Directions (Q. 14-17): Twelve people are sitting at an equal distance in two…
2025
Directions (Q. 14-17): Twelve people are sitting at an equal distance in two parallel rows. A, B, C, D, E and F are sitting in Row 1 facing north, and M, N, O, P, Q and R are sitting in Row 2 facing south, such that the persons sitting in Row 1 face the persons sitting in Row 2. Each person celebrates his/her birthday on a different date in a month of 30 days.
A, B, C, D, E and F are born on odd-numbered dates, while M, N, O, P, Q and R are born on even-numbered dates.
The person who faces E celebrates his birthday on double the date of C's birthday.
N faces the person who sits third to the left of F, who celebrates his birthday on the 1st.
D sits third to the right of B, who celebrates his birthday on the 15th, and one of them sits at the end of Row 1.
The person who celebrates his birthday on the 11th is an immediate neighbour of C.
M sits immediately right of P, who faces E.
The person who faces A celebrates his birthday on the cube of 2.
There are three people between the person who celebrates his birthday on the 15th and the person who celebrates his birthday on an odd-numbered date greater than 3 but less than 6.
The person who faces C celebrates his birthday on double the birthday date of M, while the person who sits immediately right of R celebrates his birthday on half the birth date of O.
The person who sits diagonally opposite B celebrates his birthday on the square of an even prime number.
Q sits exactly between N and R, but R does not face A.
The person who celebrates his birthday on the 25th sits immediately left of the person who celebrates his birthday on the 13th.
The person sitting at the right end of Row 2 celebrates his birthday on the 6th.
Which of the following pairs are sitting opposite each other?
- A.
B-Q
- B.
E-M
- C.
O-D
- D.
E-R
- E.
A-N
Attempted by 2 students.
Show answer & explanation
Correct answer: E
Concept
In a two-parallel-row arrangement the two rows face each other, so every person in Row 1 sits directly across from exactly one person in Row 2. Two people 'sit opposite each other' precisely when they occupy the same column - one in each row - so that their lines of sight meet. The task therefore reduces to fixing the column-by-column line-up from the clues and reading off who shares a column.
Solving the arrangement
B is born on the 15th and D sits third to the right of B, with one of the two at an end of Row 1. That allows either B at the left end (D fourth from it) or B in the third seat with D at the right end. Clue 8 needs a person exactly four seats away from B, which is impossible if B is in the third seat; so B takes the LEFT END and D the 4th seat from it.
Row 1 carries the six odd dates {1, 5, 11, 13, 15, 25}, with B = 15 (Clue 4) and F = 1 (Clue 3). The only odd date strictly between 3 and 6 is 5, and Clue 8 puts that person four seats from B, i.e. in the 5th seat. Clue 12 seats the 25th-born immediately left of the 13th-born, and Clue 5 places the 11th-born next to C.
Clue 3 refers to the seat third to the left of F, so a seat must exist three places to F's left; since the 4th seat is D and the 5th holds the 5th-born, F is forced to the right end. Fitting the 25th-left-of-13th pair and the 11th-born-next-to-C condition then fixes Row 1 as B(15), E(25), A(13), D(11), C(5), F(1) from the left end to the right end, with C in the 5th seat.
In Row 2, P faces E and M sits immediately to P's right; N faces the seat third to the left of F, which is A's seat. Q sits exactly between N and R with R not facing A, and the right-end seat of Row 2 is the 6th-born (Clue 13). The birthday links finish it: the person facing A is 8 = cube of 2 (Clue 7), the person diagonally opposite B is 4 = square of the even prime 2 (Clue 10), which fixes O = 4; the person facing C is twice M's date and the seat right of R is half of O. Row 2 becomes M(6), P(10), N(8), Q(2), R(12), O(4) from the left end to the right end.
The completed arrangement, column by column from the left end to the right end:
Seat (left to right) | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
Row 1 (facing north) | B | E | A | D | C | F |
Row 2 (facing south) | M | P | N | Q | R | O |
Orientation note: Row 1 faces north and Row 2 faces south, so the two rows' left and right run opposite to each other. The table above is drawn from a single reader's viewpoint, in which two people are 'opposite' exactly when they share a column; each clue's own 'left/right' is read from that row's own facing direction, while a count such as 'three people between' comes out the same either way. This is why the 6th-born, the right-end seat of Row 2 from that row's own view, appears at the left of the table.
Reading the opposite pairs
Reading straight down each column, the face-to-face (opposite) pairs are B-M, E-P, A-N, D-Q, C-R and F-O. Among the given options only A and N share a column, so A-N is the pair sitting opposite each other.