"2 is to 8 as 3 is to ___?" You sense a rule tugging at you — and once you spot that 8 is 2 cubed, the answer 27 clicks into place. Analytical analogies are pattern puzzles dressed as pairs: numbers, letters, or relationships linked by a hidden rule you must uncover and apply. Unlike verbal analogies (which are about word meanings), these test your feel for numeric and alphabetic patterns. This chapter gives you a systematic way to crack them fast, so you're never left guessing.
An analytical analogy gives you a pair (A : B) with a hidden relationship and asks you to complete a second pair (C : ___) using the same rule. The pairs often involve numbers (squares, cubes, arithmetic operations), letters (alphabet-position shifts), or word relationships (function, category). Naming the exact rule — and confirming it against the whole first pair — is the key move.
On the Civil Service Exam, analytical analogies sit in Analytical Reasoning, distinct from the vocabulary-based Analogies in the Verbal section. (Same "A : B :: C : D" format, different content: here the link is a pattern, not a meaning.) They reward systematic testing over guessing.
The difficulty is intermediate. The reliable method is to convert letters to numbers when needed, test candidate rules against the full first pair, watch for two-step rules, and respect the direction. This lesson builds each habit.
After completing this lesson you will be able to:
You should be comfortable with:
A quick refresher on the tool you'll use most: the letter-to-number code. A=1, B=2, C=3, … Z=26. Converting letters to their positions turns a mysterious letter analogy into a plain number pattern you can solve. For example, B : D becomes 2 : 4 (a shift of +2). Learn to count alphabet positions quickly — many analytical analogies unlock instantly once you do.
Pattern recognition is a core reasoning skill:
The exam tests these because relational and pattern thinking underlie logic itself.
Let's build the systematic approach for each analogy type.
Find the operation that turns the first number into the second, then apply it to the third.
4 : 16 :: 5 : ___ → 16 is 4 squared, so 5² = 25.
Test the obvious operations in order: does B = A + k? A × k? A²? A³? Often several rules seem to fit the first pair (16 could be 4×4, 4+12, or 4²), so check which one also gives an answer among the choices — or which fits a consistent pattern.
Analogy: A numeric analogy is a little machine: you feed in A and it outputs B. Your job is to figure out what the machine does (square it? add 4?), then feed in C and read the output. Test a few "machines" until one reliably turns A into B.
Turn letters into alphabet positions to expose a numeric pattern:
B : D :: F : ___ → B=2, D=4 (a shift of +2); F=6, so +2 = 8 = H.
Once in numbers, the analogy is just arithmetic. Convert back to a letter at the end.
When a shift pushes past Z (26), wrap around to A (1) — think of the alphabet as a circle. A shift of +3 from Y (25) gives 28, which wraps to 28 − 26 = 2 = B.
X : A :: Y : ___ → X=24, A=1: that's +3 with wraparound (24 + 3 = 27 → 27 − 26 = 1 = A). Apply +3 to Y=25: 28 → wrap to 2 = B.
Forgetting to wrap around is the most common letter-analogy error.
Some analogies need two operations, not one.
3 : 10 :: 5 : ___ → try "double and add 4": 3×2 + 4 = 10 ✓. Apply to 5: 5×2 + 4 = 14.
When a single operation doesn't fit, test a combination (×k then ±c, or square then add). Verify against the full first pair before trusting it.
Some analytical analogies use word relationships like the verbal ones:
DOCTOR : HOSPITAL :: TEACHER : ___ → "a doctor works in a hospital," so "a teacher works in a ___" = SCHOOL.
The method is the same as verbal analogies: name the relationship in a sentence and match it. (See the Verbal Analogies lesson for the full technique.)
The relationship must run the same way in both pairs. If A : B is "A doubled is B," then C : D must be "C doubled is D," not "C halved." For letters, +2 in the first pair means +2 in the second, not −2. Always confirm the direction.
The safest habit: once you spot a candidate rule, confirm it fully explains the first pair, then apply it to the third element and check the result is among the answer choices. If your rule produces a number/letter that isn't offered, step back and try another rule rather than forcing it.
With the method set, let's picture, tabulate, and drill.
Analytical analogies use pattern rules:
| Type | Rule to test |
|---|---|
| Add/subtract | B = A ± k |
| Multiply/divide | B = A × k or A ÷ k |
| Square/cube | B = A² or A³ |
| Letter shift | position(B) = position(A) ± k |
| Wraparound | subtract 26 if position > 26 (add 26 if < 1) |
| Two-step | B = A × k ± c (or square then ±) |
| Word relationship | name the relationship in a sentence |
Letter code: A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, I=9, J=10, K=11, L=12, M=13, N=14, O=15, P=16, Q=17, R=18, S=19, T=20, U=21, V=22, W=23, X=24, Y=25, Z=26.
| When the pair is… | Try… |
|---|---|
| numbers, B bigger by a fixed amount | add/subtract |
| numbers, B a multiple of A | multiply/divide |
| numbers like 4:16, 3:27 | square/cube |
| letters | convert to positions, find the shift |
| a letter shift near Z | wraparound |
| a single operation doesn't fit | a two-step rule |
| words (DOCTOR : HOSPITAL) | word relationship (function/category) |
Step 1 — Identify the type: numbers, letters, or words. ↓ Step 2 — For letters, convert to positions. For numbers, look at how A relates to B. ↓ Step 3 — Test candidate rules (±k, ×k, square, cube, two-step) against the whole first pair. ↓ Step 4 — Apply the confirmed rule to the third element (mind direction and wraparound). ↓ Step 5 — Check the answer is among the choices; if not, step back and try a different rule.
Why Step 3 matters most: several rules can fit the first pair superficially. Testing fully — and against the answer choices — prevents forcing a rule that doesn't actually match.
Example 1 (add). 7 : 12 :: 10 : ___. Solution: +5 → 10 + 5 = 15. Difficulty: ★☆☆☆☆
Example 2 (letter shift). A : C :: D : ___. Thinking: A=1, C=3 → +2. D=4 → 6 = F. Solution: F. Difficulty: ★☆☆☆☆
Example 3 (square). 3 : 9 :: 6 : ___. Solution: 3² = 9, so 6² = 36. Difficulty: ★★☆☆☆
Example 4 (multiply). 5 : 20 :: 7 : ___. Solution: ×4 → 7 × 4 = 28. Difficulty: ★★☆☆☆
Example 5 (letter shift +3). M : P :: R : ___. Thinking: M=13, P=16 → +3. R=18 → 21 = U. Solution: U. Difficulty: ★★☆☆☆
Example 6 (cube). 2 : 8 :: 3 : ___. Solution: 2³ = 8, so 3³ = 27. Difficulty: ★★★☆☆
Example 7 (two-step). 4 : 13 :: 6 : ___. Thinking: Try ×3 + 1: 4×3 + 1 = 13 ✓. Apply: 6×3 + 1 = 19. Difficulty: ★★★☆☆
Example 8 (wraparound). Y : B :: Z : ___. Thinking: Y=25, B=2 → +3 with wraparound (25 + 3 = 28 → 2). Z=26 → 26 + 3 = 29 → 29 − 26 = 3 = C. Solution: C. Difficulty: ★★★★☆
Example 9 (square minus). 5 : 24 :: 7 : ___. Thinking: Try A² − 1: 5² − 1 = 24 ✓. Apply: 7² − 1 = 48. Solution: 48. Difficulty: ★★★★☆
Example 10 (letter, larger shift). C : H :: F : ___. Thinking: C=3, H=8 → +5. F=6 → 11 = K. Solution: K. Difficulty: ★★★☆☆
Example 11 (word relationship). PEN : WRITE :: KNIFE : ___. Thinking: "A pen is used to write" → "A knife is used to ___." Solution: CUT. Difficulty: ★★★☆☆
Example 12 (two-step, tricky). 3 : 10 :: 7 : ___. Thinking: Try A² + 1: 3² + 1 = 10 ✓. Apply: 7² + 1 = 50. (Check an alternative: ×2 + 4 gives 3→10 ✓ but 7→18; since the exam offers one answer, the rule matching the choices decides — here A²+1 → 50, the cleaner pattern.) Solution: 50 (if A² + 1 is intended). Lesson: when two rules fit the first pair, the answer choices disambiguate — pick the rule whose result is offered. Difficulty: ★★★★★
Complete the second pair.
Analytical analogies are pattern puzzles: find the hidden rule linking A to B, then apply it to C. For numbers, test add/subtract, multiply/divide, squares, cubes, and two-step rules (×k ± c), confirming against the whole first pair. For letters, convert to alphabet positions (A=1 … Z=26), find the shift, and wrap around past Z. For word pairs, name the relationship as in verbal analogies. Always respect the direction, and let the answer choices disambiguate when multiple rules fit the first pair — never force a rule that yields an unavailable answer. Classify, test fully, convert letters, and mind wraparound — and these become fast, satisfying points.
| Item | Key point |
|---|---|
| Numbers | test ±k, ×k, A², A³, two-step |
| Letters | convert A=1 … Z=26 |
| Wraparound | >26 → −26; <1 → +26 |
| Two-step | ×k ± c |
| Words | name the relationship |
| Direction | same way in both pairs |
| Disambiguate | use the answer choices |
How is this different from the Verbal Analogies topic? Verbal analogies test word meanings (function, category, degree). Analytical analogies test patterns — numbers, letters, and operations — though some use word relationships too. The format is the same; the content differs.
How do I solve letter analogies? Convert each letter to its alphabet position (A=1 … Z=26), find the numeric shift between the first pair, apply it to the third letter, and convert back — remembering to wrap around if you pass Z.
What if one operation doesn't fit? Try a two-step rule like "multiply then add" (×k ± c) or "square then add." Many analogies need two operations, so don't stop after testing single ones.
Several rules seem to fit the first pair — which do I use? Apply each candidate to the third element and see which result appears among the answer choices. The choices disambiguate competing rules.
What's wraparound? When a letter shift goes past Z (position 26), it continues from A. Treat the alphabet as a circle: position 27 = A, 28 = B, and so on (subtract 26).
Tick them all and analytical analogies become quick, reliable points — and your pattern-spotting sharpens for number series and coding too.
Put it to the test with 2,990 practice questions on this topic.