Reasoning

Correct answer: B

I is correct: Four files are ordered W before X, Y after X, Z before W; the second file → W. The order is Z-W-X-Y. II is correct: Five books are left-to-right A,C,E,B,D; the middle book → E. The third of five positions is the middle.

Correct answer: C

I is correct: Six candidates ordered F,A,D,B,E,C; the first after moving C to the front → C. Moving the last candidate to the front places C first. II is incorrect: Six candidates ordered F,A,D,B,E,C; the candidate between B and C → E. The last three are B-E-C.

Correct answer: A

The order from tallest is P-M-N-O.

Correct answer: C

I is incorrect: Five books are left-to-right A,C,E,B,D; the book immediately right of E → B. B occupies the next position after E. II is incorrect: P is immediately before Q, Q immediately before R, and S is before P; the last of these four → R. The only order is S-P-Q-R.

Correct answer: A

D is third from the start, so sixth-minus-third-plus-one is fourth.

Correct answer: B

I is correct: Five books are left-to-right A,C,E,B,D; the book second from the right → B. Counting from the right gives D then B. II is incorrect: Five books are left-to-right A,C,E,B,D; the middle book → E. The third of five positions is the middle.

Correct answer: A

The order is Z-W-X-Y.

Correct answer: D

I is correct: Six candidates ordered F,A,D,B,E,C; A's new rank after F leaves → 1st. Removing the first candidate shifts A into first place. II is correct: Six candidates ordered F,A,D,B,E,C; the candidate between B and C → E. The last three are B-E-C.

Correct answer: A

B occupies the next position after E.

Correct answer: C

I is correct: Six candidates ordered F,A,D,B,E,C; the candidate two places before B → A. B is fourth and A is second. II is correct: Six candidates ordered F,A,D,B,E,C; the first after moving C to the front → C. Moving the last candidate to the front places C first.

Correct answer: B

C,E and B lie between the end books.

Correct answer: A

I is incorrect: A is left of B, B is left of C, and C is left of D in a four-person row; the leftmost person → A. The constraints force the order A-B-C-D. II is correct: Six candidates ordered F,A,D,B,E,C; A's new rank after F leaves → 1st. Removing the first candidate shifts A into first place.

Correct answer: D

I is correct: Six candidates ordered F,A,D,B,E,C; the first after moving C to the front → C. Moving the last candidate to the front places C first. II is correct: Five books are left-to-right A,C,E,B,D; the book immediately right of E → B. B occupies the next position after E.

Correct answer: D

B is fourth and A is second.

Correct answer: B

I is incorrect: Four files are ordered W before X, Y after X, Z before W; the second file → W. The order is Z-W-X-Y. II is correct: Six candidates ordered F,A,D,B,E,C; A's new rank after F leaves → 1st. Removing the first candidate shifts A into first place.

Correct answer: D

B moves from fourth to first.

Correct answer: A

I is correct: Five books are left-to-right A,C,E,B,D; the book second from the right → B. Counting from the right gives D then B. II is incorrect: Six candidates ordered F,A,D,B,E,C; D's rank from the end → 4th. D is third from the start, so sixth-minus-third-plus-one is fourth.

Correct answer: D

The last three are B-E-C.

Correct answer: A

I is correct: Six candidates ordered F,A,D,B,E,C; the candidate two places before B → A. B is fourth and A is second. II is correct: Five books are left-to-right A,C,E,B,D; the middle book → E. The third of five positions is the middle.

Correct answer: B

Counting from the right gives D then B.

Correct answer: D

I is incorrect: Six candidates ordered F,A,D,B,E,C; D's rank from the end → 4th. D is third from the start, so sixth-minus-third-plus-one is fourth. II is correct: Five books are left-to-right A,C,E,B,D; the middle book → E. The third of five positions is the middle.

Correct answer: D

People between = difference in positions − 1.

Correct answer: C

Bottom rank = total − top rank + 1 = 31−6+1.

Correct answer: B

Reverse position = 27 − ordinary position = 27 − 6.

Correct answer: C

Union count = 21 + 16 − 6; subtract the overlap counted twice.