Most reasoning marks in SSC and railway exams are lost for one reason: the aspirant sees the question, searches for a trick, and burns forty seconds before finding nothing. The questions in this family (analogy, classification, series, missing numbers, and the picture-based topics) are not tricks at all. They are a small set of rules that repeat. Learn the rules, practise recognising which one applies, and each question drops to 20 to 30 seconds.
This guide covers the whole family in order: verbal, letter and number analogy; classification (odd one out); number and letter series; missing numbers in grids and figures; matrices; and the non-verbal topics, explained in words so you can follow without any picture: mirror and water images, paper folding and cutting, counting figures, embedded figures, and cubes and dice. There are 44 worked examples, and every pattern and answer in them has been checked step by step.
Where this fits in the exam
For SSC CGL Tier 1, widely published coverage describes the reasoning section as 25 questions for 50 marks, within a combined 60-minute paper, with 0.50 marks deducted per wrong answer. SSC CHSL, MTS, GD and the RRB exams (NTPC, Group D, ALP, JE) also carry general intelligence and reasoning, but question counts, marks, timing and negative marking differ between exams and change between cycles. Check the latest notification for the exact numbers of the exam you are targeting.
What does not change is the flavour of the questions. Analogy, classification, series, and a few non-verbal questions turn up in almost every paper. These are among the quickest scoring areas in the section, which is why they should be your first priority before the slower topics such as seating arrangement and puzzles.
The three-step method for every question in this family
- Name the type. Is it a relationship (analogy), a grouping (classification), a sequence (series), or a picture? Naming it takes two seconds and narrows the rule list.
- Test the simplest rule first. Differences, then ratios, then squares and cubes, then alternating patterns. Do not start with exotic ideas.
- Confirm on every given item. A rule that explains four of five items is wrong. This single habit removes most careless errors.
Verbal analogy
An analogy gives a pair (A : B) and asks you to find the partner of a third word (C : ?). The job is to name the relationship in one short sentence, then apply the same sentence to the second pair. Common relationship types:
- Tool and its function (pen : write)
- Instrument and what it measures (thermometer : temperature)
- Worker and workplace (judge : courtroom)
- Part and whole (petal : flower)
- Young one and adult, male and female, animal and home
- Degree or intensity (warm : hot)
- Cause and effect (fire : smoke)
- Product and raw material (butter : milk)
Rule with a catch: keep the order of the pair. If the first pair is tool : function, the second must also be tool : function, not function : tool. Options are often built to trap exactly this reversal.
Example 1
Pen : Write :: Knife : ? Relationship: a tool and the job it does. A knife is used to cut. Answer: Cut.
Example 2
Thermometer : Temperature :: Barometer : ? Relationship: instrument and the quantity it measures. A barometer measures atmospheric pressure. Answer: Atmospheric pressure.
Letter analogy
Convert letters to positions (A=1 to Z=26) and look at what happens to each letter: a fixed shift, a reversal, or a pattern that grows. Keep the alphabet written on your rough sheet as 1 to 26 until the positions are automatic. Useful anchors: E=5, J=10, O=15, T=20, Z=26. The opposite letter of a position p is 27 minus p (A and Z, B and Y, and so on).
Example 3
ACE : GIK :: BDF : ? Positions: A, C, E = 1, 3, 5 becomes G, I, K = 7, 9, 11. Every letter moves forward 6. Apply to B, D, F = 2, 4, 6, which gives 8, 10, 12 = H, J, L. Answer: HJL.
Number analogy
Here you find the operation that turns the first number into the second. Test these in order: add or subtract a constant; multiply or divide; square, cube; square plus or minus the number; a product of the number and the next number. If a pair of examples is given, the rule must work for both.
Example 4
2 : 10 :: 4 : 68 :: 5 : ? Test cube plus the number. 2 cubed is 8, plus 2 is 10. 4 cubed is 64, plus 4 is 68. Both hold. For 5: 125 plus 5 is 130. Answer: 130.
Classification (odd one out)
Four or five items share a property and one does not. Check, in this order: category (fruit, mammal, metal), form (2D or 3D, living or non-living), then, for letters and numbers, positions and arithmetic properties.
Example 5 (word)
Sparrow, Eagle, Bat, Crow. Sparrow, eagle and crow are birds. A bat is a flying mammal. Odd one: Bat.
Example 6 (letter pairs)
AZ, BY, CX, DV. Add the positions in each pair: A (1) and Z (26) give 27; B (2) and Y (25) give 27; C (3) and X (24) give 27; D (4) and V (22) give 26. The last pair breaks the rule (it should have been DW). Odd one: DV.
Example 7 (numbers, squares)
16, 25, 36, 48, 64. 16 is 4 squared, 25 is 5 squared, 36 is 6 squared, 64 is 8 squared. 48 is not a perfect square (6 squared is 36, 7 squared is 49). Odd one: 48.
Example 8 (numbers, primes)
11, 13, 17, 21, 23. 11, 13, 17 and 23 are prime. 21 equals 3 times 7. Odd one: 21.
Example 9 (numbers, cubes)
27, 64, 125, 150, 216. These are 3, 4, 5 and 6 cubed, except 150. Since 5 cubed is 125 and 6 cubed is 216, 150 cannot be a cube. Odd one: 150.
Example 10 (letter clusters)
ACE, GIK, MOQ, SUY. In each cluster the letters are 2 steps apart, except one. A, C, E = 1, 3, 5; G, I, K = 7, 9, 11; M, O, Q = 13, 15, 17; S, U, Y = 19, 21, 25 (the last gap is 4). Odd one: SUY. The correct cluster would have been SUW.
Example 11 (shapes)
Triangle, Square, Pentagon, Sphere. The first three are flat (2D) figures made of straight sides; a sphere is a solid (3D) figure with no straight sides. Odd one: Sphere.
Trap: two different rules can sometimes isolate two different items. If that happens, prefer the rule that is more basic (category beats position), and re-read the question wording for hints.
Number series: the rule ladder
Work down this ladder in order. Almost every SSC and railway series falls on one of the first seven rungs.
- Constant difference (arithmetic): each term adds the same amount.
- Constant ratio (geometric): each term multiplies by the same number.
- Changing difference: the gaps themselves follow a pattern (for example 1, 2, 4, 8 or 2, 4, 6, 8).
- Squares and cubes: terms like n squared plus or minus a constant, or n cubed plus or minus a constant.
- Multiply and add: times a number, plus a constant or a growing number.
- Two interleaved series: odd positions follow one rule, even positions another.
- Sum of previous terms (Fibonacci type).
- Prime numbers and their squares or cubes.
Memorise squares up to 25 and cubes up to 12. You will see them constantly, and knowing them lets you recognise a squares series without any calculation. Handy facts: the numbers one below perfect squares (3, 8, 15, 24, 35, 48) and the numbers one below perfect cubes (7, 26, 63, 124, 215, 342) are classic series material.
Example 12 (arithmetic)
7, 12, 17, 22, ? Differences: 5, 5, 5. Next term: 22 plus 5 equals 27. Answer: 27.
Example 13 (geometric)
3, 6, 12, 24, 48, ? Each term is doubled. 48 times 2 is 96. Answer: 96.
Example 14 (differences double)
2, 3, 5, 9, 17, ? Differences: 1, 2, 4, 8. The next difference is 16, so the term is 17 plus 16 equals 33. Answer: 33.
Example 15 (squares of primes)
4, 9, 25, 49, 121, ? These are 2, 3, 5, 7, 11 squared, so the next prime is 13 and its square is 169. Answer: 169.
Example 16 (square minus one)
3, 8, 15, 24, 35, ? The terms are 2 squared minus 1 (3), 3 squared minus 1 (8), 4 squared minus 1 (15), 5 squared minus 1 (24), 6 squared minus 1 (35). Next: 7 squared minus 1 equals 48. Cross-check with differences: 5, 7, 9, 11, then 13; 35 plus 13 is 48. Answer: 48.
Example 17 (cube minus one)
7, 26, 63, 124, 215, ? These are 2, 3, 4, 5, 6 cubed minus 1: 8-1=7, 27-1=26, 64-1=63, 125-1=124, 216-1=215. Next: 7 cubed is 343, minus 1 is 342. Answer: 342.
Example 18 (two interleaved series)
5, 10, 7, 20, 9, 40, 11, ? Odd positions: 5, 7, 9, 11 (adding 2). Even positions: 10, 20, 40 (doubling). The missing term is in the 8th position, so it is 40 times 2 equals 80. Answer: 80.
Example 19 (multiply and add, fixed)
2, 5, 11, 23, 47, ? Each term is twice the previous plus 1: 2x2+1=5, 5x2+1=11, 11x2+1=23, 23x2+1=47. Next: 47x2+1 equals 95. Answer: 95.
Example 20 (multiply and add, growing)
3, 7, 16, 35, 74, ? Double and add 1, 2, 3, 4, ...: 3x2+1=7, 7x2+2=16, 16x2+3=35, 35x2+4=74. Next: 74x2+5 equals 153. Answer: 153.
Example 21 (n times n+1)
2, 6, 12, 20, 30, ? Terms are 1x2, 2x3, 3x4, 4x5, 5x6. Next: 6x7 equals 42. Differences (4, 6, 8, 10, then 12) agree: 30 plus 12 is 42. Answer: 42.
Example 22 (sum of previous two)
1, 3, 4, 7, 11, 18, ? Each term is the sum of the two before it: 1+3=4, 3+4=7, 4+7=11, 7+11=18. Next: 11+18 equals 29. Answer: 29.
Example 23 (wrong number)
2, 6, 12, 20, 31, 42. This is the n times n+1 series from Example 21: 2, 6, 12, 20, 30, 42. The fifth term is 31 instead of 30. Wrong number: 31.
Example 24 (wrong number)
4, 8, 16, 32, 60, 128. Each term should double: 4, 8, 16, 32, 64, 128. Wrong number: 60 (should be 64).
Letter series
Treat letters as numbers 1 to 26 and apply the same ladder. Add two extra ideas: a forward series and a backward series running together, and clusters where the starting letters follow one rule while letters inside each cluster follow another.
Example 25 (growing gaps)
A, C, F, J, O, ? Positions: 1, 3, 6, 10, 15. Gaps: 2, 3, 4, 5, so the next gap is 6 and the position is 21, which is U. Answer: U.
Example 26 (forward and backward)
B, Z, D, X, F, V, H, ? Odd positions go forward: B, D, F, H (2, 4, 6, 8). Even positions go backward: Z, X, V (26, 24, 22), so the next is 20, which is T. Answer: T.
Example 27 (clusters)
ACE, FHJ, KMO, ? Within each cluster the gap is 2. The first letters are A (1), F (6), K (11), so the next first letter is 16 (P). The cluster is P, R, T (16, 18, 20). Answer: PRT.
Missing numbers in grids and figures
The same ladder applies, but now the relationship is across a row, down a column, or around a centre. Always test rows first, then columns; if both seem to work, the answer is usually the same either way. Typical relationships: the third number is the sum, difference or product of the first two; the middle is a multiple of an outer number; squares and square roots; or the centre of a figure is the sum, product or average of the surrounding numbers.
Example 28 (row rule: squares)
Rows: (3, 4, 25), (5, 12, 169), (8, 15, ?). Test: 3 squared plus 4 squared is 9+16=25. 5 squared plus 12 squared is 25+144=169. So the last is 64+225 equals 289. Answer: 289.
Example 29 (multiples)
Rows: (2, 8, 4), (3, 12, 6), (5, ?, 10). In each row the middle number is 4 times the first (2 to 8, 3 to 12) and also twice the third (4 to 8, 6 to 12). For the last row: 4 times 5 is 20, and twice 10 is 20. Both agree. Answer: 20.
Example 30 (figure with a circle: average)
Imagine a circle split into four parts holding 3, 5, 7, 9 with 6 in the centre; a second identical figure holds 2, 4, 6, 8 with 5 in the centre. Check: (3+5+7+9)/4 = 24/4 = 6, and (2+4+6+8)/4 = 20/4 = 5. A third figure holds 10, 14, 6, 18 with ? in the centre. Sum is 48, divided by 4 is 12. Answer: 12.
Example 31 (triangle: product)
A triangle has three corner numbers and one number inside. Triangle one: corners 2, 3, 4, inside 24. Triangle two: corners 1, 5, 6, inside 30. Triangle three: corners 3, 4, 7, inside ? Test the product: 2x3x4=24 and 1x5x6=30 both match. So 3x4x7 equals 84. Answer: 84.
Matrices
A figure matrix is a 3 by 3 block of shapes with one cell missing. Without pictures, think of it as a puzzle with three checks: (1) does each shape appear exactly once per row and per column (Latin square); (2) do features such as shading, number of lines or number of sides grow by a fixed amount across a row; (3) do the first two cells combine to give the third (overlap, remove common parts, or add them). Test the Latin-square idea first because it is the commonest and fastest.
Example 32 (Latin square of shapes)
Row 1: circle, square, triangle. Row 2: square, triangle, circle. Row 3: triangle, circle, ? Each row and column must contain each shape once. Column 3 already has triangle and circle, so the missing cell is the square. Answer: Square.
Mirror image
A mirror (lateral) image flips left and right when the mirror stands at the right or left side of the figure; it flips top and bottom when the mirror is placed above or below. Remember the two essentials. First, the order of items reverses (the item nearest the mirror stays nearest the mirror). Second, each item is also flipped individually.
For letters, the shapes that look the same in a vertical mirror are A, H, I, M, O, T, U, V, W, X and Y. Those are the letters that have a vertical line of symmetry. All others (B, C, D, E, F, G, J, K, L, N, P, Q, R, S, Z) change shape.
Example 33 (clock mirror image)
The time on a clock is 3:20. What time does its mirror image show? Rule: mirror time equals 11:60 minus the actual time. 11:60 minus 3:20 is 8:40. Check with angles: the real hour hand is at 3x30 + 10 = 100 degrees from 12; in a mirror every angle becomes 360 minus itself, which is 260 degrees. That is where the hour hand sits at 8:40 (8x30 + 20 = 260). The minute hand at 20 minutes (120 degrees) becomes 240 degrees, which is 40 minutes. Answer: 8:40.
Example 34 (clock mirror image)
Actual time 7:45. Mirror time is 11:60 minus 7:45, which is 4:15. Answer: 4:15. Two exceptions for quick checking: 6:00 stays 6:00, and for times starting at 12 you use 11:60 minus the time with 12 treated as 0, so 12:30 becomes 11:30.
Example 35 (word in a mirror)
A mirror stands on the right of the word MOTH. What do you see? The order reverses to H, T, O, M. Each of M, O, T and H has a vertical line of symmetry, so none changes shape. Answer: HTOM, written in ordinary-looking letters. Had the word been BOX, the order would give X, O, B, with B drawn back-to-front.
Direction trap: if a mirror is on the right or left, only left and right swap; the top stays on top. Many students flip both directions and pick the wrong option.
Water image
A water image is a reflection in still water below the figure, so top and bottom swap while left and right stay put. It is the same idea as a horizontal mirror below. Letters that look the same after a top-bottom flip (they have a horizontal line of symmetry) are B, C, D, E, H, I, K, O and X.
Example 36 (word in water)
What is the water image of the word CODE? The order of letters stays the same, since left and right do not swap. Each of C, O, D and E has a horizontal line of symmetry, so each looks unchanged. Answer: CODE. By contrast, HIDE also stays HIDE, but the word MAT would turn each letter upside down, because M, A and T have no horizontal symmetry.
Paper folding and cutting
These questions fold a sheet, punch or cut it, and ask what the unfolded sheet looks like. The only method that works reliably is to unfold in reverse order and reflect each cut across the fold line you just undid. Three rules:
- The number of layers doubles with each fold (half folds), so one punch makes as many holes as there are layers at that place.
- Each hole appears as a mirror image of its partner across the fold line.
- A cut touching a fold line joins with its mirror image into one larger shape. A half circle cut along a folded edge opens into a full circle.
Example 37 (two folds, one hole)
A square sheet is folded in half left over right, then in half top over bottom. A small hole is punched in the folded square away from both fold edges. How many holes appear when the sheet is opened, and where? Layers: 2 after the first fold, 4 after the second. The punch passes through all four. Unfolding reflects the hole across the horizontal line, then across the vertical, so there is one hole in each quarter, placed symmetrically. Answer: 4 holes, one in each quadrant.
Example 38 (three folds)
A square sheet is folded in half three times, each time over a different edge, and one small hole is punched in the interior of the final small square. Layers: 2, 4, 8. If the hole is not on a fold line, no two holes overlap. Answer: 8 holes.
Counting figures
Counting by eye misses shapes. Use formulas and systematic counting instead.
- Triangles: if a vertex of a triangle is joined to points on the opposite side that divide that side into m small segments, the number of triangles is m(m+1)/2.
- Rectangles in an m by n grid of unit squares: choose two of the (m+1) vertical lines and two of the (n+1) horizontal lines. Count equals C(m+1, 2) times C(n+1, 2).
- Squares in an m by n grid (m not smaller than n): add (m-k+1)(n-k+1) for k from 1 to n.
Example 39 (triangles)
A triangle has its apex joined to three points on the base, so the base is split into 4 small segments. Triangles: 4x5/2 equals 10. Check by listing: 4 single-segment triangles, 3 of two segments, 2 of three segments, 1 whole, giving 4+3+2+1=10. Answer: 10.
Example 40 (rectangles and squares)
A rectangle is divided into a grid of 4 columns by 3 rows of unit squares. Rectangles: C(5,2) = 10 ways to choose vertical lines, C(4,2) = 6 ways to choose horizontal lines, and 10x6 equals 60. Squares: size 1 gives 4x3=12, size 2 gives 3x2=6, size 3 gives 2x1=2, for a total of 20. Answer: 60 rectangles, of which 20 are squares.
Embedded figures
In these questions a small figure is hidden inside a larger one, and you must pick the option that contains it, in the same orientation and size. Method: note the figure's most distinctive feature (a sharp angle, a particular line direction, an unusual side), then look for that feature in each option and verify the rest. Do not rotate or resize the target; the question normally keeps it fixed.
Example 41 (embedded triangle)
The hidden figure is a right-angled isosceles triangle with its right angle at the lower left. Option A is a square with its diagonal drawn from the top-left to the bottom-right corner. Option B is a plus sign. The plus sign has only horizontal and vertical lines meeting at right angles, with no slanting line, so no triangle can be traced. In the square, the left side, the bottom side and the diagonal form a triangle with the right angle at the lower left. Answer: Option A contains the figure.
Cubes and dice
Three facts solve most questions.
- Faces seen together in one view are adjacent, never opposite.
- On a standard die the opposite faces add to 7: 1 and 6, 2 and 5, 3 and 4. A question may use unlabelled dice with different pairs, so use this only when the question says standard.
- For a cube painted on all faces and cut into n by n by n small cubes: three faces painted is always 8; two faces painted is 12(n-2); one face is 6(n-2) squared; none is (n-2) cubed.
Example 42 (two views)
Two views of the same cube: the first shows 1, 2 and 3; the second shows 1, 3 and 4. Which number is opposite 2? Both views contain 1 and 3 (adjacent faces sharing an edge). The two other faces touching both of these are on opposite sides of that edge: one at each end. These are 2 and 4. Answer: 4 is opposite 2.
Example 43 (standard die)
On a standard die the top shows 4. The numbers on the four side faces add to what? The bottom shows 7-4=3. All six faces add to 1+2+3+4+5+6=21. Sides: 21-4-3 equals 14. Answer: 14. Shortcut: the sides are two opposite pairs, each adding to 7, so 7+7=14.
Example 44 (painted cube)
A cube painted on all six faces is cut into 125 equal small cubes (n=5). Three faces painted: 8. Two faces: 12x3 equals 36. One face: 6x9 equals 54. None: 3x3x3 equals 27. Check the total: 8+36+54+27=125. Answer: 8, 36, 54, 27.
Common traps
- Reversed analogy. Pairs written as tool : function must keep that order. Options with the order flipped are deliberate distractors.
- Fitting four of five terms. A series rule must explain every given term. Always verify the whole list before marking.
- Stopping at one differences row. If the first differences are not constant, take second differences, or test ratio and squares before giving up.
- Missing the interleaved series. Alternating up and down values, or numbers jumping in size, usually signal two series woven together.
- Wrong position of the missing term. In two-series questions, count whether the blank is in an odd or even position before applying a rule.
- Off-by-one with letters. Z is 26, not 25. The opposite letter of position p is 27 minus p; people often use 26.
- Treating mirror and water images alike. Mirror swaps left and right; water swaps top and bottom.
- Clock mirror images. Subtract the shown time from 11:60 (or equivalently from 12:00, which gives the same result). Do not simply swap the hour and minute digits, and do not forget that the minute hand reflects too.
- Forgetting hole overlap. A hole on a fold line is not doubled; it merges with its own reflection.
- Using the 7-sum rule on non-standard dice. Check that the question says standard.
- Spending too long. If a question is not clicking in 40 seconds, mark it, move on and return if time remains. A skipped question costs nothing; a guess costs negative marks.
A 45-day plan
This is a planning suggestion, not an official schedule. Spend 60 to 90 minutes a day, and keep a small notebook of rules and the questions you got wrong.
Days 1 to 7: foundations
- Write squares 1 to 25 and cubes 1 to 12 daily until they are automatic.
- Write the alphabet with positions and the opposite-letter pairs.
- Learn the primes below 100.
- Solve 15 simple analogies and 15 simple classification questions per day.
Days 8 to 18: series
- Days 8 to 10: arithmetic, geometric, changing differences.
- Days 11 to 13: squares, cubes, multiply-and-add.
- Days 14 to 16: interleaved, Fibonacci type, wrong-number series.
- Days 17 to 18: letter series and cluster series. Do 20 questions per day and time yourself at 30 seconds each.
Days 19 to 25: grids, figures, matrices
- Practise rows, columns and centre-of-figure rules, 15 questions daily.
- Do a timed sectional test on all verbal topics so far (analogy, classification, series, grids).
Days 26 to 38: non-verbal topics
- Days 26 to 28: mirror and water images, clocks and letters.
- Days 29 to 31: paper folding and cutting; always unfold in reverse.
- Days 32 to 34: counting figures; learn the three formulas and practise the systematic count.
- Days 35 to 36: embedded figures.
- Days 37 to 38: cubes and dice.
Days 39 to 45: mixing and testing
- Take one full-length mock every alternate day and attempt the reasoning section first or second in your usual order.
- After each mock, classify every wrong or skipped question by topic and redo it without a clock.
- On the last two days, revise only your rules notebook and re-solve the questions you missed twice.
Frequently asked questions
Which topics in this guide give the fastest marks? Analogy, classification and simple series, since most take well under 30 seconds once you know the rule ladder. Non-verbal topics take longer at first but become quick with practice.
How many questions should I expect from this family? It varies by exam and year. Check recent papers and the latest notification for the exam you are taking, rather than trusting a fixed number.
Do I need to memorise tables beyond 20? No. Squares to 25 and cubes to 12 are enough for almost every series.
How do I recognise a squares series quickly? Look for terms close to perfect squares, or differences that grow by a constant (like 5, 7, 9, 11). A constant second difference points to squares or n(n+1)-type terms.
What is the quickest way to handle a wrong-number series? Find the rule from the terms you trust, usually the first three or the last three, then check which term breaks it. Do not assume the odd-looking term is wrong without checking.
Is the 11:60 rule always right for clock images? It works for every time shown on a standard clock, with the 12 position treated as 0 when you subtract. Always sanity-check with the minute hand.
Can I solve paper folding without drawing? Yes, with the layer-counting and reverse-unfolding rules. A quick rough square on your sheet helps for harder questions.
How do I stop making silly mistakes in letter series? Write the position numbers beside each letter every time for the first two weeks. After that you will start seeing the numbers automatically.
Should I attempt every question in this family? Attempt the ones you can solve in under 40 seconds first. Leave the long non-verbal ones for the end, particularly if the exam has negative marking.
How many mocks should I take in 45 days? A common planning target is one every alternate day in the final week and sectional tests before that, but adjust to your time and the exam date.
Final word
This family of questions rewards a small toolkit used consistently: the rule ladder, the alphabet positions, the squares and cubes tables, and a few formulas. Practise them in sectional tests on Pareeksha to build speed, then take full-length mocks to see how the reasoning section fits into your overall time. Track every error by rule, not just by question, and the weak spots will show up quickly.
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