Logical Reasoning, approach + real CAT sets

SET, Coloured leaves (mathematical reasoning). On her walk through the park, Hansa collected 50 coloured leaves, all either maple or oak. She sorted them and found: A. The number of red oak leaves with spots is even and positive. B. The number of red oak leaves without any spot equals the number of red maple leaves without spots. C. All non-red oak leaves have spots, and there are five times as many of them as there are red spotted oak leaves. D. There are no spotted maple leaves that are not red. E. There are exactly 6 red spotted maple leaves. F. There are exactly 22 maple leaves that are neither spotted nor red.

SET, Paint mixing (Rang Barsey). RBPC buys RED (₹20), YELLOW (₹25), WHITE (₹15), ORANGE (₹22), PINK (₹18) per litre. ORANGE = RED + YELLOW (equal parts); PINK = RED + WHITE (equal parts). It sells CREAM = WHITE:YELLOW = 70:30, AVOCADO = equal ORANGE + PINK, WASHEDORANGE = equal ORANGE + WHITE.

SET, Basketball baskets. Facts: (a) Ganesh = Ashish − 8; (b) Dhanraj + Ramesh = 37; (c) Jugraj = Dhanraj + 8; (d) Ashish = Dhanraj + 5; (e) Ashish + Ganesh = 40.

SET, Idli-vada breakfast. Five friends each eat a different number of idlis (1,4,5,6,8) and vadas (0,1,2,4,6). Clues: (a) Ignesh's vadas = 3× the vadas of the person eating 4 idlis; (b) three persons (incl. the 4-vada one) eat without chutney; (c) Sandeep takes no chutney; (d) the 1-idli person eats no vada/chutney and is not Mukesh; (e) Daljit eats idli with chutney and also eats vada; (f) Mukesh (no chutney) eats half as many vadas as the person eating twice his idlis; (g) Bimal eats 2 more idlis than Ignesh, but Ignesh eats 2 more vadas than Bimal.

SET, Disguised firms (data-sufficiency LR). Revenue (₹ million) of four firms in three states; the firms Honest, Aggressive, Truthful and Profitable are disguised as A, B, C, D in some order.

Also: in MP, Truthful has the highest market share; Aggressive's aggregate revenue differs from Honest's by ₹5 million. (Aggregates: A=190, B=217, C=222, D=185.)

SET, Traffic network & tolls. One-way streets from S to T via junctions A, B, C, D with fuel costs: S→A=9, A→T=5, S→B=2, B→A=2, B→C=3, S→D=7, D→T=6, D→C=1, C→T=2. Motorists pick the least-cost route; ties split traffic evenly. The government levies tolls a, b, c, d at A, B, C, D.

SET, Diet formulations (selection with conditions). Five ingredients can be mixed in proportions. Cost/unit: O 150, P 50, Q 200, R 500, S 100.

SET, Department transfers (mathematical reasoning). 100 employees across five departments. Gross pay = basic + allowances. A person moving from a lower-avg-age dept to a higher one gets +10% of basic as extra allowance; moving the other way changes nothing. Questions are independent.

SET, Platform grid "can reach". A 5×5 layout of square platforms of given heights. A can reach B if: (a) same row/column; (b) A is lower than B; (c) anyone between them is lower than A. Rows top→bottom, columns left→right. Heights:

SET, Congestion routing (games/networks). Four cars go A→B via M or N. A→M and N→B: 1 car takes 6 min, each extra car +3 min/car. A→N: 6 min... actually 1 car 20 min, +1 min/car. M→B: 1 car 20 min, +0.9 min/car. Police assign routes so no car can cut its time by deviating alone.

SET, Fingerprint pass-key (counting / binary logic). A pass-key is the order of scanning five fingers T, I, M, R, L. The lab relaxes the order requirement in various ways.

SET, ATM notes (distribution / counting). An ATM dispenses exactly ₹5000 per withdrawal using ₹100, ₹200, ₹500 notes. The customer's preferred denomination's note-count must exceed the total count of the other denominations.

SET, Three committees. 24 people on research, teaching, administration committees; no shared members; all three sizes different; each has bureaucrats, educationalists, politicians (≥1 each). (1) Bureaucrats in research = teaching, and research = 75% of admin. (2) Educationalists: teaching < research, and research = average of the other two. (3) 60% of politicians in admin, 20% in teaching.

SET, Cryptarithm addition. Two six-digit numbers add to a six-digit sum; digits 0-9 coded by distinct letters A-K. The columns (left to right) are: Row1: A B H A A G F · Row2: A H J F K F · Sum row: A F G C A F (each column shown as top+top=bottom). Find the digit each letter represents.

SET, Vendor contracts (scheduling). Institutes A,B,C,D and vendors W,X,Y,Z, 2010-2019. Each institute had 2 contracts (with 2 vendors); each vendor had 2 contracts (with 2 institutes); no institute had two contracts with the same vendor. Facts: I. Z had ≥1 contract every year. II. X had contracts up to 2015, none after. III. Y had contracts in 2010 & 2019; W only in 2013. IV. Five contracts in 2012. V. Exactly four multi-year contracts: B 7-yr, D 4-yr, A & C 3-yr each; the other four single-year. VI. C had ≥1 in 2012 but none in 2011. VII. B and D each had exactly one contract in 2012; D had none in 2010.

SET, Coloured beads grid (layout). 25 beads in a 5×5 grid, each Red/Blue/Green. Along any row or column: (1) adjacent beads differ in colour; (2) ≥1 Green between any two Blues; (3) ≥1 Blue and ≥1 Green between any two Reds.

SET, Hi-Lo game (binary logic). Four players, six rounds; each bids Hi or Lo simultaneously. Scoring: 4 Hi ⇒ all −1; 3 Hi/1 Lo ⇒ Hi +1, Lo −3; 2 Hi/2 Lo ⇒ Hi +2, Lo −2; 1 Hi/3 Lo ⇒ Hi +3, Lo −1; 4 Lo ⇒ all +1. Facts: (1) after 3 rounds Arun 6, Dipak 2, Bankim & Charu −2; (2) after 6 rounds Arun 7, Bankim & Dipak −1, Charu −5; (3) Dipak's round-3 score < round-1 but > round-2; (4) in exactly two of the six rounds Arun was the only one to bid Hi.

SET, Get-together attendance (set theory). 15 girls and some boys. Events: 1-day, 2-day or 3-day (3-day attendees also do 2-day; 2-day also 1-day). 6 singers (4 boys), 10 dancers (4 girls); no dancer is a singer. Facts: (1) all girls & 80% of boys want 1-day; 60% of boys want 2-day. (2) some girls want 1-day but not 2-day; others want both. (3) 70% of boys wanting 2-day are neither singers nor dancers; 60% of girls wanting 2-day are neither. (4) no girl wants 3-day; all male singers & 2 dancers want 3-day. (5) singers wanting 2-day = dancers wanting 2-day + 1.

SET, Salesmen success rates. Three salesmen Tohri, Hokli, Lahur over two days. Success rate = items sold / households met. (1) Same total households over two days; each sold 100 items total. (2) Lahur met the same households & sold the same items on both days. (3) Hokli sold nothing on day 2 (first household complained). (4) Tohri met 30 more households on day 2 than day 1. (5) Tohri's success rate = 2× Lahur's on day 1, and = 75% of Lahur's on day 2.

SET, Supermarket products (set theory). 320 products, each cosmetic or nutrition, each foreign or domestic, each with at least one of FDA / EU approval. (1) Equal domestic and foreign. (2) Half the domestic products were FDA-approved cosmetics. (3) No foreign product had both approvals; 60 domestic had both. (4) 140 nutrition products; half foreign. (5) 200 FDA-approved products: 70 foreign, 120 cosmetic.

SET, Dean election (analytical reasoning). Faculty belong to F&A (9), M&S (7), O&Q (5), B&H (3). Four candidates, Pakrasi, Qureshi, Ramaswamy, Samuel, stood for Dean; only one was from O&Q. Everyone voted; in each department all non-candidates voted for the same candidate. Rules: ≤2 candidates per department; no self-vote; no voting for own department's candidate. Results: Pakrasi 3, Qureshi 14, Ramaswamy 6, Samuel 1. Pakrasi voted Ramaswamy, Qureshi voted Samuel, Ramaswamy voted Qureshi, Samuel voted Pakrasi.

SET, Election Campaigns. Amiya and Ramya each run a campaign at one of two intensity levels, staid = level 1, vigorous = level 2, and each either focuses on issues or attacks the opponent. Base rule (both focus on issues): voter turnout = 20 × (sum of the two levels) %, and vote share is split in proportion to the two campaign levels. Attack modifications: if Amiya attacks & Ramya stays on issues, 10% of Amiya's voters switch to Ramya and 10% don't vote; if Ramya attacks & Amiya stays on issues, 20% of Ramya's voters switch to Amiya and 5% don't vote; if both attack, 10% of each candidate's voters don't vote.

SET, Countries Visited. The chart below provides complete information about the number of countries visited by Dheeraj, Samantha and Nitesh, in Asia, Europe and the rest of the world (ROW). The following additional facts are also known: (1) 32 countries were visited by at least one of them. (2) USA (in ROW) is the only country that was visited by all three of them. (3) China (in Asia) is the only country that was visited by both Dheeraj and Nitesh, but not by Samantha. (4) France (in Europe) is the only country outside Asia, which was visited by both Dheeraj and Samantha, but not by Nitesh. (5) Half of the countries visited by both Samantha and Nitesh are in Europe.

(The source data is a bar chart of countries-visited-per-region per person; the chart image cannot be transcribed verbatim here. The official answers below are confirmed.)

SET, Employee ratings & promotions. At InnovateX, six employees (Asha, Bunty, Chintu, Dolly, Eklavya, Falguni) are split into two groups of three: Elite (managed by Kuku) and Novice (managed by Lalu). Each quarter, the members of a group receive distinct integer ratings 1-3; an employee's score at the end of a quarter is their cumulative rating from the start of the year. After each quarter, the highest-scoring Novice is promoted to Elite and the lowest-scoring Elite is demoted to Novice (ties broken by the higher rating in the latest quarter). Facts: Asha, Bunty and Chintu were in Elite at the beginning of Quarter 1, and all of them were in Novice at the beginning of Quarter 4. Dolly and Falguni were the only employees who got the same rating across all the quarters. In Quarter 3, under Lalu, Asha and Dolly received ratings of 1 and 2 respectively. Bunty received a rating of 1 in Quarter 2.

SET, Round-table seating. Seven chairs (1-7 clockwise). Four friends, Aslam, Bashir, Chhavi, Davies. Initially Aslam-Chhavi are adjacent, and Bashir and Davies each have empty chairs on both sides. On each turn a person moves to the first empty chair (clockwise or anti-clockwise). Turn order: Aslam, Bashir, Chhavi, Davies, Aslam, Bashir, Chhavi. Friends sit in adjacent chairs only after Turn 2 and Turn 6. Davies: chair 2 after Turn 1, chair 4 after Turn 5. Chhavi in chair 7 after Turn 2.

SET, Tapping game. Alia, Badal, Clive, Dilshan and Ehsaan played a game in which each asks a unique question to all the others, and they respond by tapping their feet, either once or twice or thrice. One tap means "Yes", two taps mean "No", and three taps mean "Maybe". A total of 40 taps were heard across the five questions, and each question received at least one "Yes", one "No" and one "Maybe". Also: (1) Alia tapped a total of 6 times and received 9 taps to her question; she responded "Yes" to the questions asked by both Clive and Dilshan. (2) Dilshan and Ehsaan tapped a total of 11 and 9 times respectively; Dilshan responded "No" to Badal. (3) Badal, Dilshan and Ehsaan received an equal number of taps to their respective questions. (4) No one responded "Yes" more than twice. (5) No one's answer to Alia's question matched the answer that Alia gave to that person's question. (6) Clive tapped more times in total than Badal.

SET, Balls & hoops. Six balls (B1-B6) tested on four hoops (H1-H4). A ball "pings" if its diameter ≤ hoop diameter, else it gets stuck. Facts: (1) B1 and B6 pinged H4 but B5 didn't; (2) B4 pinged H3 but B1 didn't; (3) all balls except B3 pinged H1; (4) only B2 pinged H2.

SET, Musicians & gurus. Four musicians (Ananya, Bhaskar, Charu, Devendra) trained under three gurus (Pandit Meghnath, Ustad Samiran, Acharya Raghunath), 2013-2024. Each guru trains for a different consecutive span (2, 3 or 4 years) and never more than two students at once. "Gurubhai" pairs train under the same guru in the same year. Facts: Samiran trained at most one student per year; Raghunath inactive 2015-18 and 2021-24; Ananya-Devendra and Bhaskar-Charu were never gurubhai, all other pairs were gurubhai exactly 2 years; in 2013 Ananya started under Meghnath, Bhaskar under Samiran.

SET, Research papers by authors. Four authors (Arman, Brajen, Chintan, Devon) write single-, two-, three- and four-author papers. Charts show paper counts by type and author-contribution totals. Facts: each author wrote ≥1 of each type; all four wrote different numbers of single-author papers; both Chintan and Devon wrote more three-author papers than Brajen; Brajen's single- and two-author counts were equal.

SET, International travel. Aurevia, Brelosia, Cyrenia and Zerathania are four countries, with currencies Aurels, Brins, Crowns and Zentars respectively. One Crown is worth 0.5 Zentars. Three travellers, Jano, Kira and Lian, set out from Zerathania, each visiting exactly two of the other countries, and each country is visited by exactly two travellers. Each traveller's Flight Cost is the total airfare to both countries and back; Jano's Flight Cost was 4000 Zentars and the other two were 5000 and 6000 Zentars (in some order). When visiting a country a traveller spent 1000, 2000 or 3000 in the local currency, with a different spend in each of the two countries; across all visits there were exactly two spends of 1000 and exactly one spend of 3000. Observations: Aurevia citizen, "Jano and Kira visited our country, and their Travel Costs were 3500 and 8000, respectively." Brelosia citizen, "Kira and Lian visited our country, spending 2000 and 3000, respectively. Kira's Travel Cost was 4000." Cyrenia citizen, "Lian visited our country and her Travel Cost was 36000."

SET, Passing the Buck. Seven children, Aarav, Bina, Chirag, Divya, Eshan, Farhan and Gaurav, sit in a circle facing inward (not necessarily in that order) and play 'Passing the Buck' over 10 rounds. In each round the child holding the Buck must pass it directly to a child sitting immediately to the left, immediately to the right, second to the left, or second to the right. The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. A table gives some of the pass types and the child receiving the Buck, with some entries missing (marked '?').