Question

There are 6 volumes of books on a rack kept in order (Vol. 1, Vol. 2 and so on). After some readers used them, their order got disturbed. The changes are as follows:
Vol. 5 was directly to the right of Vol. 2.
Vol. 4 has Vol. 6 to its left, and both Vol. 4 and Vol. 6 were not at Vol. 3's original place.
Vol. 1 has Vol. 3 on its right and Vol. 5 on its left.
An even numbered volume is at Vol. 5's original place.
Find the order in which the books are now kept, from the given alternatives.

• A. 6, 3, 5, 1, 4, 2
• B. 4, 6, 3, 5, 1, 2
• C. 3, 4, 1, 6, 5, 3
• D. 2, 5, 1, 3, 6, 4

Hint:

Chain the "5 right of 2" and "5 left of 1, 3 right of 1" clues into one block first, then place volumes 4 and 6 as a second block.

Answer 1

The Correct Option is D

Step 1: List what each clue requires, in short form.
Clue 1: "2" is immediately followed by "5". Clue 2: "6" is immediately followed by "4", and neither 4 nor 6 sits at the 3rd position on the shelf. Clue 3: "5" is immediately followed by "1", which is immediately followed by "3". Clue 4: the 5th position on the shelf holds an even-numbered volume.
Step 2: Test option (1), 6, 3, 5, 1, 4, 2.
Here "2" appears at the end with nothing after it, and 5 actually appears before 2, so "2" is not immediately followed by "5". Clue 1 fails, so this option is rejected.
Step 3: Test option (2), 4, 6, 3, 5, 1, 2.
Here "6" is followed by "3", not "4", so clue 2 fails immediately. This option is rejected.
Step 4: Test option (3), 3, 4, 1, 6, 5, 3.
This sequence repeats the number 3 twice and never uses volume 2, which is impossible since there are exactly six distinct volumes, numbered 1 to 6, on the rack. This option is invalid and is rejected.
Step 5: Test option (4), 2, 5, 1, 3, 6, 4.
Check clue 1: "2" is followed by "5", correct. Check clue 3: "5" is followed by "1", which is followed by "3", correct. Check clue 2: "6" is followed by "4", correct; the 3rd position holds "1", so neither 4 nor 6 is at the 3rd position, correct. Check clue 4: the 5th position holds "6", which is even, correct. Every clue is satisfied.
Step 6: Conclude.
Since options (1), (2) and (3) each break at least one clue and option (4) satisfies every clue, option (4) is the correct order: 2, 5, 1, 3, 6, 4.