Q: Coding — In a code, '146' means 'adopt good habits'. What is the code for 'habit'? Statements: I. '143' means 'like good pictures'. II. '826' means 'passion becomes habit'.

Introduction / Context: We must isolate the digit-code corresponding to the word 'habit' by using overlaps across coded sentences. Given Data / Assumptions: Base: '146' ↔ {adopt, good, habits}. I: '143' ↔ {like, good, pictures}. II: '826' ↔ {passion, becomes, habit}. Concept / Approach: Use intersection: the common word 'good' between 146 and 143 implies its code is shared between {1,4}; then intersect 146 with 826 to pin the remaining common word as 'habit(s)'. Step-by-Step Solution: Common(146,143) → word 'good' ↔ code ∈ {1,4}.Common(146,826) → shared code = 6; shared word = habit(s) ⇒ 'habit' ↔ 6.Individually, neither I nor II alone can isolate the code for 'habit'; together they do. Verification / Alternative check: Remaining codes pair consistently with the other words without contradiction. Why Other Options Are Wrong: A/B/C/D: Each single statement is insufficient; the combination is exactly sufficient. Common Pitfalls: Being distracted by plural 'habits' vs singular 'habit'; in such code problems stems map identically. Final Answer: E — Together sufficient (code for 'habit' = 6).

Q: How many students are there between Suresh and Mohan in a row of 50 students? I. Suresh is twelfth (12th) from the left end and Mohan is seventeenth (17th) from the right end. II. Suresh is six places away from Jayesh, who is twentieth (20th) from …

Introduction / Context: This Data Sufficiency problem asks for the exact number of students between two named positions in a fixed-length row (50 students). We must judge whether each statement provides enough information independently, or only together, or neither. Given Data / Assumptions: Total students in the row = 50. I: Suresh is 12th from the left end; Mohan is 17th from the right end. II: Suresh is 6 places away from Jayesh; Jayesh is 20th from the left. Concept / Approach: For position conversions, use: position_from_left = N - position_from_right + 1, where N = 50. The count of people strictly between two positions L1 and L2 (from the same end) is abs(L1 - L2) - 1. Data Sufficiency focuses on the adequacy of information rather than repetitive arithmetic. Step-by-Step Solution: 1) Using I alone: Mohan's position from the left = 50 - 17 + 1 = 34. Suresh is at 12 from the left. Students between them = 34 - 12 - 1 = 21. Hence I alone yields a unique, computable answer (21).2) Using II alone: Knowing Suresh is 6 places away from Jayesh (20th from left) gives two possibilities for Suresh (14th or 26th from left). Mohan's position is unknown; the gap to Mohan cannot be determined. Therefore II alone is insufficient.3) Combining I and II: Since I already suffices, adding II is unnecessary; the sufficiency classification remains based on I alone. Verification / Alternative check: Recompute between-count carefully to avoid off-by-one mistakes; “between” excludes end positions themselves. Why Other Options Are Wrong: B: II lacks Mohan’s position and thus cannot determine the gap. C: Not “either alone”; only I suffices. D/E: Not required since I alone is already sufficient. Common Pitfalls: Mixing “between” with inclusive counts; forgetting to convert right-to-left positions correctly; mishandling the ±6 ambiguity in II. Final Answer: Statement I alone is sufficient; Statement II alone is not.

Q: Which directions is Ali facing? I. If Ken, who is currently facing East turns 90° towards his right he would face a direction exactly opposite to the direction which Ali is facing II. If Priya who is currently facing South, turns left, walks 1m and …

Using Statement I: If ken turns 90° towards his right he will face South. So, Ali is facing north. Using Statement II: In the end Priya faces north. So, Ali also faces north.

Q: Did 300 candidates appear for the written examination for admission into College X? I. The principal of the college correctly mention that the number of candidates who had appeared for the examination was more than 200. II. According to a statistica…

Even by using both the statements together we can only determine that number of candidates appeared was more than 200.

Q: How many brothers does A have? I. A, who is B's brother, has two siblings. II. D is a brother of A and is the youngest in the family.

Introduction / Context: The task is to determine the exact number of A's brothers from two familial statements. In Data Sufficiency, we do not compute every possibility; we judge whether the information fixes a unique answer. Given Data / Assumptions: I: A is B's brother (so A is male) and A has exactly two siblings in total. II: D is a brother of A and is the youngest. “Sibling” means brother or sister; genders of unspecified siblings are unknown unless stated. Concept / Approach: Translate each statement into structure and test whether the number of A's brothers is uniquely determined. If more than one consistent family composition fits the statements, sufficiency fails. Step-by-Step Solution: 1) I alone: A has two siblings. One named sibling is B (gender unknown). The other sibling is unnamed and gender unknown. Thus, the number of A’s brothers could be 1 (if only one of {B, other} is male) or 2 (if both are male). I alone is not sufficient.2) II alone: We only learn that D is a brother of A and the youngest. Others (including B) may be brother(s) or sister(s); the total sibling count is unknown. II alone is not sufficient.3) I + II: From I, A has exactly two siblings: {B, X}. Statement II forces one sibling (say D) to be a brother; this pins either B = D or X = D. We still cannot determine B’s gender. Therefore A’s brothers = 1 (if B is sister) or 2 (if B is brother). Not unique. Verification / Alternative check: Construct two consistent families: Case 1: Siblings {D (brother), B (sister)} ⇒ brothers = 1. Case 2: {D (brother), B (brother)} ⇒ brothers = 2. Why Other Options Are Wrong: A/B/C: Neither statement alone nor “either alone” is enough. E: Together still ambiguous. Common Pitfalls: Assuming B's gender; overlooking that I limits total siblings to exactly two, not enabling gender resolution. Final Answer: Both statements together are NOT sufficient.

Q: How far is point P from point Q? (All points lie on a straight line.) I. Point T is exactly midway between P and Q. Point T is 5 km west of point R. II. Point Q is 2 km east of point R.

Introduction / Context: We must compute the exact distance between two collinear points, P and Q, using reference points T and R. Sufficiency hinges on whether a unique numeric distance results. Given Data / Assumptions: I: T is the midpoint of segment PQ and T is 5 km west of R. II: Q is 2 km east of R. Positive eastward direction; west is negative relative to R for a simple coordinate model. Concept / Approach: Place R at coordinate 0. Use directional data to place T and Q, then apply the midpoint relation to solve for P and hence the distance PQ. Step-by-Step Solution: 1) Coordinate setup: Let R = 0. From II, Q = +2. From I, T = −5 and T is midpoint of P and Q ⇒ (P + Q)/2 = −5.2) Solve for P: (P + 2)/2 = −5 ⇒ P + 2 = −10 ⇒ P = −12.3) Distance PQ = |Q − P| = |2 − (−12)| = 14 km.4) Sufficiency: I alone lacks Q's absolute placement; II alone lacks the midpoint anchor. Together they yield a unique numerical distance. Verification / Alternative check: Reverse-check midpoint: (−12 + 2)/2 = −10/2 = −5, consistent with T's position. Why Other Options Are Wrong: A/B/C: Neither statement alone fixes unique coordinates; hence not sufficient individually. D: Together they are sufficient. Common Pitfalls: Sign errors with east/west; forgetting midpoint formula requires absolute positions, not just relative gaps. Final Answer: Both statements together are sufficient, but NEITHER alone is sufficient.

Question 1

Coding — How is 'go' written in the code language? Statements: I. 'go over there' → 'pa da na'. II. 'go and sit' → 'sa ka pa'.

Accepted Answer

Introduction / Context: We must isolate the unique code for 'go' using two coded sentences that both contain the word. Given Data / Assumptions: S1 tokens {pa, da, na} ↔ {go, over, there}. S2 tokens {sa, ka, pa} ↔ {go, and, sit}. Concept / Approach: Intersection logic: common English word across sentences ('go') maps to the common token across their code sets. Step-by-Step Solution: Common English word = 'go'; common token = {pa}. Therefore, 'go' ↔ 'pa'.Neither statement alone can identify which token corresponds to 'go' without the cross-sentence intersection. Verification / Alternative check: Assign the remaining tokens bijectively to the other words; no conflicts occur. Why Other Options Are Wrong: A/B/C: Each single sentence admits multiple token-word assignments. E: While the combination is sufficient, it is also necessary since neither alone suffices; we mark this as 'together necessary' (choice D). Common Pitfalls: Assuming positional order implies mapping; DS treats them as sets. Final Answer: D — Both statements together are necessary ('go' = 'pa').

Question 2

Dates — On which exact date of the month is Meena's birthday? Statements: I. Meena's brother: after 25th but before 29th. II. Meena's father: after 27th but before 31st.

Accepted Answer

Introduction / Context: We must identify a unique calendar date from two exclusive ranges. Given Data / Assumptions: I: {26, 27, 28}. II: {28, 29, 30}. Concept / Approach: Use set intersection of the two candidate sets. Step-by-Step Solution: Intersection {26,27,28} ∩ {28,29,30} = {28} ⇒ unique.Individually, each statement leaves multiple possibilities. Verification / Alternative check: Boundaries 'after' and 'before' are exclusive, ensuring the sets above. Why Other Options Are Wrong: A/B/C/E: Neither statement alone suffices; together they yield a single date. Common Pitfalls: Including endpoints (25, 29, 31) contrary to 'after/before' wording. Final Answer: D — Both statements together are necessary (date = 28th).

Question 3

Ages — Kiran is elder to Manoj; Dilip is elder to Neelam. Who is the youngest? Statements: I. Kiran is elder to Neelam. II. Manoj is younger than Dilip.

Accepted Answer

Introduction / Context: We must identify the youngest using partial order relations among four people. Given Data / Assumptions: Base: K > M; D > N. I: K > N. II: D > M. Concept / Approach: Combine the inequalities and see if a unique minimum (youngest) is forced. Step-by-Step Solution: From all: K > M and K > N; D > N and D > M. The unresolved relation is between M and N; either could be younger.Case 1: N is youngest if N < M. Case 2: M is youngest if M < N. Both cases fit the statements. Verification / Alternative check: No contradiction arises in either case; thus no unique youngest is identified. Why Other Options Are Wrong: A/B/D/E: Neither statement alone nor their combination fixes M vs N. Common Pitfalls: Assuming transitivity across disjoint chains (K vs D) to infer M vs N. Final Answer: C — Together not sufficient.

Question 4

Coding — In a code, '146' means 'adopt good habits'. What is the code for 'habit'? Statements: I. '143' means 'like good pictures'. II. '826' means 'passion becomes habit'.

Accepted Answer

Introduction / Context: We must isolate the digit-code corresponding to the word 'habit' by using overlaps across coded sentences. Given Data / Assumptions: Base: '146' ↔ {adopt, good, habits}. I: '143' ↔ {like, good, pictures}. II: '826' ↔ {passion, becomes, habit}. Concept / Approach: Use intersection: the common word 'good' between 146 and 143 implies its code is shared between {1,4}; then intersect 146 with 826 to pin the remaining common word as 'habit(s)'. Step-by-Step Solution: Common(146,143) → word 'good' ↔ code ∈ {1,4}.Common(146,826) → shared code = 6; shared word = habit(s) ⇒ 'habit' ↔ 6.Individually, neither I nor II alone can isolate the code for 'habit'; together they do. Verification / Alternative check: Remaining codes pair consistently with the other words without contradiction. Why Other Options Are Wrong: A/B/C/D: Each single statement is insufficient; the combination is exactly sufficient. Common Pitfalls: Being distracted by plural 'habits' vs singular 'habit'; in such code problems stems map identically. Final Answer: E — Together sufficient (code for 'habit' = 6).

Question 5

How many brothers does Bharat have?  I. Sheila (Bharat's mother) has exactly three children in total. II. Meena (Bharat's grandmother) has only one granddaughter among all of her grandchildren.

Accepted Answer

Introduction / Context: Data Sufficiency problems test whether given statements provide enough information to determine a specific value or fact without necessarily computing that value. Here, we must decide if we can deduce the exact number of brothers that Bharat has using two family–relation statements. Given Data / Assumptions: We only use logical implications of the statements; we do not assume anything beyond common family terms. I: Sheila (Bharat's mother) has exactly three children in total (including Bharat). II: Meena (Bharat's grandmother) has only one granddaughter among all her grandchildren. Concept / Approach: We test sufficiency separately for each statement, then jointly. A statement is sufficient if it uniquely determines the required count (number of Bharat's brothers) under all possibilities consistent with the statement(s). Step-by-Step Solution: 1) Using I alone: Sheila has three children total. The genders of the two siblings (besides Bharat) are unknown. Depending on whether those two are brothers or sisters, Bharat could have 0, 1, or 2 brothers. Hence I alone is insufficient.2) Using II alone: Meena has exactly one granddaughter across all grandchildren. This condition constrains the overall family tree (possibly involving multiple children of Meena) but does not specify how many children Sheila has or their genders; Bharat’s sibling genders remain undetermined. Hence II alone is insufficient.3) Using I + II together: Even with I fixing the total number of Sheila’s children at three, II only caps the total count of granddaughters of Meena at one. That single granddaughter could belong to Sheila’s children set or to another child of Meena; both distributions are possible. Under allowed distributions, Bharat may still have 0, 1 or 2 brothers. Therefore, even together they do not yield a unique count. Verification / Alternative check: Construct examples: (a) If Sheila’s other two children are both girls, then Bharat has 0 brothers; II can still be satisfied by ensuring no other granddaughters exist. (b) If she has one boy and one girl, Bharat has 1 brother; II can still hold depending on other branches. (c) If both are boys, Bharat has 2 brothers; II can hold if no other granddaughter exists elsewhere. Multiple consistent models confirm non-uniqueness. Why Other Options Are Wrong: A: I alone is not sufficient (multiple possibilities remain). B: II alone is not sufficient (does not pin sibling genders or counts). C: Neither statement alone works, so “either alone” is false. E: Together still allow multiple family configurations, so not sufficient. Common Pitfalls: Do not assume only one child of Meena (there may be several). Do not assume Bharat’s siblings’ genders from II; “one granddaughter” is a global condition across all grandchildren, not confined to Sheila’s branch. Final Answer: Both statements together are NOT sufficient.

Question 6

How is the word ‘‘letter’’ written in a code language?  I. ‘‘please write a letter’’ → 7218 and ‘‘and received a Greek letter’’ → 7513. II. ‘‘write in English please’’ → 2084 and ‘‘a Greek’’ → 5714.

Accepted Answer

Introduction / Context: This is a code-decoding Data Sufficiency task. We must judge whether the provided coded phrases uniquely determine the code for the specific word ‘‘letter’’ without fully cracking the entire code. Given Data / Assumptions: I: Phrases and their codes: (1) ‘‘please write a letter’’ → 7218; (2) ‘‘and received a Greek letter’’ → 7513. II: Phrases and their codes: (3) ‘‘write in English please’’ → 2084; (4) ‘‘a Greek’’ → 5714. Each distinct word maps to a distinct code token within this context; ordering of tokens within a phrase is not guaranteed to match word order. Concept / Approach: Use overlaps across phrases to isolate the code for the target word. A statement is sufficient only if the mapping for ‘‘letter’’ is uniquely pinned down. Step-by-Step Solution: 1) From I: The common words between (1) and (2) are ‘‘a’’ and ‘‘letter’’. The common digits between codes 7218 and 7513 are {7,1}. Thus {‘‘a’’, ‘‘letter’’} ↔ {7,1}, but we cannot tell which is which. Hence I alone is insufficient.2) From II: From (3) we get the set {‘‘write’’, ‘‘in’’, ‘‘English’’, ‘‘please’’} ↔ {2,0,8,4}. From (4) we get {‘‘a’’, ‘‘Greek’’} ↔ {5,7,1,4} (two digits chosen among four due to possible re-use across sentences), which does not directly single out ‘‘letter’’ at all. Hence II alone is insufficient.3) Combine I and II: In (1) ‘‘please’’ and ‘‘write’’ are present and are known from (3) to be within {2,0,8,4}. Removing those from 7218 leaves {7,1} for {‘‘a’’, ‘‘letter’’}. From (4), ‘‘a’’ is among {5,7,1,4}, so both 7 and 1 remain possible; nothing forces a unique choice for ‘‘letter’’ between 7 and 1. Therefore, even together, the mapping for ‘‘letter’’ is not uniquely determined. Verification / Alternative check: Construct two consistent assignments: Case A: map ‘‘a’’→7 and ‘‘letter’’→1; Case B: map ‘‘a’’→1 and ‘‘letter’’→7. Both can be made consistent with all four coded phrases by adjusting the remaining word–digit pairings accordingly. Why Other Options Are Wrong: A/B/C: Neither statement alone pins the code; “either alone” is also false. E: Even combined, ambiguity remains; thus not sufficient together. Common Pitfalls: Do not assume positional alignment between words and digits; do not assume the smallest/largest digit belongs to a particular word; only intersections and eliminations count. Final Answer: Both statements together are NOT sufficient.

Question 7

Among A, B, C, D, and E seated in a straight line facing North, who sits exactly in the middle?  I. A sits third to the left of D. B sits on the immediate right of C. II. B sits second to the right of A. E is not an immediate neighbour of D.

Accepted Answer

Introduction / Context: We have five persons seated in a row facing North. We must identify the person in the exact middle position using Data Sufficiency logic—checking each statement alone and then both together. Given Data / Assumptions: Row has 5 positions, indexed left→right for North-facing seats. I: A is third to the left of D; B is immediately to the right of C. II: B is second to the right of A; E is not adjacent to D. Concept / Approach: For North-facing rows, ‘‘to the right’’ means higher index. We attempt placements consistent with each statement and test uniqueness of the middle seat occupant. Step-by-Step Solution: 1) Statement I alone: A = D − 3 forces A to be at most position 2 (since D must be ≤5). Possible pairs: (A=1, D=4) or (A=2, D=5). Also “B right of C” only fixes adjacency direction (C,B). Multiple seatings exist with different middle occupants. So I alone is insufficient.2) Statement II alone: B = A + 2 narrows relative positions of A and B (valid pairs: (A,B) = (1,3), (2,4), (3,5)). “E not neighbour of D” still allows multiple layouts; the middle seat varies across valid arrangements. So II alone is insufficient.3) Combine I + II: Test A=1 scenario. From II, B=3. From I, D=A+3=4 and C is immediately left of B (since B is immediately right of C), so C=2, placing E=5 (only seat remaining). This satisfies “E not neighbour of D” (E=5 not adjacent to D=4 is false), so A=1 is invalid due to II's E–D condition? Check: II states E is not an immediate neighbour of D—indeed 5 is neighbour of 4, so invalid. Now try A=2: Then B=4 (from II), D=5 (from I), and C=3 (since B is immediately right of C). E must be 1. E is not adjacent to D (1 not neighbour of 5) satisfied. The seating becomes [1:E, 2:A, 3:C, 4:B, 5:D], uniquely fixing the middle seat as C. Verification / Alternative check: No other A–B pair works with I + II simultaneously without violating adjacency or row bounds. Hence the combined information yields a single consistent arrangement with C in the middle. Why Other Options Are Wrong: A/B: Each alone admits multiple layouts—no unique middle person. C: “Either alone” is false because neither alone suffices. D: Together they are sufficient (unique layout), so “not sufficient” is false. Common Pitfalls: Confusing left/right with South-facing logic; forgetting the 5-seat boundary when applying ‘‘third to the left’’; ignoring the non-neighbour constraint for E and D when combining statements. Final Answer: Both statements together are sufficient, but NEITHER alone is sufficient.

Question 8

A six-storey building has an unoccupied ground floor and numbered floors 1–5 above it. Five people (A, B, C, D, E) each live on one of floors 1–5. Who lives on the 3rd floor?  I. C lives on an even-numbered floor above D. B lives immediately above A…

Accepted Answer

Introduction / Context: This Data Sufficiency puzzle assigns five distinct persons to floors 1–5 (ground is empty). We must determine exactly who is on floor 3 using the interplay of adjacency and parity constraints. Given Data / Assumptions: Floors available: 1, 2, 3, 4, 5. I: C is on an even floor above D; B is immediately above A. II: D is on an odd floor. A and B are immediate neighbours; C and E are immediate neighbours; C is not on an odd floor (so C is on 2 or 4). Concept / Approach: We test I and II separately for uniqueness and then combine. Use parity (odd/even) and immediate-neighbour constraints to reduce possibilities. ‘‘Above’’ means higher floor number. Step-by-Step Solution: 1) From I alone: C on an even floor above D implies possibilities such as (D=1,C=2), (D=2,C=4), (D=3,C=4). Also B immediately above A implies a vertical pair (A,B) occupying consecutive floors. Many arrangements satisfy I with different occupants on the 3rd floor, so I alone is insufficient.2) From II alone: D is odd (1,3,5). A–B form a consecutive pair; C–E form a consecutive pair; C is even (2 or 4). Balancing two consecutive pairs across 5 floors yields multiple layouts (e.g., C–E on 2–3 or 4–5; A–B on an adjacent pair elsewhere), so II alone is insufficient.3) Combine I + II: Since C is even (II) and above D (I), valid (D,C) pairs are (1,2) or (3,4). If (D=3, C=4), then floor 4 is C and floor 3 is D. A–B must be adjacent with B above A (I); C–E are adjacent (II). Testing placements quickly shows the only consistent packing across five floors that honours all adjacency and parity constraints leads to a unique occupant on floor 3. One valid resolution is: D=1, C=2 (satisfy ‘‘C even and above D’’), then set A=3, B=4 (‘‘B above A’’), and E=5 while honouring ‘‘C and E are neighbours’’ fails; hence adjust to D=3, C=4 and pack A–B on 1–2 (with B above A ⇒ A=1, B=2) and place E=5. All constraints now hold and uniquely give D on floor 3. Verification / Alternative check: Attempting other distributions either violates adjacency (C–E or A–B), parity (C even), or order (C above D). The consistent joint solution fixes the 3rd floor occupant uniquely as D. Why Other Options Are Wrong: A/B/C: Neither I nor II alone yields a unique answer; each allows multiple configurations. D: Together they are sufficient, not insufficient. Common Pitfalls: Misreading “immediately above” as ‘‘somewhere above’’; ignoring that two separate neighbour-pairs need disjoint consecutive slots across only five floors; overlooking the even-floor constraint for C. Final Answer: Both statements together are sufficient, but NEITHER alone is sufficient.

Question 9

Are all four friends — Abhay, Kavita, Prashant, and Yasir — who are sitting around a circular table, facing the centre?  I. Kavita sits second to the left of Abhay. Abhay faces the centre. Yasir sits immediately to the right of both Abhay and Kavita…

Accepted Answer

Introduction / Context: We must determine whether all four people at a round table face the centre. Data Sufficiency asks whether the facing-direction conclusion follows from the statements, not to draw the full diagram unless necessary. Given Data / Assumptions: I: Kavita is second to the left of Abhay; Abhay faces the centre; Yasir is immediately to the right of Abhay and also immediately to the right of Kavita. II: Prashant is third to the right of Kavita; Abhay is immediately to the right of both Prashant and Yasir (but no facing info is given). Concept / Approach: In a circular arrangement, ‘‘left’’ and ‘‘right’’ depend on facing direction. If at least one person’s facing is known (and relative left/right relations are given), we can propagate constraints to test whether everyone must face the centre. Step-by-Step Solution: 1) Using I alone: Abhay faces the centre. When someone faces the centre, the person to his immediate right is clockwise. Given ‘‘Kavita second to Abhay’s left’’ and ‘‘Yasir immediately to Abhay’s right’’ plus ‘‘Yasir immediately to Kavita’s right’’, the only way to satisfy both immediate-right relations consistently is when all are facing the centre (the ‘‘left’’/‘‘right’’ senses align consistently around the table). Any attempt to flip others outward breaks at least one given right/left statement. Thus I alone forces the facing-in configuration for all four.2) Using II alone: There is no explicit facing information. The right/left relations could be satisfied under more than one collective facing scenario (e.g., some facing centre, others outward) by suitably rotating/mirroring positions. Therefore II alone is insufficient. Verification / Alternative check: Construct a layout from I: Place Abhay, face-in; place Yasir to Abhay’s immediate right (clockwise). Now place Kavita two seats to Abhay’s left and verify that Yasir is also immediately to Kavita’s right—this holds only under the inward-facing convention for all. Why Other Options Are Wrong: B: II lacks any facing anchor; multiple facing patterns are possible. C: II alone is not sufficient; hence “either alone” is false. D/E: We already have sufficiency from I alone; no need to combine. Common Pitfalls: Confusing left/right conventions when some people might face outward; assuming symmetry implies unique facing without an anchor person. Final Answer: Statement I alone is sufficient; Statement II alone is not.

Question 10

Is R the granddaughter of C?  I. The only sister of A is the mother of R’s brother B. II. C, the mother of A, has only one grandson B.

Accepted Answer

Introduction / Context: We must determine if R is C’s granddaughter (i.e., R is female and is a child of one of C’s children). The statements define relationships among A, C, R, and B. Sufficiency depends on whether we can infer R’s lineage and gender conclusively. Given Data / Assumptions: I: A's only sister is the mother of R’s brother B. So A has exactly one sister; that sister is the mother of B and R, making B and R siblings (same mother). No information about C yet. II: C is A’s mother and has only one grandson B. That means among all grandchildren of C, there is exactly one male (B). Concept / Approach: To prove R is C’s granddaughter, we must show (1) R is indeed C’s grandchild and (2) R is female. Combine lineage from I with the sex-count constraint from II. Step-by-Step Solution: 1) From I alone: We know A’s only sister is mother of B and R ⇒ R and B are that sister’s children. But we do not know if A’s sister is also C’s child (we do not yet know who C is). Thus I alone does not link R to C; insufficient.2) From II alone: We know C is A’s mother and C has exactly one grandson B. We do not know who R is or through which child of C she might descend. Insufficient.3) Combine I + II: Since C is A’s mother, A’s only sister (from I) is also C’s daughter. Therefore, the children of A’s sister (namely B and R) are C’s grandchildren. From II, C has only one grandson—B. Hence any other grandchild (including R) must be female (otherwise there would be at least two grandsons). Thus R is a granddaughter of C. Verification / Alternative check: Could R be male? If R were male, C would have at least two grandsons: B and R, contradicting II. Therefore R must be female; and by lineage, R is C’s granddaughter. Why Other Options Are Wrong: A/B: Each statement alone misses either the lineage link (I) or the sibling/gender-count implication (II). C: Neither alone suffices; they must be combined. D: Together they are sufficient (we reach a definite Yes). Common Pitfalls: Overlooking that “only one grandson” forces every other grandchild to be female; forgetting that A’s sister is also C’s child, which connects R and B to C. Final Answer: Both statements together are sufficient, but NEITHER alone is sufficient.

Question 11

How many students are there between Suresh and Mohan in a row of 50 students?  I. Suresh is twelfth (12th) from the left end and Mohan is seventeenth (17th) from the right end. II. Suresh is six places away from Jayesh, who is twentieth (20th) from …

Accepted Answer

Introduction / Context: This Data Sufficiency problem asks for the exact number of students between two named positions in a fixed-length row (50 students). We must judge whether each statement provides enough information independently, or only together, or neither. Given Data / Assumptions: Total students in the row = 50. I: Suresh is 12th from the left end; Mohan is 17th from the right end. II: Suresh is 6 places away from Jayesh; Jayesh is 20th from the left. Concept / Approach: For position conversions, use: position_from_left = N - position_from_right + 1, where N = 50. The count of people strictly between two positions L1 and L2 (from the same end) is abs(L1 - L2) - 1. Data Sufficiency focuses on the adequacy of information rather than repetitive arithmetic. Step-by-Step Solution: 1) Using I alone: Mohan's position from the left = 50 - 17 + 1 = 34. Suresh is at 12 from the left. Students between them = 34 - 12 - 1 = 21. Hence I alone yields a unique, computable answer (21).2) Using II alone: Knowing Suresh is 6 places away from Jayesh (20th from left) gives two possibilities for Suresh (14th or 26th from left). Mohan's position is unknown; the gap to Mohan cannot be determined. Therefore II alone is insufficient.3) Combining I and II: Since I already suffices, adding II is unnecessary; the sufficiency classification remains based on I alone. Verification / Alternative check: Recompute between-count carefully to avoid off-by-one mistakes; “between” excludes end positions themselves. Why Other Options Are Wrong: B: II lacks Mohan’s position and thus cannot determine the gap. C: Not “either alone”; only I suffices. D/E: Not required since I alone is already sufficient. Common Pitfalls: Mixing “between” with inclusive counts; forgetting to convert right-to-left positions correctly; mishandling the ±6 ambiguity in II. Final Answer: Statement I alone is sufficient; Statement II alone is not.

Question 12

How is the word ‘‘never’’ written in the code language?  I. ‘‘never ever go there’’ is coded as ‘‘na ja ni ho’’. II. ‘‘go there and come back’’ is coded as ‘‘ma ho sa ni da’’.

Accepted Answer

Introduction / Context: We must determine the exact code-token for the specific word ‘‘never’’ given two coded sentences. Data Sufficiency asks whether the provided overlaps pin the mapping uniquely, not to decode the entire language exhaustively. Given Data / Assumptions: I provides a 1–1 mapping set between {never, ever, go, there} and {na, ja, ni, ho} (order within a sentence may not correspond to code order). II provides a set mapping between {go, there, and, come, back} and {ma, ho, sa, ni, da}. Distinct words correspond to distinct code-tokens within these sentences. Concept / Approach: Use common words across statements to eliminate code-tokens and isolate the word of interest. If multiple tokens remain possible for ‘‘never’’ after all eliminations, the data are insufficient. Step-by-Step Solution: 1) From I alone: The four tokens {na, ja, ni, ho} represent {never, ever, go, there}. Without any second sentence overlap, we cannot identify which one is ‘‘never’’; I alone is insufficient.2) From II alone: The common words with I are {go, there} which correspond to {ni, ho}. But II does not include ‘‘never’’ at all, so II alone does not identify ‘‘never’’.3) Combine I + II: Since {go, there} are shared, they must be {ni, ho}. Eliminating {ni, ho} from I's set leaves {na, ja} corresponding to {never, ever}. With no further constraints to distinguish them, the code for ‘‘never’’ remains ambiguous between ‘‘na’’ and ‘‘ja’’. Verification / Alternative check: Construct two consistent assignments: Case 1: never→na, ever→ja; Case 2: never→ja, ever→na. Both respect all given sentences, confirming non-uniqueness. Why Other Options Are Wrong: A/B/C: Neither statement, nor “either alone”, uniquely identifies the token. E: Together still ambiguous; hence not sufficient. Common Pitfalls: Assuming token order equals word order; forcing arbitrary tie-breakers (like alphabetical) which DS forbids. Final Answer: Both statements together are NOT sufficient.

Question 13

Among M, P, K, J, T, and W, who is lighter than only the heaviest (i.e., second heaviest)?  I. P is heavier than M and T. II. W is heavier than P but lighter than J, and J is not the heaviest.

Accepted Answer

Introduction / Context: This is a relative ordering (inequalities) Data Sufficiency question over six individuals: M, P, K, J, T, W. We must identify the unique person who is second only to the heaviest. DS requires proving uniqueness, not just listing possibilities. Given Data / Assumptions: I: P > M and P > T (P heavier than M and T). II: J > W > P and J is not the heaviest (someone heavier than J exists). Concept / Approach: Translate comparisons into partial orders, then test if the identity of the second heaviest is forced. If more than one person could occupy that rank under consistent completions, the data are insufficient. Step-by-Step Solution: 1) Using I alone: We only know P is above M and T. The positions of K, J, W relative to these are unconstrained. Several people could be second heaviest; I alone is insufficient.2) Using II alone: We know there exists someone X heavier than J (since J is not heaviest) and the chain X > J > W > P. The ranks of K, M, T relative to these are unknown. The second heaviest could be J (if X is heaviest and all others are below J), or it could be someone else above J (if both K and X exceed J), etc. II alone is insufficient.3) Combining I + II: We retain X > J > W > P > {M, T}. The person K is still unconstrained—K could be heavier than J, between J and W, or below P. If K > J and X is the heaviest, then K becomes second heaviest; if K is below J, then J could be second heaviest. Multiple consistent orders remain; identity is not fixed. Verification / Alternative check: Construct models: (a) Let X=K>J>W>P>M>T ⇒ second heaviest = J. (b) Let X=K, and also have another Y (say unknown external) heaviest > J>K... ⇒ second heaviest could be J or K depending on placements. The variability confirms insufficiency. Why Other Options Are Wrong: A/B/C: Neither statement alone nor “either alone” pins a unique second heaviest. E: Even together, multiple candidates remain. Common Pitfalls: Assuming “J is not heaviest” implies J is second heaviest; ignoring unconstrained elements like K that can overtake J. Final Answer: Both statements together are NOT sufficient.

Question 14

Who amongst A, B, C, D, and E is the tallest?  I. A is taller than B but shorter than C. D is not the tallest. II. Exactly two people are taller than C.

Accepted Answer

Introduction / Context: We must identify the unique tallest person among five, given partial comparisons. The question is about sufficiency, not computing relative heights numerically. Given Data / Assumptions: I: A < C and A > B. Also, D is not the tallest. II: Exactly two people are taller than C (so C is 3rd tallest). Concept / Approach: Translate statements into rank constraints. A statement is sufficient only if it determines the tallest uniquely in all consistent orders. Step-by-Step Solution: 1) Using I alone: We know the local order B < A < C and D is not tallest. E is unconstrained, so the tallest could be C or E (since D is ruled out). Hence I alone is insufficient.2) Using II alone: If two people are taller than C, then the tallest is either of those two—but II does not tell us who they are; hence II alone is insufficient.3) Combine I + II: Since C is exactly 3rd, nobody below C can be tallest. From I, A < C and B < A, so both A and B are below C, therefore neither can be tallest. With C at rank 3, exactly two people (from {D, E}) are taller than C. But I says D is not tallest; hence the tallest must be E uniquely. Verification / Alternative check: Check consistency: A < C, B < A, C at 3rd, D at rank 2 and E at rank 1 is a valid arrangement satisfying all conditions. Why Other Options Are Wrong: A/B: Each alone allows multiple tallest candidates. C: Not “either alone”; both are needed. D: Together they are sufficient; so “not sufficient” is false. Common Pitfalls: Overlooking that A and B being below C (from I) combined with C’s fixed rank (from II) forces the two-above set to {D, E}; then using “D not tallest” clinches E. Final Answer: Both statements together are sufficient, but NEITHER alone is sufficient.

Question 15

Which directions is Ali facing? I. If Ken, who is currently facing East turns 90° towards his right he would face a direction exactly opposite to the direction which Ali is facing II. If Priya who is currently facing South, turns left, walks 1m and …

Accepted Answer

Using Statement I: If ken turns 90° towards his right he will face South. So, Ali is facing north. Using Statement II: In the end Priya faces north. So, Ali also faces north.

Question 16

Did 300 candidates appear for the written examination for admission into College X? I. The principal of the college correctly mention that the number of candidates who had appeared for the examination was more than 200. II. According to a statistica…

Accepted Answer

Even by using both the statements together we can only determine that number of candidates appeared was more than 200.

Question 17

How many brothers does A have?  I. A, who is B's brother, has two siblings. II. D is a brother of A and is the youngest in the family.

Accepted Answer

Introduction / Context: The task is to determine the exact number of A's brothers from two familial statements. In Data Sufficiency, we do not compute every possibility; we judge whether the information fixes a unique answer. Given Data / Assumptions: I: A is B's brother (so A is male) and A has exactly two siblings in total. II: D is a brother of A and is the youngest. “Sibling” means brother or sister; genders of unspecified siblings are unknown unless stated. Concept / Approach: Translate each statement into structure and test whether the number of A's brothers is uniquely determined. If more than one consistent family composition fits the statements, sufficiency fails. Step-by-Step Solution: 1) I alone: A has two siblings. One named sibling is B (gender unknown). The other sibling is unnamed and gender unknown. Thus, the number of A’s brothers could be 1 (if only one of {B, other} is male) or 2 (if both are male). I alone is not sufficient.2) II alone: We only learn that D is a brother of A and the youngest. Others (including B) may be brother(s) or sister(s); the total sibling count is unknown. II alone is not sufficient.3) I + II: From I, A has exactly two siblings: {B, X}. Statement II forces one sibling (say D) to be a brother; this pins either B = D or X = D. We still cannot determine B’s gender. Therefore A’s brothers = 1 (if B is sister) or 2 (if B is brother). Not unique. Verification / Alternative check: Construct two consistent families: Case 1: Siblings {D (brother), B (sister)} ⇒ brothers = 1. Case 2: {D (brother), B (brother)} ⇒ brothers = 2. Why Other Options Are Wrong: A/B/C: Neither statement alone nor “either alone” is enough. E: Together still ambiguous. Common Pitfalls: Assuming B's gender; overlooking that I limits total siblings to exactly two, not enabling gender resolution. Final Answer: Both statements together are NOT sufficient.

Question 18

How far is point P from point Q? (All points lie on a straight line.)  I. Point T is exactly midway between P and Q. Point T is 5 km west of point R. II. Point Q is 2 km east of point R.

Accepted Answer

Introduction / Context: We must compute the exact distance between two collinear points, P and Q, using reference points T and R. Sufficiency hinges on whether a unique numeric distance results. Given Data / Assumptions: I: T is the midpoint of segment PQ and T is 5 km west of R. II: Q is 2 km east of R. Positive eastward direction; west is negative relative to R for a simple coordinate model. Concept / Approach: Place R at coordinate 0. Use directional data to place T and Q, then apply the midpoint relation to solve for P and hence the distance PQ. Step-by-Step Solution: 1) Coordinate setup: Let R = 0. From II, Q = +2. From I, T = −5 and T is midpoint of P and Q ⇒ (P + Q)/2 = −5.2) Solve for P: (P + 2)/2 = −5 ⇒ P + 2 = −10 ⇒ P = −12.3) Distance PQ = |Q − P| = |2 − (−12)| = 14 km.4) Sufficiency: I alone lacks Q's absolute placement; II alone lacks the midpoint anchor. Together they yield a unique numerical distance. Verification / Alternative check: Reverse-check midpoint: (−12 + 2)/2 = −10/2 = −5, consistent with T's position. Why Other Options Are Wrong: A/B/C: Neither statement alone fixes unique coordinates; hence not sufficient individually. D: Together they are sufficient. Common Pitfalls: Sign errors with east/west; forgetting midpoint formula requires absolute positions, not just relative gaps. Final Answer: Both statements together are sufficient, but NEITHER alone is sufficient.

Question 19

On which floor of the building does G stay? (Building has five floors: 1, 2, 3, 4, 5.)  I. Only the even-numbered floors are occupied and G does not stay on the second floor. II. G does not stay on an odd-numbered floor.

Accepted Answer

Introduction / Context: We must uniquely identify G's floor in a five-floor building. Data Sufficiency asks whether each statement pinpoints a single floor for G without ambiguity. Given Data / Assumptions: I: Only even floors are occupied; G is not on floor 2. II: G is on an even floor (i.e., not odd). Concept / Approach: Enumerate feasible floors from each statement and check if a unique floor is forced. Step-by-Step Solution: 1) From I: Occupied floors are {2, 4} only; since G is not on 2, G must be on 4. I alone is sufficient.2) From II: G is not on {1,3,5}; G could be on 2 or 4. II alone does not fix a unique floor.3) Therefore, answer type A holds. Verification / Alternative check: Check consistency: If only even floors are occupied, II is implied but weaker. Why Other Options Are Wrong: B: II alone leaves two possibilities. C: Not either alone; only I suffices. D/E: Not applicable since I alone is already sufficient. Common Pitfalls: Overlooking “only even-numbered floors are occupied,” which collapses the possibilities. Final Answer: Statement I alone is sufficient; Statement II alone is not.

Question 20

How many days did Raju take to complete his assignment?  I. Mohit correctly remembers that Raju took more than 3 days and less than 9 days. II. Mina correctly remembers that Raju took more than 7 days and less than 11 days.

Accepted Answer

Introduction / Context: The statements give open intervals for an integer day-count. We must see if their overlap isolates a single integer value. We adopt the Recovery-First policy to repair phrasing (“more than x less than y”) to the standard interpretation: x < days < y. Given Data / Assumptions: I: 3 < days < 9 ⇒ possible integer days = {4,5,6,7,8}. II: 7 < days < 11 ⇒ possible integer days = {8,9,10}. Concept / Approach: Intersect the two integer sets; if the intersection is a singleton, the exact value is determined only when both statements are used together. Step-by-Step Solution: 1) From I alone: Multiple candidates {4,5,6,7,8}; not sufficient.2) From II alone: Multiple candidates {8,9,10}; not sufficient.3) Intersection: {4,5,6,7,8} ∩ {8,9,10} = {8}. Unique solution: 8 days. Hence only together are they sufficient. Verification / Alternative check: Check end-point inclusivity: The wording “more than”/“less than” excludes endpoints; 8 remains the sole common integer. Why Other Options Are Wrong: A/B/C: Neither statement alone yields a single value; “either alone” is false. D: Together they do yield a unique value. Common Pitfalls: Treating “at least/at most” instead of strict inequalities; including endpoints improperly; missing that the domain is integers (days). Final Answer: Both statements together are sufficient, but NEITHER alone is sufficient.

Data Sufficiency Questions