Question 1

Data Sufficiency — Code language symbol meaning: What does the symbol ‘$’ mean? Statements: I. “5$#3” means “flowers are really good”. II. “7#35” means “good flowers are available”.

Accepted Answer

Introduction / Context:Code language problems map words to symbols. Here we must deduce the meaning of the specific symbol “”. Data sufficiency focuses on whether the given statements identify this mapping uniquely.Given Data / Assumptions:I: “5#3” → “flowers are really good”.II: “7#35” → “good flowers are available”.Each word corresponds consistently to a unique symbol across statements.Concept / Approach:Compare the two code–sentence pairs. The overlapping words across the two sentences should match the overlapping symbols. Any leftover word in one sentence should match the leftover symbol in that sentence. That leftover pair gives the required meaning for “”.Step-by-Step Solution:Common words across sentences: “flowers”, “are”, “good”.Common symbols across codes: “5”, “#”, “3”.Therefore, these three words map to {5, #, 3} in some order.Leftover word in Statement I: “really”. Leftover symbol in its code: “”.Hence, “” corresponds to “really”.Verification / Alternative check:If “” meant anything other than “really”, one of the three common words would be unmatched—contradicting the exact one-to-one leftover correspondence. Thus the mapping is unique.Why Other Options Are Wrong:I alone: Without the second sentence, “” could be any of the four words.II alone: Does not even contain “”.Either alone: Not enough to isolate “”.Neither alone: False, because together they suffice.Common Pitfalls:Overlooking “are” as a common word, which is crucial to get exactly three overlaps.Assuming many-to-one mappings; typical puzzles assume a consistent one-to-one mapping.Final Answer:Both I and II are sufficient

Question 2

Data Sufficiency — Counting sons: How many sons does D have? Statements: I. A’s father has three children. II. B is A’s brother and the son of D.

Accepted Answer

Introduction / Context:We must determine the exact number of sons of person D. Data sufficiency requires judging if the statements independently or jointly allow a unique answer, without making unstated assumptions about genders or parentage beyond what is explicit or standard in reasoning questions.Given Data / Assumptions:I: A’s father has three children (no genders specified).II: B is A’s brother and is a son of D (so D is a parent of B, and B is male).“Brother” implies A and B share parents (at least one), but D’s gender is not stated.Concept / Approach:From II, D parents at least one son (B). From I, the father of A has three children; this reveals a total child count in that nuclear family, but it does not necessarily identify D as that father, nor does it identify the genders of the other children (including A). We must avoid presuming that the mother (if D) and father have identical child sets unless explicitly connected.Step-by-Step Solution:II ⇒ D has at least one son (B). A’s gender unknown.I ⇒ A’s father has three children; genders not given, and D is not explicitly identified as A’s father.Combining I and II does not guarantee that D is the same person as “A’s father,” nor does it reveal whether the other two children are sons or daughters.Therefore, the exact number of D’s sons cannot be determined uniquely.Verification / Alternative check:Even if one assumes D is the mother, the father’s three children might be the same three as D’s, but their genders remain unknown apart from B. Multiple consistent possibilities exist (e.g., one son; two sons; or even three sons), so no unique count is possible.Why Other Options Are Wrong:I alone: Says nothing about D.II alone: Gives only a lower bound (at least one son).Either alone or both: Do not pin down a unique number.Common Pitfalls:Assuming D is necessarily the father mentioned in I.Assuming “three children” implies a fixed gender split.Final Answer:Neither I nor II is sufficient

Question 3

Data Sufficiency — Family relations: How is M related to N? Statements: I. P has exactly two children, M and N, and is the mother-in-law of Q. Q is the sister-in-law of N. II. R, the sister-in-law of M, is the daughter-in-law of S, who has exactly t…

Accepted Answer

Introduction / Context:This problem involves kinship logic and the precise meaning of “sister-in-law,” “mother-in-law,” and “daughter-in-law.” We must determine the relationship of M to N (e.g., brother, sister) based on minimal, non-contradictory information, judging each statement’s sufficiency independently and in combination.Given Data / Assumptions:“Sister-in-law” is the spouse of one’s sibling or the sister of one’s spouse, contextually resolved.“Mother-in-law” means parent of one’s spouse; “daughter-in-law” means the wife of one’s son.Each of P and S has exactly two children, M and N (as specified in the respective statements).Concept / Approach:Use Statement I to fix who is married to whom, then deduce genders and sibling relationships. For sufficiency, it is enough to identify how M is related to N (brother/sister) without fully mapping every relative in the family.Step-by-Step Solution:From I: P’s only children are M and N; P is mother-in-law of Q ⇒ Q is married to P’s child (either M or N).Given Q is the sister-in-law of N, Q must be married to N’s sibling (i.e., to M). Hence M is the son of P (because Q is a daughter-in-law), and Q is M’s wife.Therefore, M is a male sibling of N ⇒ M is N’s brother. This answers “How is M related to N?” uniquely.Statement II: R is sister-in-law of M and daughter-in-law of S; S’s only children are M and N. R must then be married to N (not M), which makes N the son of S. However, II does not reveal M’s gender. So II alone does not establish whether M is N’s brother or sister.Verification / Alternative check:Under I, no alternate consistent configuration makes Q sister-in-law of N without Q being M’s wife; thus M is male. Under II, multiple possibilities exist for M’s gender, preventing a definitive relationship label.Why Other Options Are Wrong:II alone: Insufficient—M could be male or female.Either alone / Both: Only I alone is already sufficient; adding II is unnecessary.Common Pitfalls:Misreading “sister-in-law” as necessarily spouse’s sister rather than the spouse of a sibling.Assuming equal information content of both statements; in fact, I pins down M’s gender.Final Answer:I alone is sufficient while II alone is not sufficient

Question 4

Data Sufficiency — Colour naming code: What is the colour name (in this code language) for fresh grass? Statements: I. “Blue” is called “green”, “red” is called “orange”, “orange” is called “yellow”. II. “Yellow” is called “white”, “white” is called…

Accepted Answer

Introduction / Context:These puzzles relabel standard colour words. The question asks what fresh grass would be called in this system. Fresh grass is normally green; we must map the word “green” to its coded name using the provided statements and test sufficiency.Given Data / Assumptions:I: Blue→“green”, Red→“orange”, Orange→“yellow”.II: Yellow→“white”, White→“black”, Green→“brown”, Brown→“purple”.We need the code name for the natural colour “green”.Concept / Approach:Identify which statement contains the mapping for the base colour of fresh grass. Since fresh grass is green, we require the relabelling for “green.” If Statement II directly gives it, then II alone suffices.Step-by-Step Solution:Target: Code name for “green”.Statement II explicitly states: Green→“brown”.Therefore, fresh grass would be called “brown”.Statement I does not mention “green” as an input colour; it only defines names for blue, red, and orange.Verification / Alternative check:No chaining is required beyond the single mapping because the question is about the base colour “green,” not about what “brown” might then be further called.Why Other Options Are Wrong:I alone: Does not map “green”.Either alone / Both: II alone already answers; both together are not required.Neither: Incorrect because II suffices.Common Pitfalls:Over-chaining mappings (e.g., trying to trace multiple steps) when a direct mapping is provided.Confusing the natural colour of grass with its new coded label.Final Answer:II alone is sufficient while I alone is not sufficient

Question 5

Data Sufficiency — Train selection by time: Which train did Aman catch to go to office? Statements: I. Aman missed his usual 10:25 a.m. train. II. A train arrives every 5 minutes. Aman did not catch the 10:40 a.m. train or any train after that.

Accepted Answer

Introduction / Context:We need to identify the exact train Aman boarded. Trains run at regular 5-minute intervals. Data sufficiency requires a unique determination; if multiple trains fit the conditions, the data are insufficient.Given Data / Assumptions:I: Aman missed 10:25 a.m. (his usual train).II: Trains every 5 minutes; Aman did not take the 10:40 a.m. or any later train.Typical sequence near that time: 10:25, 10:30, 10:35, 10:40, 10:45, …Concept / Approach:List feasible trains that respect both constraints. If more than one remains, the answer is not uniquely determined and the correct sufficiency choice is “Neither”.Step-by-Step Solution:From I: Aman did not take 10:25.From II: Aman did not take 10:40 or anything later.Feasible trains between 10:25 (excluded) and 10:40 (excluded): 10:30 and 10:35.Two candidates remain; the data do not single out one train.Verification / Alternative check:Unless an extra condition (e.g., “he boarded the earliest possible train”) is given, both 10:30 and 10:35 satisfy all provided constraints. Therefore, insufficiency is conclusive.Why Other Options Are Wrong:I alone: Gives only one exclusion (10:25).II alone: Excludes 10:40 and later, leaving many possibilities before 10:40.Either / Both: Even together, ambiguity remains between 10:30 and 10:35.Common Pitfalls:Assuming Aman always takes the immediate next train—this is not stated.Overlooking that two qualifying times exist within the window.Final Answer:Neither I nor II is sufficient

Question 6

Data Sufficiency — Day of the week for a visit: On which day did Hitesh visit the zoo? Statements: I. Hitesh did not visit on Tuesday or Thursday. II. Hitesh visited the zoo two days before his mother reached his house, and she arrived the day after…

Accepted Answer

Introduction / Context:We are to determine the exact weekday of Hitesh’s zoo visit. This is a timeline/offset problem framed in data sufficiency style, where specific offsets from a known reference day provide the unique answer.Given Data / Assumptions:I: Excludes Tuesday and Thursday only.II: Mother arrives “the day after Monday,” i.e., Tuesday; Hitesh visited two days earlier.Days of the week follow the usual order: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.Concept / Approach:Translate the verbal offsets into exact days. If one statement pinpoints a unique day, it is sufficient by itself. If not, see whether combining statements is necessary.Step-by-Step Solution:From II: Mother arrives on Tuesday.Two days before Tuesday is Sunday (Tuesday − 2 → Monday − 1 → Sunday).Therefore, Hitesh visited the zoo on Sunday.Statement I alone only rules out two days and cannot fix a unique day.Verification / Alternative check:Cross-check with Statement I: Sunday is neither Tuesday nor Thursday, so there is no conflict. II alone already gives a unique answer, confirming sufficiency.Why Other Options Are Wrong:I alone: Multiple days remain possible.Either / Both: II alone suffices; both are not required.Neither: Incorrect because II works.Common Pitfalls:Miscalculating offsets (some mistakenly say Monday).Thinking “the day after Monday” could be ambiguous—it is Tuesday.Final Answer:II alone is sufficient while I alone is not sufficient

Question 7

Data Sufficiency — Weekly Monday visits (third Monday skipped): When did the Chairman visit the Purchase department? Statements: I. He visited the Accounts department in the second week of September, after having visited the Purchase department on t…

Accepted Answer

Introduction / Context:The Chairman visits exactly one department every Monday, but skips the Monday of the third week of each month. We must identify when he visited the Purchase department, given partial sequencing information. In data sufficiency, we only need to know whether a unique timing can be deduced, not necessarily the full calendar date.Given Data / Assumptions:Visit rule: every Monday except the third Monday of the month (no visit that week).I: Accounts was visited in the 2nd week of September, and Purchase was visited on the earlier occasion.II: Purchase occurred immediately after Stores and before Accounts (ordering constraint only).Concept / Approach:Translate the “earlier occasion” in Statement I using the weekly pattern. Mondays progress week by week with a regular cadence; between the 1st and 2nd Monday there is no skipped Monday. Hence the “earlier occasion” before the 2nd-week Monday is the 1st-week Monday of September.Step-by-Step Solution:From I: If Accounts is in Week-2 Monday of September, the immediately previous visit is Week-1 Monday of September (no skip occurs between week 1 and week 2). That earlier visit is stated to be Purchase.Therefore, Purchase was visited on the first Monday of September.Statement II adds an ordering Stores → Purchase → Accounts, but without any calendar anchor, II alone cannot place Purchase in a specific week.Verification / Alternative check:The “skip third Monday” rule does not affect positioning between week 1 and week 2. Thus, the conclusion from I is robust and unique.Why Other Options Are Wrong:II alone: Pure ordering—no week/date can be fixed.Either / Both: I alone suffices; adding II is unnecessary.Neither: Incorrect because I alone works.Common Pitfalls:Misreading “earlier occasion” as an arbitrary earlier month rather than the immediately previous Monday visit.Letting the “third-Monday skip” confuse the straightforward week-1 to week-2 progression.Final Answer:I alone is sufficient while II alone is not sufficient

Question 8

Data Sufficiency – Code Language Mapping Question: In a certain code language, what word does the code 'nip' represent? Statements: I. 'that is very beautiful' is coded as 'se nip sre num' II. 'my house is beautiful' is coded as 'nip sto sre tip'

Accepted Answer

Introduction / Context: This is a classic Data Sufficiency problem about decoding a substitution code language. Each word in a sentence maps one-to-one to a distinct code token. We must determine whether the given statements provide enough information to identify exactly which English word corresponds to the code token 'nip'—without necessarily computing every mapping.Given Data / Assumptions: Main question uses two independent statements.Statement I: 'that is very beautiful' → 'se nip sre num'Statement II: 'my house is beautiful' → 'nip sto sre tip'Assume a consistent one-to-one mapping within this problem's universe.Concept / Approach: In code problems, compare sentences to find common words and their common codes. If two sentences share exactly one common word, their code intersection reveals that word’s code. If they share two or more words and two or more codes, the mapping may remain ambiguous unless extra information breaks the tie.Step-by-Step Solution: From I: words = {that, is, very, beautiful}; codes = {se, nip, sre, num}. From II: words = {my, house, is, beautiful}; codes = {nip, sto, sre, tip}. Common words across I and II: {is, beautiful} (two words). Common codes across I and II: {nip, sre} (two codes). Therefore, {is, beautiful} maps to {nip, sre} in some order. Without further information, 'nip' could be either 'is' or 'beautiful'.Verification / Alternative check: Even if we combine Statements I and II, the intersection yields two common words and two common codes. No uniqueness arises. We cannot pinpoint which of the two words corresponds to 'nip'.Why Other Options Are Wrong: 'I alone is sufficient' or 'II alone is sufficient': Each statement individually still leaves two possible words for 'nip'. 'Either I or II is sufficient': False, because neither alone resolves the ambiguity. 'Both I and II are sufficient': Even together, ambiguity persists.Common Pitfalls: Assuming alphabetical or positional hints in code tokens; such assumptions are not justified. Overlooking that two shared words lead to two shared codes, which is inherently ambiguous without a tie-breaker.Final Answer: Neither I nor II is sufficient

Question 9

Data Sufficiency – Percentage Salary Relations Question: What is Prashant's monthly salary? Statements: I. Prashant gets 15% more than Sumit, and Sumit gets 10% less than Lokesh. II. Lokesh's monthly salary is Rs 2,500.

Accepted Answer

Introduction / Context: This Data Sufficiency item checks whether the given percentage relationships provide enough information to compute an absolute monthly salary for Prashant. Data Sufficiency requires deciding sufficiency, not necessarily reporting the numeric answer (though we can compute it to verify).Given Data / Assumptions: I: Prashant = Sumit * (1 + 15%), Sumit = Lokesh * (1 − 10%).II: Lokesh = Rs 2,500.All salaries are monthly and in rupees (Rs).Concept / Approach: A percentage chain needs a base (an absolute figure) to produce an absolute result. Statement I provides relationships only; Statement II provides the base value needed. Together, they are sufficient to obtain an exact value.Step-by-Step Solution: From II: Lokesh = 2,500. From I: Sumit = Lokesh * 0.9 = 2,500 * 0.9 = 2,250. Prashant = Sumit * 1.15 = 2,250 * 1.15 = 2,587.50. Thus an exact figure is computable when I and II are used together.Verification / Alternative check: I alone: Only relative percentages, no absolute base → cannot yield a unique rupee value. II alone: Knowing Lokesh alone doesn’t specify Prashant's percentage relation without Statement I.Why Other Options Are Wrong: 'I alone sufficient' or 'II alone sufficient': Each is inadequate by itself. 'Either I or II': Not true, because neither alone yields Prashant’s exact salary. 'Neither': False; together they clearly suffice.Common Pitfalls: Stopping at relative values and forgetting an absolute anchor is necessary for a numeric result. Arithmetic slip-ups with percentage increase vs. decrease.Final Answer: Both I and II are sufficient

Question 10

Data Sufficiency – Sales & Percentage Increase Question: How many gift boxes were sold on Monday? Statements: I. Monday's sales were 10% more than the number of boxes sold on Sunday. II. Every third visitor purchased a box, and there were 1,500 visi…

Accepted Answer

Introduction / Context: This problem blends ratio-based conversion (visitors to buyers) with a percentage increase across days. We must check if one or both statements provide enough data to compute Monday's exact sales.Given Data / Assumptions: I: Monday = Sunday * (1 + 10%).II: On Sunday, 1 out of every 3 visitors bought a box; Sunday had 1,500 visitors.Purchasing rule is precise and constant for Sunday as stated.Concept / Approach: Statement I relates Monday to Sunday by a fixed percentage. Statement II allows us to convert Sunday's visitors into Sunday's boxes sold. Together, these fully determine Monday’s sales.Step-by-Step Solution: From II: Sunday buyers = 1,500 / 3 = 500 boxes. From I: Monday buyers = Sunday buyers * 1.10 = 500 * 1.10 = 550 boxes. Thus Monday's sales are uniquely determined using both statements.Verification / Alternative check: I alone: We know Monday is 10% over Sunday but do not know Sunday's count; insufficient. II alone: We can compute Sunday's sales (500), but Monday's percentage relation is unknown; insufficient.Why Other Options Are Wrong: Any option claiming sufficiency of a single statement is incorrect because each alone leaves a missing link.Common Pitfalls: Forgetting to convert visitors to buyers exactly as stated (every third visitor). Applying the 10% to visitors instead of to Sunday’s boxes sold.Final Answer: Both I and II are sufficient

Question 11

Data Sufficiency – Code Language (Three-Digit Words) Question: In a code language, '297' means 'tie clip button'. Which single digit represents 'button'? Statements: I. '926' means 'clip your tie'. II. '175' means 'hole and button'.

Accepted Answer

Introduction / Context: Another code-language Data Sufficiency item. We know '297' encodes three distinct words: tie, clip, button. We must decide if Statement I or II (or both) lets us isolate which single digit stands for 'button'.Given Data / Assumptions: Base: '297' → {tie, clip, button}.I: '926' → {clip, your, tie}.II: '175' → {hole, and, button}.One-to-one mapping within the problem’s language.Concept / Approach: Use set intersections. If two coded strings share exactly the words 'clip' and 'tie', then the shared digits correspond to those two words; the remaining digit in '297' must then be 'button'. Similarly, if you compare a string containing 'button' with the base, the unique common digit reveals the code for 'button'.Step-by-Step Solution (using I only): '297' → {2,9,7} for {tie, clip, button}. '926' → {9,2,6} for {clip, your, tie}. Common words between base and I: {clip, tie} → common digits {9,2}. Therefore the remaining digit in '297', which is 7, must represent 'button'.Alternative (using II only): '175' encodes {hole, and, button}. Intersect digits with '297': {1,7,5} ∩ {2,9,7} = {7}. Since both code groups contain the word 'button', the unique common digit 7 must be 'button'.Why Other Options Are Wrong: 'I alone sufficient while II alone not' and vice versa are both too restrictive because each statement, independently, already pins down 'button'. 'Both I and II' is stronger than necessary. 'Neither' is incorrect because we actually can deduce the digit.Common Pitfalls: Forgetting that the base information '297' → 'tie clip button' is always available when testing each statement’s sufficiency.Final Answer: Either I or II is sufficient

Question 12

Data Sufficiency – Positions in a Row Question: What is Sumit’s position from the right end in a row of children? Statements: I. There are 10 children between Sumit and Rajan. II. Rajan is 20th from the left end of the row.

Accepted Answer

Introduction / Context: This Data Sufficiency question concerns linear arrangement indices. We are asked for Sumit’s position from the right end, which requires both his absolute position and the total number of children (or an equivalent piece of information).Given Data / Assumptions: I: Exactly 10 children lie between Sumit and Rajan.II: Rajan is 20th from the left end.Total number of children in the row is not directly given.Concept / Approach: Knowing a gap between two persons plus one absolute position can still leave two possible positions for the other person (to the left or to the right), unless additional constraints or boundaries are given. To find a position from the right, we typically also need the total count or a right-end reference.Step-by-Step Reasoning: From II: Rajan = 20th from the left. From I: Sumit is either 11 places to the right of Rajan or 11 places to the left of Rajan (since 10 in between implies a separation of 11 positions). Thus Sumit could be either 31st from the left or 9th from the left. Without the total number of children, Sumit’s position from the right remains undetermined in both cases.Verification / Alternative check: Even combining I and II, we do not know the total size of the row. Two distinct possibilities remain, giving different answers from the right end.Why Other Options Are Wrong: 'I alone' or 'II alone': Each is clearly insufficient. 'Either' or 'Both': Incorrect, because ambiguity persists without row length.Common Pitfalls: Assuming the person must be to one specific side without justification. Forgetting that 'from the right' demands knowing the total count.Final Answer: Neither I nor II is sufficient

Question 13

Data Sufficiency – Decoding a Three-Word Code Question: In a certain code, 'nop al ed' means 'They like flowers'. Which code stands for 'flowers'? Statements: I. 'id nim nop' means 'They are innocent'. II. 'gob ots al' means 'We like roses'.

Accepted Answer

Introduction / Context: We must find the unique code token for the word 'flowers' from a three-word coded sentence. Data Sufficiency requires checking whether Statement I, Statement II, or both provide enough information without necessarily deriving all mappings.Given Data / Assumptions: Base: 'nop al ed' → 'They like flowers'.I: 'id nim nop' → 'They are innocent'.II: 'gob ots al' → 'We like roses'.One-to-one mapping assumed.Concept / Approach: Use overlaps. If we can identify the code for 'like' or 'they', then, by elimination within the base triple, the remaining code must represent 'flowers'.Step-by-Step Solution: Base codes: {nop, al, ed} correspond to {They, like, flowers} in some order. From I, common word with base is 'They'. Common code is 'nop' (since 'nop' appears in I and in the base triple). Hence, 'They' → 'nop'. Now base remaining words {like, flowers} map to {al, ed} (order unknown so far). From II, common word with base is 'like'. The common code is 'al' (present in II and in the base triple). Therefore, 'like' → 'al'. Consequently, the only remaining code in the base for the remaining word is 'ed' → 'flowers'.Verification / Alternative check: I alone: Identifies 'They' → 'nop', but cannot distinguish between 'al' and 'ed' for 'flowers' vs 'like'. II alone: Directly identifies 'like' → 'al' using the base; then within the base triple, 'ed' must be 'flowers'.Why Other Options Are Wrong: 'I alone sufficient': Not enough; ambiguity remains between 'al' and 'ed'. 'Either I or II': Incorrect because I alone fails. 'Both I and II': Overkill; II alone suffices. 'Neither': False; II works.Common Pitfalls: Not leveraging the base sentence as shared information when testing each statement alone.Final Answer: II alone is sufficient while I alone is not sufficient

Question 14

Data Sufficiency – Linear Arrangement (Middle Position) Question: In a row of five children A, B, C, D, and E, who stands in the middle? Statements: I. D is immediately to the right of E, and B is immediately to the left of E. II. B is at the extrem…

Accepted Answer

Introduction / Context: Determine the middle position (third from either end) among five children using relative and absolute placement clues. Data Sufficiency focuses on whether the given statements provide enough information to answer uniquely.Given Data / Assumptions: Exactly five positions in a single row.I: B is immediately left of E; D is immediately right of E → the trio B-E-D must be consecutive in that exact order.II: B is at the extreme left of the row.Concept / Approach: Use Statement I to form a rigid consecutive block and Statement II to anchor the block in the row. With five positions, anchoring resolves the middle position uniquely.Step-by-Step Solution: From I: consecutive order must be B, E, D. From II: B is at position 1 (leftmost). Therefore positions 1–3 are B–E–D respectively. Hence the middle (position 3) is D, and A, C occupy positions 4 and 5 in some order.Verification / Alternative check: I alone: The block B–E–D could be at positions (1–3), (2–4), or (3–5), leading to different middles (D/E/B respectively). Insufficient. II alone: Knowing only B is at the extreme left gives no full order. Insufficient. I + II: Unique placement; sufficient.Why Other Options Are Wrong: Any claim that a single statement suffices contradicts the multiple possible placements with I alone and the lack of detail with II alone.Common Pitfalls: Misreading 'immediate' as 'somewhere left/right' rather than exactly adjacent.Final Answer: Both I and II are sufficient

Question 15

Data Sufficiency – Counting Employees Opting for VRS Question: How many employees of Bank Z opted for Voluntary Retirement Scheme (VRS)? Statements: I. 18% of the 950 officer-cadre employees and 6% of the 1,100 other-cadre employees opted for VRS. I…

Accepted Answer

Introduction / Context: We must determine if the provided information is enough to compute the exact number of employees opting for VRS. One statement gives cadre-wise counts and percentages; the other gives age-wise percentages without population counts.Given Data / Assumptions: I: Officers = 950 with 18% opting; Others = 1,100 with 6% opting.II: Percentages given by age bands (28% and 17%) but no headcounts per band.Populations are disjoint within each categorization (cadre or age) but totals are needed to compute a number.Concept / Approach: To compute a number from a percentage, you need both the rate and the base count. Statement I provides both rates and their corresponding base counts by cadre, which is sufficient. Statement II lacks the required base counts by age groups, which is insufficient.Step-by-Step Solution: Using I: Officers opting = 0.18 * 950 = 171. Using I: Others opting = 0.06 * 1,100 = 66. Total opting = 171 + 66 = 237. Thus I alone yields the exact figure.Verification / Alternative check: II alone: We do not know how many employees are in 51–56 vs. the rest. Without those base counts, no numeric total can be computed.Why Other Options Are Wrong: 'II alone' or 'Either': Not valid because II lacks base counts. 'Both': Overstated; I already suffices. 'Neither': False; I works.Common Pitfalls: Attempting to use percentages without the relevant base population sizes.Final Answer: I alone is sufficient while II alone is not sufficient

Question 16

Data Sufficiency – Relative Earnings Ordering Question: Among M, N, D, P, and K, who earns more than only the least earner (i.e., who is second from the bottom)? Statements: I. N earns more than M and P but less than only D. II. M earns more than P,…

Accepted Answer

Introduction / Context: The task is to identify the person who is exactly above the least earner (second-lowest) using partial order information. This is a common ranking-style Data Sufficiency problem.Given Data / Assumptions: I: N earns less than only D, and N earns more than M and P. No explicit info on K in I.II: M > P and K > P but M > K is not implied (only P All five individuals are distinct and have total orderings with no ties implied.Concept / Approach: Combine statements to construct a complete chain from lowest to highest. Statement I places N second-highest and D highest. Statement II orders P Step-by-Step Solution: From I: D is highest; N is second-highest; also N > M and N > P. From II: P P and K > P but no K–M reversal is stated; M > K is not forced by II alone, but I has N > M, consistent with placing M below N). Combine: The only consistent total order is P Hence the person who earns more than only the least earner (second from bottom) is K.Verification / Alternative check: I alone leaves K's position unknown; II alone gives only a partial chain among three people. Together they produce a unique full ordering.Why Other Options Are Wrong: Any option claiming single-statement sufficiency is invalid because neither I nor II alone yields the exact second-lowest person.Common Pitfalls: Assuming relationships not stated (e.g., M compared to K beyond what II provides) without integrating I's constraints.Final Answer: Both I and II are sufficient

Question 17

Data Sufficiency — Ranks in a Class (Total = 25 students) Question: What is Sachin's rank from the top in a class of 25 students? Statements: I. Sachin ranks three positions above Amit, who ranks 18th from the bottom. II. Sachin's rank from the top …

Accepted Answer

Introduction / Context: This is a classic Data Sufficiency problem on ranking. We must determine whether the information in the statements is enough to find Sachin's exact rank from the top out of 25 students. We do not need to compute the rank twice if either statement independently gives a unique answer. Given Data / Assumptions: Total students = 25. From bottom to top conversion: top_rank = total - bottom_rank + 1. “Above” from the top means a smaller (better) top rank number. Concept / Approach: Convert any rank given from the bottom into rank from the top, then apply the stated positional gaps. If one statement yields a unique rank for Sachin without using the other, that statement alone is sufficient. Step-by-Step Solution: From I: Amit = 18th from bottom → Amit from top = 25 - 18 + 1 = 8. Sachin is three positions above Amit (from top), so Sachin from top = 8 - 3 = 5. Statement I alone gives a unique rank (5th), so I is sufficient. From II: Deepti = 23rd from bottom → Deepti from top = 25 - 23 + 1 = 3. Sachin is two positions below Deepti (from top), so Sachin from top = 3 + 2 = 5. Statement II alone also gives a unique rank (5th), so II is sufficient. Verification / Alternative check: Both statements independently produce rank 5 from the top, confirming internal consistency and uniqueness. Why Other Options Are Wrong: I alone not sufficient / II alone not sufficient: False, each alone gives the exact rank 5. Neither sufficient: False. Both required: Overkill; either one suffices. Common Pitfalls: Mixing up “from bottom” conversions or misinterpreting “above/below” in rank order leads to incorrect arithmetic. Always convert bottom ranks to top ranks before applying relative positions. Final Answer: Either I or II is sufficient.

Question 18

Data Sufficiency — Bus Timetable Question: It is 8:00 p.m. in Dhanpur. When can Hemant get the next bus for Ramnagar? Statements: I. Buses for Ramnagar leave after every 30 minutes, till 10:00 p.m. II. Fifteen minutes ago, one bus left for Ramnagar.

Accepted Answer

Introduction / Context: This Data Sufficiency item checks understanding of periodic events and whether knowing the phase (i.e., the last departure time) is necessary to determine the next departure time. Given Data / Assumptions: Current time = 8:00 p.m. Departures occur every 30 minutes (from Statement I). A bus left 15 minutes ago (from Statement II), i.e., at 7:45 p.m. Concept / Approach: For periodic schedules, frequency alone is not enough unless the timing offset (a recent or reference departure) is known. A known last-departure time lets us add the period to get the next departure. Step-by-Step Solution: Using I only: Frequency = every 30 minutes till 10:00 p.m. However, without knowing whether buses leave at :00/:30 or at :15/:45, the exact next time from 8:00 p.m. cannot be pinned down. Thus, I alone is not sufficient. Using II only: One bus left 15 minutes ago at 7:45 p.m. With 30-minute periodicity implied by the context of bus operations, the next is at 7:45 p.m. + 30 minutes = 8:15 p.m. Therefore, II alone is sufficient to answer “When is the next bus?” Verification / Alternative check: Whether or not the service runs until 10:00 p.m. does not affect the immediate next departure at 8:15 p.m., since 8:15 p.m. is before 10:00 p.m. Why Other Options Are Wrong: I alone sufficient: No, phase unknown. Either alone sufficient: No, only II works. Neither sufficient: Incorrect because II works. Both required: Unnecessary; II already suffices. Common Pitfalls: Assuming default departure times (e.g., exactly on the hour/half-hour) without evidence; overlooking that a single recent departure time fixes the phase immediately. Final Answer: II alone is sufficient while I alone is not sufficient.

Question 19

Data Sufficiency — Taller Girls Than Shravan Question: How many girls are taller than Shravan in his class? Statements: I. Ranking all students in descending height, Shravan is 17th from the top overall and 12th among boys. II. Shravan's rank from t…

Accepted Answer

Introduction / Context: Determine the number of girls taller than Shravan using ranking information. Treat the class as a single ordered list while also using the boys-only ordering. Data Sufficiency asks whether the statements give enough information independently. Given Data / Assumptions: From Statement I: Shravan is 17th overall from the top; 12th among boys from the top. From Statement II: Shravan is 18th among boys from the bottom; 29th among all from the bottom. Total class size is not explicitly provided; it may or may not be needed. Concept / Approach: Number of people taller than Shravan overall is (overall top rank - 1). Number of boys taller than Shravan is (boys top rank - 1). Girls taller than Shravan = (overall taller) - (boys taller). Step-by-Step Solution: Using I: Overall taller than Shravan = 17 - 1 = 16. Boys taller than Shravan = 12 - 1 = 11. Girls taller than Shravan = 16 - 11 = 5. So Statement I alone is sufficient. Using II: From bottom ranks, we need totals to convert to top ranks: overall top rank = N - 29 + 1; boys top rank = B - 18 + 1. Without knowing N (total students) and B (total boys), we cannot compute a definite count of taller girls. Hence II alone is not sufficient. Verification / Alternative check: The result 5 depends only on relative positions from Statement I and does not require total class or total boys counts. Why Other Options Are Wrong: II alone sufficient: False—totals unknown. Either alone sufficient: False—only I works. Neither sufficient: False—I suffices. Both required: Unnecessary; I alone is enough. Common Pitfalls: Forgetting to subtract 1 when converting a rank to the count of people ahead; assuming totals that are not given; mixing up top and bottom rankings. Final Answer: I alone is sufficient while II alone is not sufficient.

Question 20

Data Sufficiency — Family Relations Question: How is R related to M? Statements: I. M's brother is the husband of P. II. P is the mother of R's sister.

Accepted Answer

Introduction / Context: A kinship (blood-relation) Data Sufficiency problem. We must decide if the statements together or individually are enough to fix the relationship between R and M (e.g., nephew/niece, child, sibling, etc.). Given Data / Assumptions: I: M's brother is P's husband. II: P is the mother of R's sister (standard assumption: same mother implies P is R's mother). Gender of R is not specified, so the answer will be in the form nephew/niece (child of M's brother). Concept / Approach: Build the family links: if P is married to M's brother and P is R's mother, then R is the child of M's brother. Therefore, R is M's brother's child, i.e., R is M's nephew or niece (depending on R's gender). Step-by-Step Solution: From I: M's brother ↔ married to P. Thus P is M's sister-in-law. From II: P is the mother of R's sister ⇒ P is R's mother. Combine I and II: Since P (R's mother) is married to M's brother (from I), R is the child of M's brother. Therefore, R is M's nephew/niece (child of a sibling of M). Verification / Alternative check: Neither I nor II alone links R to M conclusively. Only together do they establish that R is the child of M's brother. Why Other Options Are Wrong: I alone sufficient: No, links M↔P but not R. II alone sufficient: No, identifies R's mother but no link to M. Either alone sufficient: False for the same reason. Neither sufficient: False because together they are sufficient. Common Pitfalls: Ignoring that “mother of R's sister” implies “mother of R”; assuming genders not given; misreading “brother of M” versus “brother-in-law of M”. Final Answer: Both I and II are sufficient.

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