Logical reasoning in placement tests: six patterns, worked answers

The first move for each pattern

Number series

Q. 3, 7, 15, 31, 63, ? Differences: 4, 8, 16, 32 — doubling. Next difference is 64, so the answer is 127. Equivalent rule: each term is double the previous plus 1.

Q. 2, 6, 12, 20, 30, ? Differences: 4, 6, 8, 10 — rising by 2. Next difference 12, answer 42. Also, each term is n × (n + 1): 1×2, 2×3, … 6×7.

If the first differences show no pattern, try second differences, then alternate terms (two interleaved series), then squares and cubes nearby.

Coding-decoding

Q. If COLD is written as DPME, how is WARM written? C→D, O→P, L→M, D→E: each letter moves one place forward. W→X, A→B, R→S, M→N. Answer: XBSN.

Q. If MANGO is 13-1-14-7-15, what is APPLE? These are alphabet positions. A=1, P=16, P=16, L=12, E=5. Answer: 1-16-16-12-5.

Memorise the positions of E (5), J (10), O (15), T (20) and Y (25). You can reach any letter in two steps from one of these.

Blood relations

Q. Pointing to a man, Riya says, "His mother is the only daughter of my mother." How is the man related to Riya? "The only daughter of my mother" — Riya is a daughter of her mother, so if her mother has only one daughter, that daughter is Riya. So the man's mother is Riya. Answer: he is Riya's son.

Draw it: Riya's mother at the top, Riya below, the man below Riya. Mark females with a circle and males with a square so you never lose track.

Direction sense

Q. Aman walks 5 km north, turns right and walks 3 km, then turns right again and walks 9 km. How far is he from the start, and in which direction? North 5, then right (east) 3, then right again (south) 9. Net north–south: 5 − 9 = 4 km south. Net east–west: 3 km east. Distance = √(4² + 3²) = √25. Answer: 5 km, towards the south-east.

Right turns go clockwise: north → east → south → west. Say it aloud at each turn.

Seating arrangement

Q. Five friends A, B, C, D and E sit in a row facing north. C is in the middle. A is at the extreme left. D sits immediately to the right of C. E is not at either end. Who sits at the extreme right, and who sits between A and C? Number seats 1 to 5 from left. A = 1, C = 3, D = 4. B and E remain for seats 2 and 5. E is not at an end, so E = 2 and B = 5. Answer: B is at the extreme right; E sits between A and C.

Facing matters. If they faced south, "right" would be your left as you read the diagram.

Syllogisms

Q. Statements: All analysts are graduates. Some graduates are engineers. Conclusions: I. Some analysts are engineers. II. Some engineers are graduates. Draw the analysts circle inside the graduates circle. The engineers circle overlaps graduates, but it can overlap without touching analysts. So I does not necessarily follow. II is just the second statement read the other way ("some A are B" means "some B are A"), so it follows. Answer: only II follows.

The rule to remember: a conclusion follows only if it is true in every possible diagram, not just the one you drew first.

Check a seating puzzle by brute force

When you write your own practice puzzles, check that the clues give exactly one answer. This standard-library script tries every arrangement of the seating question above and keeps the ones that satisfy all clues.

from itertools import permutations

solutions = []
for row in permutations("ABCDE"):          # row[0] is the extreme left
    pos = {person: i for i, person in enumerate(row)}
    if pos["C"] != 2:
        continue
    if pos["A"] != 0:
        continue
    if pos["D"] != pos["C"] + 1:
        continue
    if pos["E"] in (0, 4):
        continue
    solutions.append("".join(row))

print(solutions)            # ['AECDB'] means exactly one valid arrangement

If the list has more than one entry, your puzzle is missing a clue; if it is empty, two clues contradict each other. The same idea — state every rule, then test all cases — is how you would check a business rule in data too.

A two-week drill

Days 1–6: one pattern per day, 20 questions, untimed, with the first move written before solving. Days 7–10: mixed sets of 25 in 30 minutes. Days 11–14: full mock sections, then log each wrong answer by pattern and trap. Pair this with quantitative aptitude practice and the verbal ability set so no section surprises you.

Careful rule-checking is also most of what junior analysts do with data; the Data Analyst programme turns that habit into SQL checks and reconciliations.