32Directions: Study the following information carefully and answer the…
2025
32
Directions: Study the following information carefully and answer the questions that follow.
Ten different books - History, Science, Geography, Economics, Literature, Mathematics, Psychology, Philosophy, Biology, and Politics are kept in an almirah having four vertical stacks: Stack 1, Stack 2, Stack 3, and Stack 4. Stack 2 is to the east of Stack 1, Stack 3 is to the east of Stack 2, and Stack 4 is to the east of Stack 3. Each stack contains a different number of books. The number of books decreases from west to east, i.e., Stack 1 has more books than Stack 2, Stack 2 has more books than Stack 3, and Stack 3 has more books than Stack 4. At least one book is kept in each stack, and the top of all four stacks contains a book.
Science is kept immediately above History in the same stack. The geography book is kept two books above the Mathematics book in the same stack. The psychology book is kept to the east of the Politics book, which is not kept in Stack 3. Philosophy is kept at the top of Stack 3. History is kept two positions above Biology in the same stack. The literature book is not kept in Stack 4.
Which book is kept at the top of Stack 1?
- A.
Psychology
- B.
Science
- C.
Literature
- D.
Mathematics
- E.
Geography
Attempted by 1 students.
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Correct answer: B
In a vertical-stack arrangement, first fix each stack's capacity from the counting clue, then treat every statement of the form "X is n positions above Y" as a rigid block that needs a stack tall enough to hold its full span. A chain like this can only sit inside the one stack whose height matches that span, which pins its position without any guesswork.
Stack 1 has more books than Stack 2, Stack 2 more than Stack 3, and Stack 3 more than Stack 4, with all four counts distinct positive integers summing to 10. The smallest possible strictly decreasing set of four distinct positive integers is 4, 3, 2, 1, and it already sums to 10, so it is the only option: Stack 1 has 4 books, Stack 2 has 3, Stack 3 has 2, and Stack 4 has 1 (numbering positions 1 at the bottom up to the top of each stack).
Chain the two clues that share Biology: History is kept two positions above Biology, and Science is kept one position above History. So Science ends up three positions above Biology in the same stack - a span of 4 positions from Biology to Science.
Only a stack with at least 4 positions can hold a span of 4, and Stack 1 is the only stack with 4 positions. So this Biology-History-Science block must sit in Stack 1, and the only way it fits inside positions 1 to 4 is Biology at position 1, History at position 3, and Science at position 4.
Position 4 is the top of Stack 1, so Science is the book kept at the top of Stack 1.
Cross-check with the other span clue: Geography is kept two positions above Mathematics, a span of 3, which needs either positions 1 and 3, or positions 2 and 4, in the same stack. In Stack 1, positions 1, 3, and 4 are already taken by the Biology-History-Science block, leaving only position 2 free - not enough room for a span-3 pair. So Geography and Mathematics must go into Stack 2 (3 positions) instead, forcing Mathematics at position 1 and Geography at position 3 there. Philosophy is given directly at the top of Stack 3. The remaining clues - Politics is west of Psychology and not in Stack 3, and Literature is not in Stack 4 - only decide how Economics, Literature, Psychology, and Politics fill the one leftover slot in each stack; none of them touch Stack 1's top slot, so the result is unaffected by exactly how those four books settle.
Science is the book kept at the top of Stack 1.