Verbal Reasoning — Analogy, Series, Coding & Relations

Every letter question in the paper — analogy, series, coding, alphabet test — becomes arithmetic the moment you know positions. There are only two facts to hold: the forward position (A = 1 … Z = 26) and the rule backward position = 27 − forward position. That single subtraction replaces all the counting-on-fingers that costs candidates their time. Check it once: A is 1st from the left and 27 − 1 = 26th from the right; Z is 26th from the left and 27 − 26 = 1st from the right.

Two-step position questions. "Which letter is 7th to the left of the 15th letter from the right end?" Solve the inner phrase first: the 15th letter from the right sits at forward position 27 − 15 = 12, which is L. Now 7th to the left of L means subtract: 12 − 7 = 5, which is E. Answer E. A second one: "Which letter is 8th to the right of the 12th letter from the left?" The 12th letter is L (position 12); 12 + 8 = 20 = T. Left means subtract, right means add — but only when you are counting in the normal A-to-Z direction.

Two more standard sub-types. Midway letters: the letter exactly midway between H and R is at position (8 + 18) ÷ 2 = 13, which is M. Letters in between: the number of letters strictly between D (4) and K (11) is 11 − 4 − 1 = 6, namely E, F, G, H, I, J — always remember the "− 1". Word formation: to decide whether TRAIN can be built from the letters of TRANSPORTATION, tick off T, R, A, I, N one by one against the long word; all five are present, so yes. Dictionary order: compare letter by letter from the left. Sale, Salt, Sand, Sane — S-a-l comes before S-a-n because l precedes n; within Sal-, e precedes t; within San-, d precedes e.

A classification question gives four items of which three share one property and the fourth does not. The discipline is the reverse of analogy: instead of naming a relationship between two items, you look for the property held by a majority. Say the property out loud — "these are all flowers", "these are all prime", "these are all cubes" — and then find the item that fails it. If you can find two different properties that each leave a different odd item out, you have picked too loose a property; keep tightening until exactly one item is excluded.

• Rose, Lotus, Lily, Mango → Mango. The other three are flowers; mango is a fruit.
• 17, 27, 37, 47 → 27. The other three are prime numbers; 27 = 3 × 9 is composite.
• 121, 144, 169, 200 → 200. The others are 11², 12² and 13²; 200 is not a perfect square.
• 8, 27, 64, 100 → 100. The others are 2³, 3³ and 4³; 100 is a square but not a cube.
• BDF, CEG, DFH, EGJ → EGJ. In the first three the gaps are 2 and 2 (B 2, D 4, F 6). In EGJ the positions are 5, 7, 10 — gaps of 2 and 3.
• Barometer, Thermometer, Speedometer, Periscope → Periscope. The first three measure a quantity; a periscope only lets you see.

A series question hands you an ordered list with one term missing — at the end, or awkwardly in the middle. The one reliable first move is to write the differences underneath. If the differences are constant you have an arithmetic series; if they themselves form a neat pattern you have a second-order series; if the differences grow multiplicatively, look at ratios instead. Only after the differences and the ratios have both failed should you start testing squares and cubes.

Worked number series 1 — 2, 3, 5, 9, 17, ? Write the differences: 1, 2, 4, 8. Those are doubling, so the next difference is 16 and the answer is 17 + 16 = 33. Note that the differences, not the terms, were the doubling series — a very common the paper construction. Worked series 2 — 3, 8, 18, 38, ? Differences are 5, 10, 20, which double, giving 40 and the answer 78; the same series also obeys the rule ×2 + 2 (3 × 2 + 2 = 8, 8 × 2 + 2 = 18, 18 × 2 + 2 = 38, 38 × 2 + 2 = 78). When two descriptions give the same answer, you are safe. Worked series 3 — 2, 12, 36, 80, 150, ? These are n³ + n²: 1 + 1 = 2, 8 + 4 = 12, 27 + 9 = 36, 64 + 16 = 80, 125 + 25 = 150, so next is 216 + 36 = 252.

Letter series. Convert to positions, find the pattern, convert back. B, D, G, K, P, ? — positions 2, 4, 7, 11, 16, with gaps +2, +3, +4, +5, so the next gap is +6 and the answer is 16 + 6 = 22 = V. A, C, F, J, O, ? — 1, 3, 6, 10, 15 with the same growing gaps, so 15 + 6 = 21 = U. Z, W, T, Q, ? — 26, 23, 20, 17, falling by 3, so 14 = N. A, B, D, H, ? — 1, 2, 4, 8, doubling, so 16 = P. And the mirror family AZ, BY, CX, DW, ? — each pair adds to 27, and the first letters advance by one, so the next pair is E with 27 − 5 = 22 = V, giving EV.

Letter blocks of growing length. AB, DEF, HIJK, ? — the blocks are 2, 3, 4 letters long, so the next has 5. The starting letters are A = 1, D = 4, H = 8, gaps of +3 and +4, so the next start is 8 + 5 = 13 = M and the block is MNOPQ. Alphanumeric series. Handle the letters and the numbers as two independent series. 2B, 4D, 6F, 8H, ? — numbers 2, 4, 6, 8 and letters at positions 2, 4, 6, 8, so the next is 10 with the 10th letter: 10J. C3X, F6U, I9R, ? — first letters 3, 6, 9 → 12 = L; numbers 3, 6, 9 → 12; last letters 24, 21, 18 → 15 = O. Answer L12O. 2A, 5D, 10I, 17P, ? — the numbers are 2, 5, 10, 17 with gaps +3, +5, +7, so the next gap is +9 giving 26; the letters sit at 1, 4, 9, 16 (perfect squares), so the next is 25 = Y. Answer 26Y.

Every coding question belongs to one of six families, and identifying the family takes about five seconds. Look at the coded word: does it have the same number of letters as the original? Then it is a letter-shift or a mirror code. Is it a number? Then it is position-based. Is the whole sentence coded in nonsense words? Then it is substitution. Are there conditions printed above the question? Then it is conditional coding. Name the family first; the arithmetic afterwards is trivial.

1. Letter shift. If TEACHER is coded as VGCEJGT, check each letter: T (20) → V (22), E (5) → G (7), A (1) → C (3), C (3) → E (5), H (8) → J (10), E → G, R (18) → T (20). Every letter moved forward by 2. So CHILD → C (3) + 2 = E, H (8) + 2 = J, I (9) + 2 = K, L (12) + 2 = N, D (4) + 2 = F, giving EJKNF. Backward shifts work the same way but need one extra rule: A − 1 wraps round to Z. MANGO with a shift of −1 becomes L, Z, M, F, N — that is LZMFN, because A (1) − 1 falls off the front and lands on Z (26).

2. Mirror (opposite-letter) coding. Each letter is replaced by its mirror partner, the one whose position makes the pair add to 27. If SIT is coded as HRG, verify: S (19) → 27 − 19 = 8 = H, I (9) → 18 = R, T (20) → 7 = G. Confirmed. So CAT → C (3) → 24 = X, A (1) → 26 = Z, T (20) → 7 = G, giving XZG; and POLICE → K, L, O, R, X, V, that is KLORXV (16→11, 15→12, 12→15, 9→18, 3→24, 5→22).

3. Position-value (number) coding. Add the position numbers of the letters. DELHI = 4 + 5 + 12 + 8 + 9 = 38. MUMBAI = 13 + 21 + 13 + 2 + 1 + 9 = 59. MOTHER = 13 + 15 + 20 + 8 + 5 + 18 = 79. Some variants take the sum and then divide by the number of letters, or multiply the first and last positions — so always test the given example both ways before applying anything to the asked word.

4. Substitution (message) coding. Here whole words stand for whole words, and the technique is set intersection. Given "mit fa dor" = "you are good", "fa lin ka" = "are they here", and "dor ka nes" = "good here now". Compare sentences 1 and 2: the only shared code word is fa and the only shared meaning is are, so fa = are. Compare 1 and 3: shared code word dor, shared meaning good, so dor = good. Compare 2 and 3: shared code word ka, shared meaning here, so ka = here. Note the discipline — you only ever conclude when exactly one word and exactly one meaning are shared.

5. Symbol coding simply swaps each letter or digit for a symbol from a printed key; the only skill is copying carefully. 6. Conditional coding is where marks are lost. A key is printed, then two or three conditions that override it. Suppose the key is A = 7, B = 4, D = 9, E = 1, H = 5, K = 3, M = 6, with these conditions:
(i) if the first letter is a vowel, interchange the codes of the first and last letters;
(ii) if the last letter is a vowel, code it as 8;
(iii) if both conditions apply, apply only (i).

Nobody solves blood relations in their head reliably. Use a family tree drawn in generations: put the oldest generation on the top line, their children on the next line down, grandchildren below that. Mark a male with +, a female with −, join a married couple with =, join siblings with a horizontal dash, and drop a vertical line from parents to children. Once the tree is on paper the question answers itself, and — crucially — you can see which relations the question has left undetermined.

Worked example 1 — the photograph type. Pointing to a photograph, a man said, "She is the daughter of the only son of my grandmother." Unpack the phrase from the inside out. "My grandmother's only son" — the speaker is a grandson, not a son, so his grandmother's only son must be his own father. Then "the daughter of my father" is his sister. Answer: sister. The whole difficulty in this family of questions is resisting the urge to read the phrase left to right; always start with the innermost possessive.

Worked example 2 — chain of statements. A is the brother of B. C is the father of A. D is the sister of E. E is the son of B. How is D related to C? Build the tree: C is on the top line, and since C fathers A while A and B are siblings, C fathers B as well. On the next line down sit A and B. E is B's son, so E is on the third line — C's grandchild. D is E's sister, so D is also B's child and therefore also on the third line. D is female, so D is C's granddaughter. Notice that the puzzle never told you B's gender, and it did not need to.

Coded relations. Here symbols replace relationship words: suppose A + B means A is the father of B, A − B means A is the sister of B, A × B means A is the brother of B, and A ÷ B means A is the mother of B. Read a chain strictly left to right, one link at a time. In P ÷ Q × R − S: P is the mother of Q; Q is the brother of R; R is the sister of S. Since Q and R are siblings, R is also P's child; since R and S are siblings, S is P's child too. So P is the mother of S. Write each link as a separate line of the tree before combining — combining in your head is where sign errors creep in.

Draw a small compass cross in the corner of your rough sheet with North up, and draw the walk as a path of arrows. Two rules cover everything. First, a right turn is 90° clockwise and a left turn is 90° anticlockwise, where the clockwise order of the compass is North → East → South → West → North. Second, turns are relative to the direction you are currently facing, never to the original direction — this is the single most common error.

Worked example — shortest distance. A man starts facing North and walks 8 m. He turns right and walks 15 m, turns right and walks 3 m, then turns right again and walks 3 m. How far is he from his starting point? Track the facings with the table: North, then East, then South, then West. So he covered 8 m North, 15 m East, 3 m South and 3 m West. Net vertical movement = 8 − 3 = 5 m North. Net horizontal movement = 15 − 3 = 12 m East. The two nets are at right angles, so by Pythagoras the shortest distance is √(5² + 12²) = √(25 + 144) = √169 = 13 m, and he is North-East of the start.

The shadow and sunrise sub-type. The sun rises in the East and sets in the West, so a shadow always falls away from the sun: in the morning shadows point West, in the evening they point East. Combine that with the turn table. "In the morning a man walks so that his shadow falls to his right — which way is he facing?" The shadow is to the West, and the West is to his right, so he faces South (facing South, the right hand points West). Same question in the evening: the shadow is to the East, and the East is to his right, so he faces North. And if the evening shadow falls to his left, he faces South, because facing South the left hand points East.

Ranking questions rest on one identity: total = position from left + position from right − 1. The "− 1" is there because the person himself is counted from both ends and so counted twice. Every other ranking result is this identity rearranged. If a girl is 18th from the left in a row of 45, her position from the right is 45 − 18 + 1 = 28th. If a boy is 13th from the left and 17th from the right, the row holds 13 + 17 − 1 = 29 students.

Two people, one row. In a class of 60, A is 22nd from the top and B is 31st from the bottom. How many are between them? Bring both to the same end first: B from the top = 60 − 31 + 1 = 30th. A is 22nd, B is 30th, so the number strictly between them = 30 − 22 − 1 = 7. The shortcut is 60 − 22 − 31 = 7, and the "− 1" is already baked into it. Forgetting it and answering 8 is the classic slip.

Comparison and ordering. When the question gives statements like "A is taller than B but shorter than C", turn each into a ">" sign and merge everything into one single line, tallest on the left. A > B and C > A combine to C > A > B. Add D > C and the line becomes D > C > A > B. Add E < B, which is the same as B > E, and you get D > C > A > B > E. Now every question is a matter of counting along the line: the tallest is D, the second tallest is C, the middle one is A. Keep one line only — the moment you have two half-lines you will misjoin them.

Tier-I gives you 60 minutes for 100 questions, so the reasoning section deserves roughly 12 to 14 minutes for its 25 questions — about 30 seconds each. That budget is only achievable if you take the section in two passes. On the first pass answer analogy, classification, series, alphabet tests and ranking, which are nearly all sub-20-second questions. On the second pass return to coding with conditions, blood relations with long chains, and anything needing a diagram.

1. For any analogy, write the relationship as a sentence before glancing at the options.
2. For any letter question, write the position numbers first. Never count on fingers.
3. For any series, write the row of differences underneath before trying anything clever.
4. For any coding, verify the rule on every letter of the given example, right to left.
5. For blood relations, direction and ranking, draw — a tree, a compass path, a single line of ">" signs.