Analogy: Word, Number and Letter Relationships

1. Meaning of analogy#

An analogy compares relationships, not merely things that belong to the same topic. In A : B :: C : D, read “A is related to B in the same way that C is related to D”. First describe A → B in a short sentence, then apply that sentence to C. The direction must stay the same.

Example: Bird : Nest :: Bee : Hive. The relation is animal → typical shelter. “Honey” is connected to bees, but it describes a product, so it does not preserve the relation. Being associated with the third word is not enough.

This chapter covers verbal, numerical and letter analogies, matching pairs, combined operations and the basic method for figure analogies. The online bank has 20 verbal, 20 number, 20 letter and 20 advanced mixed questions. Many foundation questions state the relation explicitly so that you can learn the method before solving inference questions.

2. A reliable five-step method#

1. Read the first pair carefully, including its order.
2. Name a precise relationship: part → whole, unit → quantity, x → x², or a letter shift.
3. Check the relationship against the complete first pair.
4. Apply it to the third item without changing its direction or operation order.
5. Compare the predicted answer with all options and reject relation mismatches.

For Wheel : Bicycle :: Key : ?, the relation is component → whole. A keyboard is a whole containing keys. “Lock” is associated with a key but expresses tool → object operated, a different relationship. Context determines which sense of a word is intended; the options and first pair must support the same sense.

3. Verbal relations: identify the exact category#

Relation	Example	Direction check
Member → class	Rose → Flower	A rose is a kind of flower
Part → whole	Page → Book	A page is part of a book
Material → product	Clay → Pot	Clay is used to make a pot
Creator → work	Poet → Poem	A poet creates a poem
Tool → function	Knife → Cut	Cutting is a typical function
Worker → tool	Tailor → Scissors	A tailor uses scissors
Instrument → quantity	Thermometer → Temperature	The instrument measures the quantity
Unit → quantity	Metre → Length	The unit expresses the quantity
Organ → sense	Eye → Sight	The organ supports the sense
Young → adult kind	Lamb → Sheep	A lamb is a young sheep
Synonym	Rapid → Swift	Similar meaning in this context
Antonym	Expand → Contract	Opposite meaning in this context

Do not collapse all these into “related words”. A ruler is an instrument for length; a metre is a unit of length. They relate to length differently. Likewise, potter → pot and clay → pot have the same second word but different relations.

4. Verbal traps, context and precision#

Direction: Page : Book does not match Library : Books. The first is part → whole; the second points from a place to its contents. If an option is Book : Page, its direction is reversed.

Level of specificity: Rose : Flower is member → class. Rose : Garden is plant → place; both are plausible associations but only one matches a class relationship. Prefer the relation stated or demonstrated by the question.

Word sense: “Act” can mean an action or a division of a play. Chapter : Book :: Act : Play uses the literary division sense. Translate meanings, not isolated words. “Contract” is a verb meaning become smaller in Expand : Contract; it is not a legal document here.

Typical versus universal: A bird–nest analogy uses a conventional shelter relation, not a claim that all birds always live in nests. Do not introduce an exception that changes the question’s intended relation; equally, do not turn a conventional association into a universal scientific rule.

5. Number analogies: start with simple operations#

Check addition/subtraction, multiplication/division, squares/cubes, roots and then combined operations. Try the same transformation on every supplied example. Do not choose a rule because it happens to fit only one convenient number.

Examples:

• Square: 4 : 16 :: 7 : 49, because y = x².
• Square plus one: 5 : 26 :: 8 : 65, because y = x² + 1.
• Product with the next integer: 5 : 30 :: 9 : 90, because y = x(x + 1).
• Positive square root: 49 : 7 :: 121 : 11. The word positive distinguishes the requested root from the two solutions of x² = 121.
• Triple then subtract two: 6 : 16 :: 11 : 31, because y = 3x − 2.

Maintain operation order. For x = 5, x² + 1 = 26 while (x + 1)² = 36. Multiplying before adding is different from adding before multiplying.

6. Digit-based analogies#

A rule can act on the whole number or on its individual digits. Decide which one the question establishes. For a two-digit number with tens digit t and units digit u, the number is 10t + u.

Digit rule	Example	Worked target
Sum	35 → 8	68 → 6 + 8 = 14
Product	46 → 24	79 → 7 × 9 = 63
Reverse	27 → 72	46 → 64
Sum of squares	34 → 25	57 → 25 + 49 = 74
Absolute difference	82 → 6	93 → 6

For three-digit 456, “hundreds × units + tens” gives 4 × 6 + 5 = 29. It does not mean 456 × something. If a reversal produces a leading zero, distinguish a digit string such as 03 from the numerical value 3; follow the question’s format.

7. Can one pair determine a unique rule?#

Not always. The pair 2 : 4 fits both doubling and squaring. For input 3 these give 6 and 9. A single pair cannot mathematically prove that one of infinitely many possible functions is intended. Exam questions usually expect a simple conventional relation, with examples, wording and options helping to select it.

In this chapter, explicit-rule foundation questions remove that ambiguity. Advanced inference questions restrict the rule family when needed. If two equally simple relations satisfy all given information but lead to different offered answers, identify the ambiguity instead of pretending the answer is certain.

Worked inference: y = a×x² + b, with fixed integers a and b. Given 2 → 11 and 3 → 21, subtraction gives 10 = a(9 − 4), so a = 2. Then 11 = 2×4 + b gives b = 3. For x = 7, y = 2×49 + 3 = 101. The specified family makes the two examples sufficient.

8. English-letter positions and cyclic shifts#

Use A = 1, B = 2, …, Z = 26. A forward shift adds positions; a backward shift subtracts them. Wrap from Z to A only when a cyclic alphabet is specified or clearly established. In our shift questions the cyclic convention is explicit.

Examples: ACE → BDF shifts every letter forward by 1. DOG under the same rule becomes EPH. For a backward shift by 2, CAT becomes AYR: C → A, A → Y and T → R. Check each character; do not read the group as a word and guess a related word.

For a position p shifted by k, the cyclic result is ((p − 1 + k) mod 26) + 1, where mod returns a value from 0 to 25. On paper, boundary letters can be handled by adding or subtracting 26 once for small shifts.

9. Opposite letters and reversal are different#

Alphabet-opposite pairs are A–Z, B–Y, C–X, D–W and so on. Their positions sum to 27, so the opposite of position p is 27 − p. DOG becomes WLT: D → W, O → L, G → T.

Reversing a group changes its order, not the letters: DOG becomes GOD. Replacing each letter by its opposite changes identities while preserving order. A question may combine both, but do not substitute one operation for the other.

Useful anchors: A–Z, E–V, I–R, M–N. There is no single self-opposite letter in the 26-letter English alphabet because the midpoint is between M and N. These are alphabet-position opposites, not mirror images of letter shapes.

10. Multi-step letter analogies#

Write intermediate results. “Reverse, then shift forward by 1” turns DOG → GOD → HPE. Reversing after a uniform shift gives the same result in this particular case, but that coincidence does not hold for position-dependent shifts.

Example: reverse DOG, then shift the new first, second and third letters by +1, −2 and +3. First DOG → GOD. Next G → H, O → M and D → G, yielding HMG. If you shift the original positions first and then reverse, you get a different answer. Always attach positional instructions to the stage specified.

For mixed groups such as A3C, state whether the digit changes, whether only letters are shifted and whether positions are counted separately. Do not silently apply alphabet arithmetic to numbers or vice versa.

11. Pair selection, sets and figure analogies#

Some questions ask for a matching pair rather than a missing fourth term. For Kilogram : Mass, Second : Time preserves unit → quantity. Ruler : Length is instrument → quantity, and Mass : Kilogram reverses direction. Test both words in every option.

For number sets such as (3, 9, 27), a proposed relationship must involve the relevant positions consistently. If the rule is “second is the square and third is the cube of the first”, (4, 16, 64) fits. Do not judge only the first two entries and ignore the third.

For figure analogies, compare A to B using one feature at a time: rotation angle/direction, reflection axis, position, number of elements, shading and size. Apply the same transformation to C. Rotation is not reflection: an arrow pointing up rotated 90° clockwise points right; reflected across a vertical line, it still points up. Use asymmetric figures to distinguish transformations that symmetric shapes can conceal.

12. Worked elimination of close options#

Question: Page : Book :: Brick : ? Options: Clay, Wall, Kiln, Builder. Name the first relation: a page is a component of a book. A brick is a component of a wall, so Wall fits. Clay is a material used to make the brick; kiln is a place used in production; builder is a user of bricks. Each distractor is associated with bricks, but each expresses a different relationship.

Question: 5 : 26 :: 8 : ?, explicitly using x² + 1. Options: 63, 64, 65, 81. Squaring gives 64; adding one gives 65. Choosing 64 stops one operation too early. Choosing 81 incorrectly squares x + 1. Read the complete rule rather than a familiar part of it.

13. Revision and exam practice#

• Preserve the arrow: A → B and C → answer must have the same direction.
• Prefer a precise sentence over “these are connected”.
• Distinguish member/class, part/whole, material/product and worker/tool.
• Separate whole-number operations from digit operations.
• Distinguish x² + 1 from (x + 1)².
• Use A = 1 to Z = 26; opposite positions add to 27.
• Reverse order and opposite-letter substitution are different operations.
• In several-step questions, keep intermediate results.
• Check every supplied example and every relevant feature.
• If the rule is genuinely underdetermined, do not claim certainty.

Practise in three rounds: identify the relation without options, calculate the answer, then explain why one tempting distractor is wrong. Record errors by type—relation, direction, arithmetic, letter boundary or operation order—so revision targets the actual mistake.

Practice set: 30 questions#

Practice 01#

Complete the analogy using the relation animal → typical shelter: Bird : Nest :: Bee : ?

• A. Hive
• B. Web
• C. Den
• D. Stable

Practice 02#

Complete the analogy using the relation tool → primary action: Pen : Write :: Knife : ?

• A. Read
• B. Hear
• C. Cut
• D. Measure

Practice 03#

Complete the analogy using the relation component → whole made from components: Page : Book :: Brick : ?

• A. Wall
• B. Paper
• C. Clay
• D. Kiln

Practice 04#

Complete the analogy using the relation instrument → measured quantity: Thermometer : Temperature :: Barometer : ?

• A. Distance
• B. Electric current
• C. Atmospheric pressure
• D. Time

Practice 05#

Complete the analogy using the relation word → close synonym: Rapid : Swift :: Silent : ?

• A. Quiet
• B. Noisy
• C. Distant
• D. Heavy

Practice 06#

Complete the analogy using the relation word → opposite meaning: Increase : Decrease :: Expand : ?

• A. Enlarge
• B. Contract
• C. Continue
• D. Repeat

Practice 07#

Complete the analogy using the relation member → broader class: Rose : Flower :: Sparrow : ?

• A. Bird
• B. Nest
• C. Wing
• D. Tree

Practice 08#

Complete the analogy using the relation polygon → number of sides: Triangle : Three sides :: Pentagon : ?

• A. Four sides
• B. Five sides
• C. Six sides
• D. Eight sides

Practice 09#

Use the rule "square" on each input: 4 : 16 :: 7 : ?

• A. 49
• B. 48
• C. 50
• D. 52

Practice 10#

Use the rule "square plus 1" on each input: 5 : 26 :: 8 : ?

• A. 64
• B. 66
• C. 65
• D. 68

Practice 11#

Use the rule "product of x and x + 1" on each input: 5 : 30 :: 9 : ?

• A. 89
• B. 91
• C. 90
• D. 93

Practice 12#

Use the rule "divide by 4" on each input: 20 : 5 :: 36 : ?

• A. 8
• B. 10
• C. 9
• D. 12

Practice 13#

Use the rule "sum of the two digits" on each input: 35 : 8 :: 68 : ?

• A. 14
• B. 13
• C. 15
• D. 17

Practice 14#

Use the rule "sum of the squares of the two digits" on each input: 34 : 25 :: 57 : ?

• A. 73
• B. 75
• C. 77
• D. 74

Practice 15#

Use the rule "square of x + 1" on each input: 5 : 36 :: 8 : ?

• A. 80
• B. 82
• C. 81
• D. 84

Practice 16#

Use the cyclic English alphabet (after Z comes A): shift each letter forward by 1. ACE : BDF :: BDF : ?

• A. CEG
• B. DFH
• C. BDF
• D. EGI

Practice 17#

Use the cyclic English alphabet (after Z comes A): shift each letter forward by 5. BDF : GIK :: GIK : ?

• A. LNP
• B. MOQ
• C. KMO
• D. NPR

Practice 18#

Use the cyclic English alphabet (after Z comes A): shift each letter backward by 4. ABC : WXY :: BCD : ?

• A. XYZ
• B. YZA
• C. WXY
• D. ZAB

Practice 19#

Use the cyclic English alphabet (after Z comes A): replace each letter by its opposite (A ↔ Z, B ↔ Y). ABC : ZYX :: DOG : ?

• A. XMU
• B. VKS
• C. WLT
• D. YNV

Practice 20#

Use the cyclic English alphabet (after Z comes A): reverse the order, then shift each letter forward by 1. ABC : DCB :: DOG : ?

• A. IQF
• B. GOD
• C. JRG
• D. HPE

Practice 21#

Use the cyclic English alphabet (after Z comes A): reverse the order, then shift each letter forward by 1. ACE : FDB :: RST : ?

• A. VUT
• B. TSR
• C. WVU
• D. UTS

Practice 22#

The same rule y = a×x² + b applies, with fixed integer a and b. Given 2 : 11 and 3 : 21, complete 7 : ?

• A. 101
• B. 100
• C. 102
• D. 104

Practice 23#

The same rule y = a×x² + b applies, with fixed integer a and b. Given 2 : 18 and 3 : 38, complete 5 : ?

• A. 101
• B. 103
• C. 102
• D. 105

Practice 24#

The same rule y = a×x² + b applies, with fixed integer a and b. Given 2 : 21 and 3 : 46, complete 4 : ?

• A. 81
• B. 80
• C. 82
• D. 84

Practice 25#

First reverse the three-letter group. Then shift its new first, second and third letters by 1, -2, 3 positions respectively; positive means forward and negative backward, wrapping A–Z. ACE : FAD :: DOG : ?

• A. INH
• B. HMG
• C. GLF
• D. JOI

Practice 26#

First reverse the three-letter group. Then shift its new first, second and third letters by 4, -5, 6 positions respectively; positive means forward and negative backward, wrapping A–Z. BDF : JYH :: RAT : ?

• A. XVX
• B. YWY
• C. WUW
• D. ZXZ

Practice 27#

For each three-digit input, multiply the hundreds digit by the units digit, then add the tens digit. 234 : 11 :: 456 : ?

• A. 28
• B. 30
• C. 29
• D. 32

Practice 28#

For each three-digit input, multiply the hundreds digit by the units digit, then add the tens digit. 527 : 37 :: 839 : ?

• A. 74
• B. 75
• C. 76
• D. 78

Practice 29#

Choose the pair with the same directional relationship as Carpenter : Furniture.

• A. Poet : Poem
• B. Poem : Poet
• C. Pen : Poet
• D. Page : Book

Practice 30#

Choose the pair with the same directional relationship as Oak : Tree.

• A. Tree : Oak
• B. Fish : Water
• C. Fin : Fish
• D. Shark : Fish

Answers and explanations#

Answer 01#

A. Hive

Bird relates to Nest as animal → typical shelter. In the same direction, Bee relates to Hive. The relation must match, not just the topic.

Answer 02#

C. Cut

Pen relates to Write as tool → primary action. In the same direction, Knife relates to Cut. The relation must match, not just the topic.

Answer 03#

A. Wall

Page relates to Book as component → whole made from components. In the same direction, Brick relates to Wall. The relation must match, not just the topic.

Answer 04#

C. Atmospheric pressure

Thermometer relates to Temperature as instrument → measured quantity. In the same direction, Barometer relates to Atmospheric pressure. The relation must match, not just the topic.

Answer 05#

A. Quiet

Rapid relates to Swift as word → close synonym. In the same direction, Silent relates to Quiet. The relation must match, not just the topic.

Answer 06#

B. Contract

Increase relates to Decrease as word → opposite meaning. In the same direction, Expand relates to Contract. The relation must match, not just the topic.

Answer 07#

A. Bird

Rose relates to Flower as member → broader class. In the same direction, Sparrow relates to Bird. The relation must match, not just the topic.

Answer 08#

B. Five sides

Triangle relates to Three sides as polygon → number of sides. In the same direction, Pentagon relates to Five sides. The relation must match, not just the topic.

Answer 09#

A. 49

Rule: x². It gives 4 → 16 and 7 → 49. Apply the operation to the input before comparing options.

Answer 10#

C. 65

Rule: x² + 1. It gives 5 → 26 and 8 → 65. Apply the operation to the input before comparing options.

Answer 11#

C. 90

Rule: x(x + 1). It gives 5 → 30 and 9 → 90. Apply the operation to the input before comparing options.

Answer 12#

C. 9

Rule: x ÷ 4. It gives 20 → 5 and 36 → 9. Apply the operation to the input before comparing options.

Answer 13#

A. 14

Rule: tens + units. It gives 35 → 8 and 68 → 14. Apply the operation to the input before comparing options.

Answer 14#

D. 74

Rule: tens² + units². It gives 34 → 25 and 57 → 74. Apply the operation to the input before comparing options.

Answer 15#

C. 81

Rule: (x + 1)². It gives 5 → 36 and 8 → 81. Apply the operation to the input before comparing options.

Answer 16#

A. CEG

ACE → BDF follows the stated transformation. Apply the same operation to BDF: BDF → CEG. Preserve the stated operation order.

Answer 17#

A. LNP

BDF → GIK follows the stated transformation. Apply the same operation to GIK: GIK → LNP. Preserve the stated operation order.

Answer 18#

A. XYZ

ABC → WXY follows the stated transformation. Apply the same operation to BCD: BCD → XYZ. Preserve the stated operation order.

Answer 19#

C. WLT

ABC → ZYX follows the stated transformation. Apply the same operation to DOG: DOG → WLT. Preserve the stated operation order.

Answer 20#

D. HPE

ABC → DCB follows the stated transformation. Apply the same operation to DOG: DOG → HPE. Preserve the stated operation order.

Answer 21#

D. UTS

ACE → FDB follows the stated transformation. Apply the same operation to RST: RST → UTS. Preserve the stated operation order.

Answer 22#

A. 101

The output difference is 10 = a(9 − 4), so a = 2. Then b = 11 − 4×2 = 3. For x = 7, y = 2×49 + (3) = 101.

Answer 23#

C. 102

The output difference is 20 = a(9 − 4), so a = 4. Then b = 18 − 4×4 = 2. For x = 5, y = 4×25 + (2) = 102.

Answer 24#

A. 81

The output difference is 25 = a(9 − 4), so a = 5. Then b = 21 − 4×5 = 1. For x = 4, y = 5×16 + (1) = 81.

Answer 25#

B. HMG

Reverse DOG to GOD. The shifts give G → H, O → M, D → G, hence HMG.

Answer 26#

A. XVX

Reverse RAT to TAR. The shifts give T → X, A → V, R → X, hence XVX.

Answer 27#

C. 29

456: 4 × 6 + 5 = 29. The operation uses individual digits, not the whole number.

Answer 28#

B. 75

839: 8 × 9 + 3 = 75. The operation uses individual digits, not the whole number.

Answer 29#

A. Poet : Poem

Carpenter : Furniture expresses creator → product. Poet : Poem has the same relation and direction; related vocabulary alone is insufficient.

Answer 30#

D. Shark : Fish

Oak : Tree expresses member → class. Shark : Fish has the same relation and direction; related vocabulary alone is insufficient.

Online exams#

Four tests contain 20 questions each: verbal, number, letter and advanced mixed analogies. The complete test contains all 80 questions. State the relation before answering and check direction and operation order.

This is AI-generated information.