 35, 36: Each fails to satisfy the conversion right = N − 16 + 1 = 22.None of these: There is a valid choice (37).Common Pitfalls:Confusing “to the right of” with a right-end rank; or forgetting the +1 in right = N − left + 1.Final Answer:37

Question 20

Class ranking change: A class has 45 students and a boy is ranked 20th from the top. Two boys join, and his rank drops by one place. What is his new rank from the bottom?

Accepted Answer

Introduction / Context:When class size changes, relative ranks can shift. Here, two students join and the given student drops by one from the top. We are to compute his rank from the bottom after the change.Given Data / Assumptions:Initial size = 45; boy's top-rank = 20.Two new boys join ⇒ new size = 47.His rank “drops by one” from the top ⇒ new top-rank = 21.Concept / Approach:Rank-from-bottom after change is computed by: bottom-rank = N − top-rank + 1 with the new N and the new top-rank.Step-by-Step Solution:1) New class size N = 45 + 2 = 47.2) New top-rank of the boy = 21.3) Bottom-rank = 47 − 21 + 1 = 27.Verification / Alternative check:Counting positions: if he is 21st from top in 47, then 26 stand below him, making his bottom-rank 26 + 1 = 27.Why Other Options Are Wrong:25th, 26th, 28th: Each assumes an incorrect conversion or class size.None of these: The correct answer is present.Common Pitfalls:Forgetting to use the new class size (47) or ignoring the “drops by one” detail.Final Answer:27th

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