Q: Height ordering with partial information: Mukesh is taller than Suresh but shorter than Rakesh. Rakesh is taller than Harish but shorter than Amar. Who is the shortest?

Introduction / Context:The problem provides two chains that overlap only at Rakesh. We must find the shortest person, but some cross-comparisons are missing, leading to multiple consistent orders.Given Data / Assumptions:Suresh < Mukesh < Rakesh.Harish < Rakesh < Amar.No direct comparison between Suresh and Harish.Concept / Approach:Build allowable orders consistent with both chains. If the identity of the shortest varies across valid orders, the answer cannot be uniquely determined.Step-by-Step Exploration:Case 1: If Suresh < Harish, then Suresh may be the shortest.Case 2: If Harish < Suresh, then Harish may be the shortest.Both cases satisfy Suresh < Mukesh < Rakesh and Harish < Rakesh < Amar, so both are possible.Verification / Alternative check:Try sample numeric heights consistent with the inequalities. You can realize both “Suresh shortest” and “Harish shortest” assignments without violating the statements.Why Other Options Are Wrong:Mukesh: Always above Suresh and possibly above Harish.Suresh or Harish individually: Either could be shortest depending on missing cross-comparison.None of these: The intent is that uniqueness fails; the correct meta-answer is “Cannot be determined.”Common Pitfalls:Assuming unprovided comparisons (e.g., assuming Suresh < Harish) without justification.Final Answer:Cannot be determined

Q: Tallest person cannot be fixed: P, Q, T, A, and B have different heights. T is taller than P and B, but shorter than A and Q. P is not the shortest. Who is the tallest?

Introduction / Context:The relations place T below both A and Q, and above P and B. However, there is no comparison between A and Q. With all heights distinct, the tallest must be either A or Q, but we cannot tell which.Given Data / Assumptions:T > P and T > B.T < A and T < Q.P is not the shortest (so B may be the shortest).All heights are distinct.Concept / Approach:Construct consistent orders. Since A and Q are both above T and un-compared with each other, each of the two can be the global maximum in some valid arrangement.Step-by-Step Illustration:1) Put B at the bottom (since P is not the shortest).2) Place P above B but below T (as given).3) Place T above P and B.4) A and Q are above T, but no order is specified between them.5) Scenario A: A > Q > T > P > B ⇒ tallest is A.6) Scenario B: Q > A > T > P > B ⇒ tallest is Q.Verification / Alternative check:Both scenarios satisfy all statements, proving non-uniqueness.Why Other Options Are Wrong:A or Q alone: Either could be tallest; not uniquely determined.P or B: Both lie below T explicitly; neither can be tallest.Common Pitfalls:Forcing an order between A and Q without evidence.Final Answer:Cannot be determined

Question 1

Two-end ranks in one class: Sohan is 7th from the top and 26th from the bottom. How many students are in the class?

Accepted Answer

Introduction / Context:When both top-rank and bottom-rank of the same student are known in a single line, total strength is computed by adding the two and subtracting 1 (as the student is counted twice otherwise).Given Data / Assumptions:Sohan's top-rank = 7.Sohan's bottom-rank = 26.Concept / Approach:Total N = top-rank + bottom-rank − 1.Step-by-Step Solution:N = 7 + 26 − 1 = 32.Verification / Alternative check:7 above Sohan and 25 below him sum to 32 when including Sohan.Why Other Options Are Wrong:31, 33, 34: Off by ±1 or ±2 due to missing the minus 1.None of these: Correct option exists.Common Pitfalls:Forgetting to subtract 1 when combining the two ranks.Final Answer:32

Question 2

Letter positions from both ends: A letter is 5th from the left and 12th from the right in a row. How many letters are in the row?

Accepted Answer

Introduction / Context:When the same object's position is given from both ends in a single row, the total count equals the sum of the two positions minus 1.Given Data / Assumptions:Left-position = 5.Right-position = 12.Concept / Approach:Use N = left + right − 1.Step-by-Step Solution:N = 5 + 12 − 1 = 16.Verification / Alternative check:Converting right to left via N − left + 1 should return 12 for N = 16: 16 − 5 + 1 = 12, consistent.Why Other Options Are Wrong:15, 17, 18: Typical arithmetic slips around the −1 rule.None of these: Correct answer listed.Common Pitfalls:Adding positions without subtracting 1.Final Answer:16

Question 3

Same rank from both ends: Sunita is 11th from both the left end and the right end of a row of girls. How many girls are there in the row?

Accepted Answer

Introduction / Context:If a person is the k-th from both ends in a single row, the total number is 2k − 1 because the person is counted twice when simply adding.Given Data / Assumptions:Sunita is 11th from left and also 11th from right.Concept / Approach:Total N = 2 * 11 − 1.Step-by-Step Solution:N = 22 − 1 = 21.Verification / Alternative check:Positions from both ends sum to N + 1 ⇒ 11 + 11 = 22 = N + 1 ⇒ N = 21.Why Other Options Are Wrong:19, 20, 22: Do not satisfy the symmetry condition 11 + 11 = N + 1.None of these: Correct answer available.Common Pitfalls:Forgetting to subtract 1 after doubling.Final Answer:21

Question 4

Two independent rows: Veena is 12th from the start and 19th from the end in one row, while Sunita is 14th from the start and 20th from the end in another row. How many girls are there in both rows together?

Accepted Answer

Introduction / Context:This item gives two separate rows. For each, use the “sum minus 1” rule to find the individual row size, then add the two totals.Given Data / Assumptions:Row 1 (Veena): left = 12, right = 19.Row 2 (Sunita): left = 14, right = 20.Concept / Approach:For a single row: N = left + right − 1. Compute for both rows and add.Step-by-Step Solution:Row 1: N1 = 12 + 19 − 1 = 30.Row 2: N2 = 14 + 20 − 1 = 33.Total = N1 + N2 = 30 + 33 = 63.Verification / Alternative check:Check each row via right = N − left + 1: For N1 = 30, right = 30 − 12 + 1 = 19; for N2 = 33, right = 33 − 14 + 1 = 20.Why Other Options Are Wrong:61, 65, 72: Misapplication of the formula or arithmetic slips.None of these: A correct option exists (63).Common Pitfalls:Confusing the two rows as one, or forgetting to subtract 1 for each.Final Answer:63

Question 5

Height order logic: Anil is taller than Sunny. Sunny is shorter than Baby. Anil is taller than Bose, and Bose is shorter than Sunny. Baby is shorter than Anil. Who is the shortest?

Accepted Answer

Introduction / Context:We are given comparative height statements. Translating each sentence into inequalities and merging them yields a total order. The question asks for the minimum (shortest).Given Data / Assumptions:Anil > Sunny.Sunny < Baby ⇒ Baby > Sunny.Anil > Bose and Bose < Sunny ⇒ Bose is below Sunny.Baby < Anil ⇒ Anil is above Baby.Concept / Approach:Combine all relations. From Bose < Sunny and Sunny < Baby < Anil (since Baby < Anil and Anil > Sunny), we get a chain: Bose < Sunny < Baby < Anil. The shortest is at the left end.Step-by-Step Solution:1) From “Anil is taller than Sunny” and “Baby is shorter than Anil,” top two are Anil (top) then Baby (below Anil).2) From “Sunny is shorter than Baby,” insert Sunny below Baby.3) From “Bose is shorter than Sunny,” place Bose below Sunny.4) Final order (short to tall): Bose < Sunny < Baby < Anil.Verification / Alternative check:Each original relation is satisfied by the chain above.Why Other Options Are Wrong:Anil/Baby/Sunny: Each is taller than at least one other person.None of these: A correct explicit option exists (Bose).Common Pitfalls:Overlooking “Bose is shorter than Sunny” which pushes Bose to the bottom.Final Answer:Bose

Question 6

Height ordering with partial information: Mukesh is taller than Suresh but shorter than Rakesh. Rakesh is taller than Harish but shorter than Amar. Who is the shortest?

Accepted Answer

Introduction / Context:The problem provides two chains that overlap only at Rakesh. We must find the shortest person, but some cross-comparisons are missing, leading to multiple consistent orders.Given Data / Assumptions:Suresh < Mukesh < Rakesh.Harish < Rakesh < Amar.No direct comparison between Suresh and Harish.Concept / Approach:Build allowable orders consistent with both chains. If the identity of the shortest varies across valid orders, the answer cannot be uniquely determined.Step-by-Step Exploration:Case 1: If Suresh < Harish, then Suresh may be the shortest.Case 2: If Harish < Suresh, then Harish may be the shortest.Both cases satisfy Suresh < Mukesh < Rakesh and Harish < Rakesh < Amar, so both are possible.Verification / Alternative check:Try sample numeric heights consistent with the inequalities. You can realize both “Suresh shortest” and “Harish shortest” assignments without violating the statements.Why Other Options Are Wrong:Mukesh: Always above Suresh and possibly above Harish.Suresh or Harish individually: Either could be shortest depending on missing cross-comparison.None of these: The intent is that uniqueness fails; the correct meta-answer is “Cannot be determined.”Common Pitfalls:Assuming unprovided comparisons (e.g., assuming Suresh < Harish) without justification.Final Answer:Cannot be determined

Question 7

Tallest person cannot be fixed: P, Q, T, A, and B have different heights. T is taller than P and B, but shorter than A and Q. P is not the shortest. Who is the tallest?

Accepted Answer

Introduction / Context:The relations place T below both A and Q, and above P and B. However, there is no comparison between A and Q. With all heights distinct, the tallest must be either A or Q, but we cannot tell which.Given Data / Assumptions:T > P and T > B.T < A and T < Q.P is not the shortest (so B may be the shortest).All heights are distinct.Concept / Approach:Construct consistent orders. Since A and Q are both above T and un-compared with each other, each of the two can be the global maximum in some valid arrangement.Step-by-Step Illustration:1) Put B at the bottom (since P is not the shortest).2) Place P above B but below T (as given).3) Place T above P and B.4) A and Q are above T, but no order is specified between them.5) Scenario A: A > Q > T > P > B ⇒ tallest is A.6) Scenario B: Q > A > T > P > B ⇒ tallest is Q.Verification / Alternative check:Both scenarios satisfy all statements, proving non-uniqueness.Why Other Options Are Wrong:A or Q alone: Either could be tallest; not uniquely determined.P or B: Both lie below T explicitly; neither can be tallest.Common Pitfalls:Forcing an order between A and Q without evidence.Final Answer:Cannot be determined

Question 8

Who is the shortest? A, B, C, D, and E have different heights. D is only shorter than B (so D is second-tallest). E is shorter than both A and C. Identify the shortest person.

Accepted Answer

Introduction / Context:We must infer a full order (or enough of it) from pairwise comparisons. “D is only shorter than B” pins D as the second-tallest and B as tallest. Another clause pushes E below A and C. Combined, these fix E at the bottom.Given Data / Assumptions:D is only shorter than B ⇒ B is tallest, D is second-tallest.E is shorter than A and C ⇒ A > E and C > E.All heights are distinct.Concept / Approach:Since D is taller than everyone except B, D > A, D > C, and D > E. Also B > D. Because E is shorter than A and C, and also shorter than D (second-tallest) and B (tallest), E must be the global minimum.Step-by-Step Ordering:1) Fix B at top, D second.2) E is below A and C, and also below D and B ⇒ E is below all others.3) The relative order among A and C is unspecified, but the shortest (E) is uniquely determined.Verification / Alternative check:Try any heights consistent with B > D and D > (A, C, E) and (A, C) > E. E always ends up at the bottom.Why Other Options Are Wrong:A or C: Each is above E.Data inadequate: Not so; E is forced to the bottom by the constraints.Common Pitfalls:Misreading “only shorter than B” as “shorter than only B and someone else.” It strictly means D is second-tallest.Final Answer:E

Question 9

Tallest building: Four buildings A, B, C, D have distinct heights. A is only higher than D. B is shorter than C but higher than A. Which building is the highest?

Accepted Answer

Introduction / Context:We are to find the maximum (tallest) in a partially ordered set of four items using concise comparative statements.Given Data / Assumptions:A is only higher than D ⇒ A > D and A < (B, C).B is shorter than C but higher than A ⇒ C > B > A.All heights are distinct.Concept / Approach:Combine the inequalities: C sits above B, which sits above A, which sits above D. Therefore, C is the tallest and D is the shortest.Step-by-Step Ordering:From “A only higher than D” we place A above D and below both B and C.From “B shorter than C but higher than A,” place B between C and A.Final chain: C > B > A > D.Verification / Alternative check:Every original relation is satisfied by C > B > A > D.Why Other Options Are Wrong:A, B, D: Not the maximum in the derived chain.None of these: A specific correct choice exists (C).Common Pitfalls:Misinterpreting “only higher than D” (it fixes A exactly one place above D and below the other two).Final Answer:C

Question 10

Most intelligent among four: N is more intelligent than M. M is not as intelligent as Y (so Y > M). X is more intelligent than Y but not as good as N. Who is the most intelligent?

Accepted Answer

Introduction / Context:We have four entities with a strict ordering induced by comparative statements. The goal is to identify the maximum.Given Data / Assumptions:N > M.Y > M (since M is not as intelligent as Y).X > Y but X < N.Concept / Approach:Place X above Y, and both above M, but keep X below N. As N is above M and also above X, N must be the overall maximum.Step-by-Step Solution:1) Start with Y > M.2) Insert X with X > Y.3) Place N such that N > M and N > X (since X < N).4) Final order (low→high): M < Y < X < N.Verification / Alternative check:All statements are satisfied by the chain above; N is on top.Why Other Options Are Wrong:M, Y, X: Each is explicitly below someone else; none is the absolute maximum.Common Pitfalls:Forgetting that “X is not as good as N” puts N above X.Final Answer:N

Question 11

Tallest among four: Barun is taller than Sanjay. Bipul is taller than Barun. Krishna is shorter than Bipul but taller than Barun. Who is the tallest?

Accepted Answer

Introduction / Context:We are to identify the maximum in a set of four with provided pairwise comparisons.Given Data / Assumptions:Barun > Sanjay.Bipul > Barun.Krishna < Bipul and Krishna > Barun.Concept / Approach:From the relations: Bipul exceeds Barun and also exceeds Krishna (since Krishna < Bipul). Sanjay is below Barun, so he is below Bipul too. Therefore, Bipul is the tallest.Step-by-Step Ordering:1) Place Sanjay at the bottom relative to Barun (Barun > Sanjay).2) Place Bipul above Barun (Bipul > Barun).3) Insert Krishna between Bipul and Barun as Krishna > Barun but < Bipul.4) Final order (short→tall): Sanjay < Barun < Krishna < Bipul.Verification / Alternative check:All original statements are satisfied by the chain above; the top is Bipul.Why Other Options Are Wrong:Barun/Krishna: Each is below Bipul.Sanjay: Lowest among the four.Common Pitfalls:Missing that “Krishna is shorter than Bipul” rules out Krishna as tallest.Final Answer:Bipul

Question 12

Shortest among five: J, K, L, M, N have different heights. M is only shorter than J (so M is second-tallest). K is not as tall as N, and N is shorter than L. Who is the shortest?

Accepted Answer

Introduction / Context:We must locate the minimum height given several partial comparisons, including a strong statement that pins J and M near the top.Given Data / Assumptions:M is only shorter than J ⇒ J is tallest, M is second-tallest.K is not as tall as N ⇒ N > K.N is shorter than L ⇒ L > N.All distinct heights.Concept / Approach:From “M only shorter than J,” we know J > M and M ≥ everyone else. That means M ≥ L, N, K. Combined with L > N > K, it follows that among {L, N, K}, K is at the bottom. Since both J and M are above that trio, K is the global minimum.Step-by-Step Ordering:1) Fix top: J (1st), M (2nd).2) From L > N > K, place K at the bottom within this sub-chain.3) Because M is not shorter than any of L, N, K, none of them can lie above M; hence the shortest overall is K.Verification / Alternative check:Assign sample heights (e.g., J=10, M=9, L=8, N=7, K=6). All statements hold and K is shortest.Why Other Options Are Wrong:J, L, N: Each is above at least one other person.M: Second tallest by statement.Common Pitfalls:Misreading “only shorter than J” and accidentally placing someone above M.Final Answer:K

Question 13

Age order from statements: Amit and Sumit are twins (same age). Richa is younger than Sumit. Richa is younger than Jyotsana but older than Saurabh. Sumit is younger than Jyotsana. Who is the eldest among them?

Accepted Answer

Introduction / Context:This is an age-ordering problem with clear pairwise comparisons, including a twin pair (equal ages). We must identify the oldest person given the constraints.Given Data / Assumptions:Amit and Sumit are twins ⇒ Amit = Sumit.Richa < Sumit.Richa < Jyotsana and Richa > Saurabh.Sumit < Jyotsana.Concept / Approach:Combine all inequalities into a single order. From Sumit < Jyotsana and Amit = Sumit, both twins are below Jyotsana. With Richa less than Sumit, and Saurabh less than Richa, the unique topmost candidate is Jyotsana.Step-by-Step Solution:1) Twins: Amit = Sumit.2) Sumit < Jyotsana ⇒ Jyotsana above both Sumit and Amit.3) Richa < Sumit and Richa < Jyotsana; also Saurabh < Richa.4) Consolidated order (youngest→oldest): Saurabh < Richa < (Amit = Sumit) < Jyotsana.Verification / Alternative check:Every relation is satisfied by the chain above; no one is above Jyotsana, so she is the eldest.Why Other Options Are Wrong:Amit: Same age as Sumit, and Sumit is younger than Jyotsana.Richa, Saurabh: Each is explicitly younger than at least two others.None of these: A correct explicit option exists (Jyotsana).Common Pitfalls:Overlooking that “twins” implies equality, not relative order between the two but still below Jyotsana per the given.Final Answer:Jyotsana

Question 14

Relative ages and eldest identification: Ram is twice the age of Shyam and half the age of Sohan. Shyam is older than Mohan. Who is the eldest among Ram, Shyam, Sohan, and Mohan?

Accepted Answer

Introduction / Context:Ranking-test problems with ages usually give proportional relations (e.g., “twice,” “half”) and a couple of comparative statements. The task is to translate the language into simple algebra or consistent ordering and then identify the extreme (eldest or youngest).Given Data / Assumptions:Ram = 2 * Shyam.Ram = (1/2) * Sohan ⇒ Sohan = 2 * Ram.Shyam is older than Mohan.All ages are positive and measured at the same time (no time shift).Concept / Approach:Convert each sentence to a relation. From Ram = 2*Shyam, Ram is older than Shyam. From Sohan = 2*Ram, Sohan is older than Ram (and hence older than Shyam). The note that Shyam is older than Mohan only affects the lower end of the order; it does not challenge Sohan’s status at the top.Step-by-Step Solution:Let Shyam = x (x > 0).Then Ram = 2x.Sohan = 2 * Ram = 4x.Given Shyam > Mohan ⇒ Mohan Thus, in descending order: Sohan (4x) > Ram (2x) > Shyam (x) > Mohan (< x).Verification / Alternative check:Pick an easy numeric example for intuition: let Shyam = 10. Then Ram = 20, Sohan = 40, and Mohan < 10 (say 9). Clearly, 40 (Sohan) is the maximum age. Any positive scaling preserves the order.Why Other Options Are Wrong:Mohan: Explicitly younger than Shyam, so cannot be eldest.Shyam: Half of Ram; cannot exceed Ram or Sohan.Ram: Half of Sohan; therefore younger than Sohan.None of these: Incorrect because Sohan fits and is in the list.Common Pitfalls:Confusing “twice” and “half,” or treating “Shyam older than Mohan” as impacting who is eldest at the top. Proportional relations dominate extremes here.Final Answer:Sohan

Question 15

Arrange by age and by wealth (decreasing): P, Q, R, and S are four males. • P is the eldest but not the poorest. • R is the richest but not the eldest. • Q is older than S, but not older than P or R. • P is richer than Q, but not richer than S. Find…

Accepted Answer

Introduction / Context:This classic two-criterion ranking puzzle asks you to produce two separate orders—by age and by wealth—given comparative constraints. The key is to keep the two orderings independent and avoid mixing statements across criteria.Given Data / Assumptions:Age statements: P is eldest; R is not eldest; Q older than S, but Q is not older than P or R ⇒ R is older than Q; all ages distinct.Money statements: R is richest; P richer than Q but not richer than S ⇒ S > P > Q; since R is richest, overall: R > S > P > Q; all amounts distinct.Concept / Approach:Treat age and money as two separate partial orders. For age, “P eldest” and “Q not older than P or R” forces R above Q, giving P > R > Q > S. For money, combine “R richest” with “S > P > Q” to get R > S > P > Q.Step-by-Step Solution:Age (descending): P (eldest) > R > Q > S ⇒ PRQS.Money (descending): R (richest) > S > P > Q ⇒ RSPQ.Match with options: PRQS, RSPQ appears in option B.Verification / Alternative check:Try to violate any relation: making Q older than R contradicts “Q is not older than R.” Making P richer than S contradicts “P is not richer than S.” The found orders satisfy all constraints simultaneously.Why Other Options Are Wrong:Orders placing Q above R in age or P above S in wealth break the given conditions.Any option with different sequences fails at least one bullet.Common Pitfalls:Mixing age and wealth statements (e.g., using “richest” to infer age). Keep dimensions separate, then pick the option that matches both.Final Answer:PRQS (age), RSPQ (money)

Question 16

Shortest among five cricketers: Dhoni is taller than Virat but shorter than Raina. Rohit is shorter than Dhoni but taller than Shikhar. Who is the shortest?

Accepted Answer

Introduction / Context:Height-order questions often yield a full chain, but sometimes the data underdetermine the extremes. Here we must decide the shortest person using two mini-chains that do not fully connect all five individuals.Given Data / Assumptions:Raina > Dhoni > Virat.Dhoni > Rohit > Shikhar.No direct comparison between Virat and Shikhar.Concept / Approach:Combine the chains where possible: Raina is above Dhoni; Dhoni is above both Virat and Rohit; Rohit is above Shikhar. We know Shikhar is below Rohit, and Virat is below Dhoni, but we lack Virat vs. Shikhar relation.Step-by-Step Solution:Chain 1: Raina > Dhoni > Virat.Chain 2: Dhoni > Rohit > Shikhar.Merge around Dhoni: Raina > Dhoni > (Virat and Rohit ...), with Rohit > Shikhar. But Virat vs. Shikhar is unknown.Hence the shortest could be Shikhar (if Shikhar < Virat) or Virat (if Virat < Shikhar). Both orders fit the clues.Verification / Alternative check:Construct two consistent examples: (a) Make Virat 170 cm and Shikhar 168 cm ⇒ Shikhar shortest; (b) Make Virat 165 cm and Shikhar 168 cm ⇒ Virat shortest. All constraints remain satisfied in both scenarios.Why Other Options Are Wrong:Picking Dhoni/Rohit as shortest contradicts given “>” relations.Picking Virat or Shikhar alone claims certainty we don’t have.Common Pitfalls:Forcing a total order when the data allow multiple valid arrangements. Always check if a missing comparison exists.Final Answer:Cannot be determined

Question 17

Find the youngest from layered age comparisons: Lakshmi is older than Meenu. Leela is older than Meenu but younger than Lakshmi. Latha is younger than both Meenu and Hari, and Hari is younger than Meenu. Who is the youngest?

Accepted Answer

Introduction / Context:This problem provides two mini-chains: one among Lakshmi, Leela, Meenu; another among Meenu, Hari, Latha. We must merge them to find the youngest person.Given Data / Assumptions:Lakshmi > Leela > Meenu.Meenu > Hari > Latha (since Latha is younger than both Meenu and Hari, and Hari is younger than Meenu).All ages distinct and measured at the same time.Concept / Approach:Place the two chains on a single line anchored at Meenu. Everyone to the left of Meenu is older; everyone to the right is younger. Identify the extreme rightmost (youngest).Step-by-Step Solution:Chain A: Lakshmi > Leela > Meenu.Chain B: Meenu > Hari > Latha.Merged: Lakshmi > Leela > Meenu > Hari > Latha.The youngest (rightmost) is Latha.Verification / Alternative check:Any numeric assignment consistent with the inequalities (e.g., 50, 45, 40, 35, 30 years respectively) preserves the order; Latha remains youngest.Why Other Options Are Wrong:Lakshmi/Leela/Meenu/Hari are each explicitly older than at least one other person; none can be the youngest.Common Pitfalls:Misreading “younger than both Meenu and Hari” as “younger than either,” which would weaken the constraint. It is a strict placement below both.Final Answer:Latha

Question 18

Find the youngest using age differences: Sashi is 2 years older than Sunita. Sunita is 3 years older than Bindu. Shekhar is 1 year older than Bindu. Who is the youngest in the group?

Accepted Answer

Introduction / Context:Age-difference questions are easily handled by setting a baseline variable and expressing others relative to it. The youngest will be the one with the smallest algebraic value.Given Data / Assumptions:Sashi = Sunita + 2.Sunita = Bindu + 3.Shekhar = Bindu + 1.All ages are integers in the same time frame.Concept / Approach:Let Bindu = b. Then compute each other person in terms of b and compare magnitudes.Step-by-Step Solution:Let Bindu = b.Sunita = b + 3.Sashi = (b + 3) + 2 = b + 5.Shekhar = b + 1.Ordering by age: Sashi (b+5) > Sunita (b+3) > Shekhar (b+1) > Bindu (b).Verification / Alternative check:Sample values: if Bindu = 10, then Shekhar = 11, Sunita = 13, Sashi = 15. Clearly Bindu is youngest. Any other b preserves this order.Why Other Options Are Wrong:Sashi/Sunita/Shekhar: Each is defined as Bindu plus a positive number, hence older than Bindu.None of these: Not applicable because Bindu is explicitly the youngest among the listed names.Common Pitfalls:Mixing up “older than” direction or forgetting to propagate differences correctly (e.g., computing Sashi as Sunita − 2).Final Answer:Bindu

Question 19

Identify the lowest scorer from pairwise comparisons: Priti scored more than Rahul. Yamuna scored as much as Divya. Lokita scored less than Manju. Rahul scored more than Yamuna. Manju scored less than Divya. Who scored the lowest?

Accepted Answer

Introduction / Context:Score-ordering problems use inequality chains and equalities to derive a total order or at least extremes. Here we must find the minimum scorer using consistent pairwise relations.Given Data / Assumptions:Priti > Rahul.Yamuna = Divya.Lokita < Manju.Rahul > Yamuna.Manju < Divya.Concept / Approach:Start from the equality Yamuna = Divya, then use Rahul > Yamuna to place Rahul above both. Since Manju < Divya (and Divya = Yamuna), Manju is below that equal pair; and Lokita < Manju places Lokita at the bottom. Priti > Rahul puts Priti at or near the top but does not affect the minimum.Step-by-Step Solution:From Rahul > Yamuna and Yamuna = Divya ⇒ Rahul > Divya and Rahul > Yamuna.From Manju < Divya ⇒ Manju below (Divya = Yamuna).From Lokita < Manju ⇒ Lokita is below Manju.Priti > Rahul is above all these; the bottom remains Lokita.Verification / Alternative check:Construct a numeric example: Let Divya = Yamuna = 80; Rahul = 85; Priti = 90; Manju = 78; Lokita = 70. All statements hold and Lokita is clearly the lowest.Why Other Options Are Wrong:Manju: Above Lokita.Yamuna/Divya: Equal to each other and above Manju, hence above Lokita.Rahul: Above the equal pair and thus far from the bottom.Common Pitfalls:Overlooking the equality (Yamuna = Divya) and misplacing Manju relative to them, which would flip the minimum incorrectly.Final Answer:Lokita

Question 20

Heights of P, Q, R, S, T, U (all different): R is taller than only P and U. S is shorter than only T and Q (i.e., only T and Q are taller than S). Standing in descending order (tallest to shortest), who is at the third place?

Accepted Answer

Introduction / Context:This problem mixes two relative statements to pin down specific ranks in a unique descending order. The language “shorter than only …” and “taller than only …” precisely indicates positions from the ends.Given Data / Assumptions:All heights are distinct.“R taller than only P and U” ⇒ exactly two people are shorter than R (P and U). Therefore, in tallest→shortest order, R is 4th place.“S shorter than only T and Q” ⇒ only T and Q are taller than S. Therefore, S is 3rd place (after T and Q).Concept / Approach:Translate the exclusivity terms into fixed positions. With six people, being “taller than only two” means exactly the 4th position from the top. Being “shorter than only two” means exactly the 3rd position from the top.Step-by-Step Solution:Positions 1–6 (tallest→shortest):1st: {T or Q}2nd: {Q or T}3rd: S (since only T and Q are above).4th: R (since only P and U are below R).5th/6th: P and U (order unknown).Verification / Alternative check:No other placement satisfies both exclusivity statements simultaneously. Any attempt to move S to 2nd would break “only T and Q taller,” and any attempt to move R would change the count of people below him.Why Other Options Are Wrong:R: 4th, not 3rd.P: 5th or 6th.Q: 1st or 2nd.Common Pitfalls:Misreading “only” as “at least,” which would loosen constraints and lead to multiple answers.Final Answer:S

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