Practice Set 6 — Reasoning & Quantitative Aptitude

Answer (d).

Method — circular table, facing the centre. Facing the centre, a person's left is clockwise and a person's right is anticlockwise — the opposite of the north-facing row, and the single commonest slip in this topic. With eight seats, the seat exactly opposite is four seats away, since three persons then sit between on either side. Only relative positions matter, so fix A anywhere: number the seats 1 to 8 clockwise with A at seat 1.

Step 1 — clue (i). C is third to A's left and left is clockwise, so C = seat 1 + 3 = seat 4.

Step 2 — clue (ii). B is opposite C, four seats away: B = seat 4 + 4 = seat 8.

Step 3 — clue (iii). E is second to B's right and right is anticlockwise, so E = seat 8 − 2 = seat 6.

Step 4 — clue (iv). F is an immediate neighbour of A, so F is at seat 2 or seat 8; seat 8 is B, so F = seat 2. Confirm the second half of the clue: C is at seat 4, whose neighbours are seats 3 and 5, and F is at neither, so F is indeed not C's neighbour.

Step 5 — clue (v). G is third to E's right, that is three seats anticlockwise: G = seat 6 − 3 = seat 3.

Step 6 — clue (vi). B is at seat 8, whose neighbours are seats 7 and 1; seat 1 is A, so the clue only bars seat 7 for D. The free seats are 5 and 7, so D = seat 5 and H = seat 7.

Step 7 — the completed circle. Clockwise from A : A (1), F (2), G (3), C (4), D (5), E (6), H (7), B (8). Every clue fixed one seat, so the arrangement is unique. The opposite pairs, four apart, are A–D, F–E, G–H and C–B.

Step 8 — test the statements. 1. A is at seat 1 and D at seat 5, four apart. Correct. 2. E is at seat 6 and her left is clockwise, so second to her left is seat 8, which is B. H sits at seat 7, that is immediately to E's left, not second. Incorrect. 3. Clockwise from C (seat 4) the seats are 5 then 6; seat 6 is E, so exactly one person, D at seat 5, lies between. Correct. 4. G is at seat 3 and its neighbours are seats 2 and 4, that is F and C. Correct. Statements 1, 3 and 4 are correct.

Why each of the other options is wrong

(a) 1 and 4 only — Statement 3 rejected through a counting slip on a correct circle: either the endpoints are counted in, so that C, D, E is read as two persons between instead of one, or the clockwise direction named in the statement is travelled anticlockwise, in which case five persons lie between. “Between” excludes both named persons, and a named direction must be obeyed.

(b) 3 and 4 only — “opposite” taken as three seats away, which is the rule for a six-seat table, not an eight-seat one. That misreading also corrupts clue (ii), so the whole circle shifts and Statement 1 fails with it. In a circle of n seats the opposite seat is n/2 away, and n is not always 6.

(c) 1, 2, 3 and 4 — an ordinal counted off by one, the immediate neighbour being called the “second”. H is immediately to E's left, so Statement 2 is wrongly passed and every statement then looks correct. “Second to the left” means skip one seat and take the next.

(d) 1, 3 and 4 only — correct.

Trap: ch12 — facing the centre, left is clockwise and right is anticlockwise; the opposite seat is half the table away; and “second to the left” always means two seats, never one.

Answer (d).

Method — a south-facing row reverses left and right. Draw the row once, from west to east, and never redraw it. A person facing south has the east on his left hand and the west on his right hand. So for these five teachers “to the left” means towards the eastern end and “to the right” means towards the western end. Number the chairs 1 (west) to 5 (east).

Step 1 — place the most definite clue. Clue (i): Deepak is in the middle chair, chair 3.

Step 2 — chain the remaining clues. Clue (ii): Anita is second to Deepak's left, and his left runs east, so Anita is at chair 3 + 2 = chair 5. Clue (iii): Chetan is an immediate neighbour of Deepak, so Chetan is at chair 2 or chair 4. Anita sits at chair 5 and her only neighbour is chair 4; since Chetan is not Anita's neighbour, Chetan is at chair 2. Clue (iv): Farhan is immediately to Chetan's right, and Chetan's right runs west, so Farhan is at chair 2 − 1 = chair 1. One chair, chair 4, is left, and it must be Bharti's.

Step 3 — the completed row, west to east. chair 1 Farhan | chair 2 Chetan | chair 3 Deepak | chair 4 Bharti | chair 5 Anita Each of the four clues fixed exactly one seat, so this arrangement is unique — there is no second seating consistent with the clues, and every statement below has a definite verdict.

Step 4 — test the statements against the grid. 1. Farhan is at chair 1 and his left runs east, so third to his left is chair 1 + 3 = chair 4, which is Bharti. Correct. 2. Chetan is at chair 2 and his right runs west, so second to his right would be chair 2 − 2 = chair 0, which does not exist — Chetan has only one chair to his right. Incorrect. (Bharti is in fact second to Chetan's left.) 3. The second chair from the western end is chair 2, and chair 2 is Chetan's. Correct. Statements 1 and 3 are correct.

Why each of the other options is wrong

(a) 1 only — the candidate who never reverses left and right for the south facing. He builds the mirror row Anita, Bharti, Deepak, Chetan, Farhan and then judges the statements in the same un-reversed sense, so the two errors cancel on the relative Statements 1 and 2 and he marks them exactly as the correct solver does. Statement 3 names an absolute end of the row, and in his mirror row the second chair from the west holds Bharti, so he rejects it. A mirror-image solution stays invisible until an absolute direction is asked for.

(b) 2 and 3 only — the reversal used while seating the teachers and then forgotten while testing the statements. On the correct grid read without the reversal, “third to the left of Farhan” runs off the western end (Statement 1 wrongly rejected) and “second to the right of Chetan” lands on chair 4, Bharti (Statement 2 wrongly accepted).

(c) 1, 2 and 3 — the same forgetfulness applied to one statement only: the reversal is used on Statement 1 and dropped on Statement 2, so everything appears correct. What fails here is consistency, not knowledge of the rule.

(d) 1 and 3 only — correct.

Trap: ch12 — in a south-facing row reverse left and right once, when you draw the grid, and then keep that reversed sense for every clue and every statement; a statement phrased in compass terms is the only one that can expose a mirror-image solution.

Answer (b).

Method — two rows that face each other need two different left-right rules. Row 1 faces south, so for Row 1 the left runs east, towards chair 4, and the right runs west, towards chair 1. Row 2 faces north, so for Row 2 the left runs west and the right runs east — the exact opposite. Both rows are numbered from the same end, west to east, and chair k of one row faces chair k of the other.

Step 1 — fix Row 1 from the end clue. Clue (i): Bhaskar is at chair 1 or chair 4. Clue (ii): Anjali is immediately to his right, that is one chair to the west. If Bhaskar were at chair 1 there would be no chair to his west, so Bhaskar = chair 4 and Anjali = chair 3. Clue (i) also gives Gopal = chair 4 of Row 2.

Step 2 — finish Row 1. Clue (iii): one teacher between Dinesh and Anjali means the two sit two chairs apart. Anjali is at chair 3, so Dinesh is at chair 1 or chair 5; chair 5 does not exist, so Dinesh = chair 1 and the remaining chair 2 is Chitra's.

Step 3 — finish Row 2. Clue (iv): Hema faces Dinesh, so Hema = chair 1 of Row 2. Clue (v): Farida is immediately to Imran's right, and Row 2's right runs east, so Farida sits one chair east of Imran. The free chairs are 2 and 3, so Imran = chair 2 and Farida = chair 3.

Step 4 — the completed grid. Row 1 (facing south) : 1 Dinesh | 2 Chitra | 3 Anjali | 4 Bhaskar Row 2 (facing north) : 1 Hema | 2 Imran | 3 Farida | 4 Gopal Facing pairs : Dinesh–Hema, Chitra–Imran, Anjali–Farida, Bhaskar–Gopal. Each clue fixed one seat, so the arrangement is unique.

Step 5 — test the statements. 1. Chitra is at chair 2 of Row 1 and chair 2 of Row 2 is Imran. Correct. 2. Anjali is at chair 3 of Row 1 and chair 3 of Row 2 is Farida, not Imran. Incorrect. 3. Anjali is at chair 3 and her right runs west, so second to her right is chair 3 − 2 = chair 1, which is Dinesh. Correct. Statements 1 and 3 are correct.

Why each of the other options is wrong

(a) 1 and 2 only — clue (v) never used. Without it Imran and Farida remain interchangeable between chairs 2 and 3, so both facing statements look possible and both are ticked; and Statement 3 is rejected because the south facing of Row 1 has been forgotten, which sends “second to the right of Anjali” off the eastern end. A statement that is merely possible is not correct.

(b) 1 and 3 only — correct.

(c) 2 and 3 only — the second row drawn from east to west while the first is drawn from west to east, so that chair k of Row 1 is paired with chair 5 − k of Row 2. Chitra then appears to face Farida and Anjali to face Imran, which reverses both facing statements; Statement 3 lies wholly inside Row 1 and is untouched. Number both rows from the same compass end before you pair anybody.

(d) 1, 2 and 3 — clue (v) again left unused, so both facing statements are passed as possible, while Statement 3 is handled correctly. This candidate has solved the puzzle up to the last clue and has not noticed that the last clue is the one that turns “possible” into “certain”.

Trap: ch12 — in a two-row puzzle number both rows from the same compass end, reverse left and right only for the row that faces the other way, and use every clue before you judge anything.