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📌 Section 1 is Logical reasoning specially designed for CAT
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SET 1 — 🔍 CAT Level
There are four schools — A, B, C, and D. With the CBSE board examinations approaching, students from these schools are allotted to other schools to appear for their exams. No student appears for the examination in their own school. Each school has six batches, namely B1, B2, B3, B4, B5, and B6.
During the examination process, each school sends its students to exactly two other schools and hosts students from exactly two schools. The total capacity of a school to conduct examinations is equal to the total number of students it sends to other schools. Students are transferred only in complete batches, and no batch is split across schools.
Further information is known:
(i) School B receives 130 students from one school, comprising three batches. School A receives 50 students from one school, comprising two batches.
(ii) School C receives 110 students from one school, consisting of two batches, and receives the remaining students from another school, consisting of three batches.
(iii) School B received B4 of both the schools whose examinations it is hosting.
Question 1
How many total batches did School B receive?
Question 2
What is the absolute difference between the number of students hosted by School D from two schools?
Question 3
Which of the following combinations of school–batch definitely defines the students received by School A?
School D – B6
School C – B1
School B – B4
School B – B3
Question 4
Which of the following statements is FALSE?
School C received batch B5 of school D.
School D received batch B6 of school B.
School B received batch B3 of school A.
School A received batch B2 of school C.
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✅ Answers & Explanations
Hosting School | Students received from School 1 | Students received from School 2 | Total Hosted |
|---|---|---|---|
A | B = 200 | C = 50 | 250 |
B | C = 140 | D = 130 | 270 |
C | A = 110 | D = 80 | 190 |
D | A = 140 | B = 70 | 210 |
Set 1
Batch-wise Allocation
A sends:
C → B1, B4 = 50 + 60 = 110
D → B2, B3, B5, B6 = 40 + 40 + 30 + 30 = 140
B sends:
A → B1/B2/B3/B5 = 200
D → Remaining 2 batches = 70
C sends:
A → B2, B5 = 20 + 30 = 50
B → B1, B3, B4, B6 = 25 + 40 + 35 + 40 = 140
D sends:
B → B1, B3, B4 = 40 + 50 + 40 = 130
C → B2, B5, B6 = 30 + 30 + 20 = 80
Why this works
School B receives 130 students from one school in 3 batches.
That is D → B: B1, B3, B4 = 40 + 50 + 40 = 130.
School A receives 50 students from one school in 2 batches.
That is C → A: B2, B5 = 20 + 30 = 50.
School C receives 110 students from one school in 2 batches.
That is A → C: B1, B4 = 50 + 60 = 110.
School B receives B4 of both schools it hosts.
B receives C-B4 and D-B4.
Answers
1️⃣ School B received total batches = 4 from C + 3 from D = 7
2️⃣ School D hosted 140 students from A and 70 students from B.
Absolute difference = 140 - 70 = 70
3️⃣ Definitely received by School A = School B – B3
Answer: Option 4
4️⃣ False statement = School B received batch B3 of School A
School B received students from C and D, not A.
Answer: Option 3
Final Answers
1️⃣ 7
2️⃣ 70
3️⃣ Option 4
4️⃣ Option 3
⚡ Brain teasers are not just about getting the right answer — they train you to think differently under pressure.
Stay consistent with your daily practice, challenge your assumptions, and keep sharpening your reasoning skills.
See you in tomorrow’s challenge!