Quick Summary: Analogy, Series and Numerical Relations give 1 to 3 marks in GATE General Aptitude 2027 in every paper (DA, RA, CS, ME, EE, CE, EC). The questions are short: find the missing number in a series, the next letter group, the odd one out, the word pair with the same relationship, or the code for a word. Every one of them is a pattern-spotting race against the clock. This guide gives you the difference method and the ratio method for number series, the alphabet-position method for letter series and coding, the relationship checklist for analogies, 8 solved previous-year and GATE-style questions, a 5-question practice set and a one-page rule sheet.
📋 Table of Contents
- Why this topic matters in GATE GA
- What the official GA syllabus says
- Number series: differences, ratios and mixed patterns
- Letter series and alphabet positions
- Analogy: word pairs, number pairs and odd one out
- Coding and decoding
- Numerical relations: grids, triangles and operator puzzles
- Shortcuts and traps
- Solved PYQs and GATE-style questions
- Practice set
- One-page rule sheet
- Common mistakes
- FAQs
Why this topic matters in GATE GA
Series and analogy questions are the oldest residents of the GATE GA section. The very first GA papers in 2010 and 2011 had number series and odd-one-out questions, and they have continued every year since, now officially listed under “Analytical Aptitude: Analogy, Numerical relations and reasoning”. They are almost always 1-mark questions, which is exactly why they matter: a 1-mark question should take 45 seconds, and every extra minute you spend hunting for a pattern is stolen from a 2-mark question later.
The good news is that GATE uses a small set of patterns. Constant differences, growing differences, constant ratios, growing multipliers, squares and cubes of primes, alternating series, and alphabet positions. Once you have a fixed order in which you test these, the pattern reveals itself in two or three attempts and you never freeze.
Here is roughly how much the topic has contributed. Candidates targeting 15/15 in GA should settle any series question in under a minute.
| Year | Marks from this topic (approximate, across papers) | Typical question type |
|---|---|---|
| 2019 | 1 to 2 | Missing number, cubes of primes |
| 2020 | 1 to 2 | Letter coding, word analogy |
| 2021 | 1 to 3 | Number grid, operator puzzle |
| 2022 | 1 to 2 | Odd one out, mixed series |
| 2023 | 1 to 3 | Analogy with numbers, letter series |
| 2024 | 1 to 2 | Coding-decoding with a rule, series with alternating operations |
| 2025 | 1 to 2 | Number relation in a figure |
| 2026 | 1 to 3 | Word analogy, missing term |
What the official GA syllabus says
This post covers analogy, series (number and letter), coding-decoding and numerical relations. Deduction and induction were the previous post in the series; puzzles and arrangements are the next post. The complete GA syllabus and weightage are in the GATE General Aptitude 2027 hub.
Number series: differences, ratios and mixed patterns
Test the patterns in this fixed order, and stop at the first one that works for every gap:
- First differences. Subtract neighbours. Constant difference means arithmetic progression. If the differences themselves form a familiar sequence (1, 2, 3 or 1, 3, 5 or 2, 4, 8), you have found it.
- Second differences. If the first differences are not obvious, difference them again. Constant second difference means the n-th term is quadratic (squares plus something).
- Ratios. Divide neighbours. Constant ratio means geometric progression. Growing multipliers (×1.5, ×2, ×2.5) or shrinking multipliers (×6, ×5, ×4) are a GATE favourite.
- Squares, cubes and primes. Check whether each term is n2, n3, n2 + 1, n2 − 1 or a power of a prime. 343, 1331 and 2197 are 73, 113 and 133.
- Alternating or interleaved series. If nothing fits, split into odd-position and even-position terms and test each separately.
- Mixed operations. Patterns like ×2 + 1, or ×3 − 2, applied repeatedly. Check by computing from the first term.
Solution: First differences: 4, 8, 16, 32 (doubling). Next difference 64, so next term 63 + 64 = 127. Cross-check: each term is 2n − 1, and 27 − 1 = 127.
Answer: 127.
Solution: Differences: 3, 5, 7, 9, 11, so next difference is 13 and the next term is 37 + 13 = 50. Cross-check: terms are n2 + 1 for n = 1 to 7, and 72 + 1 = 50.
Answer: 50.
Solution: Differences 6, 12, 24 double each time, so the next difference is 48 and the missing term is 47 + 48 = 95. Check the last gap: 191 − 95 = 96, which continues the doubling. Equivalent rule: each term is 2 × previous + 1.
Answer: 95.
Letter series and alphabet positions
Letter questions are number questions in disguise. Write the alphabet positions (A = 1, B = 2, … Z = 26) and apply the same difference method. Three facts save time in the hall:
- Memorise the anchor letters: E = 5, J = 10, O = 15, T = 20, Y = 25. Every other letter is within two of an anchor.
- Opposite letters (positions adding to 27): A-Z, B-Y, C-X, D-W, E-V, F-U, G-T, H-S, I-R, J-Q, K-P, L-O, M-N. Reverse coding uses exactly these.
- Positions wrap around: after Z (26) comes A again, so Z + 2 = B. Count modulo 26.
Letter groups (such as B, FH, LNP) usually grow by one letter per group while the gaps between consecutive letters stay fixed. Write the positions of the last letter of each group and the first letter of the next, and the step is visible immediately.
Solution: First letters A, C, F, J are positions 1, 3, 6, 10 (differences 2, 3, 4), so the next is 10 + 5 = 15 = O. Second letters Z, X, U, Q are positions 26, 24, 21, 17 (differences 2, 3, 4), so the next is 17 − 5 = 12 = L. Each pair is also an opposite pair (sum 27), and O + L = 15 + 12 = 27, confirming it.
Answer: OL.
Solution: Inside each group the letters step by 2. The first letters B, G, L are positions 2, 7, 12, stepping by 5, so the next group starts at 17 = Q and reads Q, S, U. The group after that starts at 22 = V, matching VXZ.
Answer: QSU.
Analogy: word pairs, number pairs and odd one out
An analogy “A : B :: C : ?” asks you to name the relationship between A and B in one sentence, then apply the same sentence to C. The sentence must be specific. “Doctor : Hospital” is not “a doctor is related to a hospital”; it is “a doctor works in a hospital”. Then “Teacher : ?” is “School”, not “Student”.
The relationships GATE has used, roughly in order of frequency:
| Relationship | Example | Test sentence |
|---|---|---|
| Synonym or antonym | Brave : Timid | A is the opposite of B |
| Degree or intensity | Warm : Scorching | B is an extreme form of A |
| Worker and tool, worker and product | Sculptor : Chisel | A uses B |
| Part and whole | Petal : Flower | A is a part of B |
| Cause and effect | Virus : Infection | A causes B |
| Unit and quantity | Newton : Force | A measures B |
| Number relation | 4 : 17 :: 7 : 50 | B = A2 + 1 |
For number analogies, try B = A2, A2 ± 1, A3, A2 + A, 2A ± 1, and A × (A + 1) in that order. For “odd one out” questions, find the property three of the four items share (all primes, all squares, all vowels, same letter gap) and pick the one that breaks it. The trap is choosing a property that only two items share.
Solution: 42 = 6 × 7 = 6 × (6 + 1). Apply to 9: 9 × 10 = 90. Check alternatives: 62 + 6 = 42 is the same rule. (B) 81 would be 92, but 62 = 36, not 42, so that rule fails.
Answer: (C) 90.
Solution: 17, 23, 29 and 41 are prime. 33 = 3 × 11 is composite.
Answer: 33.
Coding and decoding
A coding question gives you a word and its code and asks you to encode or decode another word. Compare letter by letter and find the rule. The common rules:
- Constant shift: every letter moves forward or backward by the same amount (CAT to FDW is +3).
- Increasing shift: the first letter moves +1, the second +2, the third +3, and so on.
- Reverse alphabet: each letter is replaced by its opposite (A to Z, B to Y), position 27 − n.
- Reversal plus shift: the word is written backwards and then shifted.
- Position sums: the code is a number such as the sum of letter positions, or the product of the first and last positions.
- Substitution: words stand for other words (“sky is called sea, sea is called water”). Follow the chain carefully, exactly one step.
Solution: R (18) to U (21) is +3, O (15) to R (18) is +3, B (2) to E (5) is +3, O to R is +3, T (20) to W (23) is +3. Apply +3 to DRONE: D (4) to G (7), R (18) to U (21), O (15) to R (18), N (14) to Q (17), E (5) to H (8).
Answer: GURQH.
Solution: D = 4, A = 1, T = 20, A = 1. Sum = 4 + 1 + 20 + 1 = 26.
Answer: 26.
Numerical relations: grids, triangles and operator puzzles
GATE likes to hide a series inside a figure: a 3 × 3 grid with one cell missing, a triangle with numbers at the corners and one in the middle, or a circle divided into sectors. The rule connects the numbers in each row, column or figure, and it is the same rule in every row or figure. Work with the complete rows first, state the rule in words, then apply it to the incomplete one.
Rules that recur: middle = sum of corners; middle = product of two corners minus the third; third column = first column × second column; bottom row = top row + middle row; diagonal sums equal; each row sums to the same total.
Operator puzzles redefine symbols (“if + means × and × means −”) or define a new operation (a △ b = a2 − b). Substitute mechanically and evaluate. When symbols are swapped, apply the standard BODMAS order after substitution, not before.
Solution: Row 1: 3 × 5 + 1 = 16. Row 2: 4 × 7 + 1 = 29. Rule: third = first × second + 1. Row 3: 6 × 2 + 1 = 13. Cross-check an alternative such as sum of squares: 9 + 25 = 34, not 16, so the product rule stands.
Answer: 13.
Solution: 3 △ 2 = 9 − 6 + 4 = 7. Then 7 △ 1 = 49 − 7 + 1 = 43.
Answer: 43.
Shortcuts and traps
❌ Treating a letter series as cyclic (Z to A) when the question treats it as linear, or the reverse. Check with the given terms.
❌ In a word analogy, matching on the same topic (“both about school”) instead of the same relationship.
❌ In odd-one-out, picking a property that only two items share.
❌ In substitution coding, following the chain two steps instead of one.
❌ Applying BODMAS before substituting the swapped operators.
❌ Miscounting alphabet positions; O is 15, not 14; T is 20, not 19.
Solved previous-year and GATE-style questions
Years are given only where I am confident the question appeared; the rest are built to the same pattern. Many more are solved in the PiyushAI Aptitude Test Series with video explanations.
Solution: Ratios: 3/2 = 1.5, 6/3 = 2, 15/6 = 2.5. The multiplier grows by 0.5 each step. Next: 15 × 3 = 45. Check: 45 × 3.5 = 157.5 and 157.5 × 4 = 630. Both match.
Answer: 45.
Solution: Positions. ALRVX: 1, 12, 18, 22, 24, differences 11, 6, 4, 2. EPVZB: 5, 16, 22, 26, 2 (that is 28 after wrapping), differences 11, 6, 4, 2. ITZDF: 9, 20, 26, 4 (30), 6 (32), differences 11, 6, 4, 2. OYEIK: 15, 25, 5 (31), 9 (35), 11 (37), differences 10, 6, 4, 2. The first gap breaks the pattern.
Answer: OYEIK.
Solution: Positions: B = 2; F, H = 6, 8; L, N, P = 12, 14, 16. Inside a group letters step by 2. From the last letter of a group to the first of the next: 2 to 6 is +4, 8 to 12 is +4, so the next group starts at 16 + 4 = 20 = T and has four letters: T, V, X, Z (20, 22, 24, 26).
Answer: TVXZ.
Solution: 343 = 73, 1331 = 113, 4913 = 173. The bases 7, 11, 17 are consecutive primes with 13 missing. 133 = 2197.
Answer: 2197.
Solution: Ratios: 12/2 = 6, 60/12 = 5, 240/60 = 4, 720/240 = 3. The multiplier falls by 1 each step, so the next is 720 × 2 = 1440.
Answer: 1440.
Solution: A thermometer is an instrument that measures temperature. A barometer is an instrument that measures pressure. A clock is not an instrument that measures a wall; an engine consumes fuel; a calendar displays months but “month” is a unit, not a measured quantity.
Answer: (B).
Solution: M (13) to N (14) is +1, O (15) to Q (17) is +2, T (20) to W (23) is +3, O (15) to S (19) is +4, R (18) to W (23) is +5. Increasing shift. PUMP: P (16) + 1 = Q, U (21) + 2 = W, M (13) + 3 = P, P (16) + 4 = T.
Answer: QWPT.
Solution: Test sum of squares on figure 1: 16 + 25 + 36 = 77, not 74. Test sum of pairwise products: 4 × 5 + 5 × 6 + 6 × 4 = 20 + 30 + 24 = 74. Verify on figure 2: 2 × 3 + 3 × 7 + 7 × 2 = 6 + 21 + 14 = 41. Both match, so the rule is centre = ab + bc + ca. Figure 3: 3 × 5 + 5 × 8 + 8 × 3 = 15 + 40 + 24 = 79.
Answer: 79.
★ PiyushAI Test Series
Best GATE Aptitude Test Series 2027
General Aptitude is 15 marks in every GATE paper and the easiest 15 marks to lose to silly mistakes. The PiyushAI Aptitude Test Series by Piyush Wairale (IIT Madras) gives you topic-wise tests on exactly this chapter, full-length GA mocks in the real GATE interface, detailed video and text solutions, and All-India rank analysis.
Practice set
Attempt these in 6 minutes before opening the key.
- Find the next term: 1, 4, 10, 22, 46, ___ (A) 70 (B) 94 (C) 92 (D) 90
- Find the next term: CFI, FIL, ILO, LOR, ___ (A) ORU (B) OQS (C) PSV (D) NQT
- Pen : Write :: Knife : ? (A) Sharp (B) Cut (C) Kitchen (D) Steel
- In a certain code, HEAT is written as SVZG. How is COLD written in that code? (A) XLOW (B) XOLW (C) WLOX (D) XLWO
- Rows of a grid: (2, 3, 13), (4, 1, 17), (5, 2, ?). The missing number is (A) 27 (B) 29 (C) 23 (D) 21
Show answer key
- (B) 94. Differences 3, 6, 12, 24 double; next difference 48; 46 + 48 = 94. (Equivalent rule: next = 2 × previous + 2.)
- (A) ORU. Each group steps by 3 inside (C 3, F 6, I 9) and each group starts 3 after the previous start: C, F, I, L, so the next starts at O (15): O, R, U.
- (B) Cut. A pen is used to write; a knife is used to cut (tool and function).
- (A) XLOW. H (8) to S (19), 8 + 19 = 27: reverse alphabet. C (3) to X (24), O (15) to L (12), L (12) to O (15), D (4) to W (23).
- (B) 29. 22 + 32 = 13, 42 + 12 = 17, so 52 + 22 = 29.
One-page rule sheet
2. Constant second difference means a quadratic rule (n2 family). Doubling differences means 2n family.
3. Growing multipliers (×1.5, ×2, ×2.5) and falling multipliers (×6, ×5, ×4) are standard GATE patterns.
4. Letter positions: A = 1, E = 5, J = 10, O = 15, T = 20, Y = 25, Z = 26. Opposite letter = 27 − position.
5. Letter groups: step inside the group and step between group starts are usually both constant.
6. Analogy: write the A to B relationship as one specific sentence, then apply it to C.
7. Number analogy tests: A2, A2 ± 1, A3, A(A + 1), 2A ± 1.
8. Odd one out: the property must be shared by all but one item.
9. Coding: compare positions letter by letter; look for constant shift, increasing shift, reverse (sum 27) or reversal plus shift.
10. Grid and figure puzzles: derive the rule from the complete rows, verify on a second complete row, then apply.
11. Operator puzzles: substitute first, then apply BODMAS.
12. Any series rule must be verified on every given term, including the ones after the gap.
Common mistakes
❌ Confusing a difference pattern with a ratio pattern when the numbers are small (2, 4, 8 fits both +2 then +4, and ×2).
❌ Miscounting alphabet positions, especially in the O to V range.
❌ Forgetting that the alphabet wraps (Z + 1 = A) in cyclic letter series.
❌ Picking an analogy option on the same topic rather than the same relationship.
❌ Applying the rule from one row of a grid without checking it on the other complete row.
❌ Spending more than 90 seconds on a 1-mark pattern question.
FAQs
How many series and analogy questions appear in GATE GA?
Usually 1 question, occasionally 2, almost always of 1 mark each. Across papers the topic contributes 1 to 3 marks a year.
Should I memorise squares and cubes for this topic?
Yes, squares up to 30 and cubes up to 15. Recognising 2197 as 133 or 729 as 93 instantly is what makes a series question a 30-second question.
What if I cannot find the pattern?
Give it 90 seconds with the fixed test order, then mark for review. Return at the end; a fresh look usually finds it. Never guess on a 1-mark MCQ with negative marking unless you can eliminate two options.
Is the PiyushAI Aptitude Test Series enough for GA?
Yes. The Best GATE Aptitude Test Series 2027 has dedicated tests on series, analogy and coding, tests on every other GA chapter, full-length GA mocks in the GATE interface, solved PYQs from 2010 to 2026 and All-India rank analysis. With the free guides on this site it covers the whole GA section.
Are these questions different for GATE DA and GATE RA?
No. The GA section is identical across papers, so the same series, analogy and coding patterns appear whether you write DA, RA, CS or ME.
Stop losing easy marks. Practise this topic under exam pressure.
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