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Reasoning · Chapter 1

Analogy

Find the relationship in the given pair, then apply exactly the same relationship to the new one. The rule is never "something similar" — it is always identical arithmetic.

Concept video — watch on the AAI ATC Exam Prep channel
2–3questions per shift
35 sectarget time each
5analogy types
4verified PYQs inside
Objectives 1. Letter analogy 2. Number pairs 3. Number triads 4. Rotation analogies 5. Meaning analogies Summary Assessment Free PDF
Before you start

Learning objectives and outcomes

An analogy has exactly one correct relationship. Your job is to state it precisely in words before you look at any option.

Objective 1Extract the shift or mapping between two letter groups and apply it letter by letter.
Objective 2Work through the standard checklist on number pairs — add, multiply, square, square root, digit operations.
Objective 3Handle three-number sets by finding the relation of the first number to each of the other two.
Objective 4Recognise rotation and rearrangement analogies, where letters move rather than change.
Outcome AState the relationship in one sentence before checking any option.
Outcome BReject an option that fits loosely in favour of the one that fits exactly.
Subtopic 1

Letter analogy

Two words are given with their coded partners, and a third word needs its partner. The relationship is almost always a uniform shift applied to every letter. Two examples are given so you can confirm the rule before applying it.

Confirm on both given pairs

The exam gives you two worked pairs for a reason: it wants you to check. Find the shift from the first pair, verify it on the second, then apply it. If the two pairs disagree, you have misread a letter.

P → T  is  +4  ·  A → E  is  +4  ·  S → W  is  +4
A1 B2 C3 D4 E5 F6 G7 H8 I9 J10 K11 L12 M13
N14 O15 P16 Q17 R18 S19 T20 U21 V22 W23 X24 Y25 Z26
Figure 1.1 — Uniform shift applied letter by letter The word PARENTS written above TEVIRXW with a +4 arrow drawn between each pair of letters, and the wrap highlighted where it occurs. Upload image here
✈ AAI ATC relevance — letter analogy appeared in the 2025 Shift 1 paper as a seven-letter uniform shift
Memory trick — "Check letter one, then the last"

Find the shift on the first letter, confirm it on the final letter, and apply. The middle letters almost never differ, and checking them all costs you twenty seconds.

Worked example — 2025 Shift 1 paper

PARENTS is related to TEVIRXW. In the same way ACHIEVE is related to EGLMIZI. To what is PROUDLY related?

  1. P = 16 and T = 20, so the shift is +4. S = 19 and W = 23 confirms it.
  2. Check the second pair: A = 1 to E = 5 is +4, and the final E = 5 to I = 9 is +4. Rule confirmed.
  3. Apply to PROUDLY: P→T, R→V, O→S, U→Y, D→H, L→P.
  4. The final letter Y = 25, and 25 + 4 = 29, which wraps to 29 − 26 = 3 = C.
  5. Answer: TVSYHPC.
EasyATC Pattern
TOWER is related to VQYGT. In the same way RADAR is related to:
T = 20 to V = 22 is +2, and R = 18 to T = 20 confirms it. Applying +2 to RADAR gives R→T, A→C, D→F, A→C, R→T, so the answer is TCFCT.
ModeratePYQ 2025 · Shift 1
PARENTS is related to TEVIRXW based on English alphabetical order. In the same way, ACHIEVE is related to EGLMIZI. To which option is PROUDLY related?
The shift is +4 throughout, confirmed on both given pairs. PROUDLY becomes T, V, S, Y, H, P and then Y wraps past Z to C, giving TVSYHPC. Every wrong option differs by exactly one or two letters, so the last letter must be computed rather than guessed.
HardATC Pattern
FLIGHT is related to UORTSG. In the same way, PILOT is related to:
This is not a shift but the opposite-letter rule, where each letter maps to 27 minus its position. Check it: F = 6 becomes 21 = U, and T = 20 becomes 7 = G. Applying it to PILOT — P = 16 → 11 = K, I = 9 → 18 = R, L = 12 → 15 = O, O = 15 → 12 = L, T = 20 → 7 = G — gives KROLG. Option 1 swaps the third and fourth letters, which is easy to do when L and O map onto each other.
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Subtopic 2

Number pair analogy

Written as 15 : 5 :: 26 : ? The relationship connecting 15 to 5 must connect 26 to the answer in exactly the same way. Run the checklist rather than guessing.

The checklist, in order

1. Add or subtract a constant  ·  2. Multiply or divide
3. Square or square root  ·  4. Square root after adding a constant
5. Digit sum or digit product  ·  6. Number of factors

Test 4 is the one people skip, and it is exactly the one the 2021 paper used. If a plain square root fails, try adding a small number first.

Figure 1.2 — Number pair checklist A flowchart running through add, multiply, square, root-after-adding, digit operations, with a stop marker at the first rule that fits both sides. Upload image here
Memory trick — "If root fails, add ten and root again"

Adding a constant before taking the square root is a favourite AAI construction. It looks impossible until you try it, and then it is instant.

Worked example — 2021 Shift 3 paper

15 : 5 :: 26 : ?

  1. Subtraction: 15 − 5 = 10, so try 26 − 10 = 16. Not an option, so keep going.
  2. Division: 15 ÷ 3 = 5, but 26 ÷ 3 is not a whole number. Rejected.
  3. Square root after adding: 15 + 10 = 25, and √25 = 5. That fits.
  4. Confirm the same operation on 26: 26 + 10 = 36, and √36 = 6.
  5. Answer: 6.
EasyATC Pattern
7 : 49 :: 11 : ?
49 is 7 squared, so the relationship is squaring. 11 squared is 121. Option 3 comes from repeating the digit and option 4 from multiplying by 12.
ModeratePYQ 2021 · Shift 3
Select the option related to the third number in the same way as the second is related to the first: 15 : 5 :: 26 : ?
Add ten and take the square root: 15 + 10 = 25 and √25 = 5, so 26 + 10 = 36 and √36 = 6. Option 4 is the digit sum of 26, which fits the second number but not the first — a classic near-miss.
HardATC Pattern
63 : 8 :: 143 : ?
63 is one less than 64, which is 8 squared, so the rule is add one and take the square root. 143 + 1 = 144, and √144 = 12. Options 1 and 2 are the two factors of 143, planted for anyone who factorises instead.
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Subtopic 3

Number triad analogy

You are given a set of three numbers and asked which option follows the same internal relationship. Anchor on the first number and describe how the other two relate to it.

Anchor on the first number

(18, 6, 36)  →  second is first ÷ 3, third is first × 2

Once stated that way, testing four options takes ten seconds. Describing the set as "6 times 3 is 18 and 18 times 2 is 36" is a chain, and chains are much slower to test.

(18,  6,  36)  →  ÷3  and  ×2  ✓ given set
(30, 15,  60)  →  ÷2  and  ×2
(40, 10,  80)  →  ÷4  and  ×2
(24,  8,  48)  →  ÷3  and  ×2  ✓ match
(25,  5,  50)  →  ÷5  and  ×2
Figure 1.3 — Anchoring on the first number The triad drawn with two arrows leaving the first number, one labelled ÷3 to the second and one labelled ×2 to the third. Upload image here
Memory trick — "Both arrows leave the first number"

Never describe a triad as a chain. Two arrows, both starting at the first number. Every option then reduces to two quick divisions.

EasyATC Pattern
Which set follows the same relationship as (12, 4, 24)?
In the given set the second number is the first divided by 3 and the third is the first doubled. Only (21, 7, 42) matches on both counts: 21 ÷ 3 = 7 and 21 × 2 = 42.
ModeratePYQ 2021 · Shift 3
Select the option in which the numbers are related in the same way as the numbers of the set (18, 6, 36).
The rule is second equals first divided by 3, third equals first doubled. Only (24, 8, 48) satisfies both. Every wrong option gets the doubling right but the division wrong, which is why the second number is the one to test first.
HardATC Pattern
Which set follows the same relationship as (7, 50, 12)?
Here the middle number is the first squared plus one: 7 squared is 49, plus 1 gives 50. The third is the first plus 5, so 7 + 5 = 12. Testing option 4: 9 squared is 81, plus 1 gives 82, and 9 + 5 = 14. Both conditions hold. Option 1 satisfies the squaring rule but not the addition.
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Subtopic 4 · highest yield

Rotation and rearrangement analogies

The 2025 Shift 2 paper introduced a format where the letters do not change at all — they move. Given triads like NAMASTE – AMASTEN – MASTENA, the rule is that the first letter goes to the end each time.

Nothing changes, everything shifts

NAMASTE  →  AMASTEN  →  MASTENA
first letter moves to the back, once per step

Because no letter is altered, you can check an option almost instantly: every term must contain exactly the same letters as the original word. Any option with a scrambled interior is wrong immediately.

Figure 1.4 — Letter rotation step by step The word NAMASTE with a curved arrow lifting the N from the front and placing it at the end, repeated for the second step. Upload image here
Memory trick — "Same letters, new order"

Scan the options for any that reorder the middle of the word. Those are decoys. Only the option where every step is a clean front-to-back move can be correct.

Worked example — 2025 Shift 2 paper

NAMASTE – AMASTEN – MASTENA and ETHICAL – THICALE – HICALET. Which option follows the same logic?

  1. In NAMASTE the leading N moves to the back, giving AMASTEN.
  2. In AMASTEN the leading A moves to the back, giving MASTENA. The rule is confirmed on the second triad too.
  3. Apply to CURTAIN: moving C to the back gives URTAINC.
  4. Moving U to the back of URTAINC gives RTAINCU.
  5. Answer: CURTAIN – URTAINC – RTAINCU. The other three options quietly swap two interior letters, which the rule never does.
EasyATC Pattern
RADAR – ADARR – DARRA. Which follows the same logic?
Each step moves the leading letter to the back with no other change. TOWER becomes OWERT, and OWERT becomes WERTO. Options 2 and 4 swap interior letters, which the rule never does.
ModeratePYQ 2025 · Shift 2
In the following triads each group of letters is related to the next by a certain logic. Select the option that follows the same logic. NAMASTE – AMASTEN – MASTENA; ETHICAL – THICALE – HICALET
The rule is a single front-to-back rotation at each step. Only option 1 performs it cleanly twice. Each of the other three inserts a small interior swap that the original triads never show, which is what makes them look right at a glance.
HardATC Pattern
SIGNAL – LANGIS – ANGISL. Which follows the same logic?
Two rules apply in sequence. First the word is reversed: SIGNAL becomes LANGIS, and RUNWAY becomes YAWNUR. Then the leading letter moves to the back: LANGIS becomes ANGISL, so YAWNUR becomes AWNURY. Option 3 is correct.
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Subtopic 5

Meaning-based analogies

Word analogies test the relationship, not the topic. State the link in a short sentence, then find the option where the identical sentence is true.

Name the relationship out loud

Common relationship types: worker to tool, part to whole, cause to effect, item to category, degree of intensity, and product to raw material. Say the sentence before you read the options.

Pilot : Aircraft  →  "the first operates the second"
Controller : Radar  →  the same sentence is true
Figure 1.5 — Relationship types chart Six labelled boxes — worker to tool, part to whole, cause to effect, item to category, degree, product to material — each with one aviation example. Upload image here
Memory trick — "Write the sentence, then test it"

If your sentence is true for two different options, it is too vague. Make it more specific until only one option survives.

EasyATC Pattern
Pilot : Aircraft :: Driver : ?
The sentence is "the first operates the second". A driver operates a bus. A road is where the operating happens, a licence permits it and a passenger is carried by it — none of those is the same relationship.
ModerateATC Pattern
Wing : Aircraft :: Rudder : ?
The sentence is "the first is a structural part of the second". A rudder is a structural part of a ship. Sailor is a worker, anchor is separate equipment and water is the medium — different relationships each time.
HardATC Pattern
Drizzle : Downpour :: Breeze : ?
The sentence is "the second is a far more intense form of the first". A gale is a far more intense form of a breeze. Air is the substance, cool is a property and weather is the category — this is a degree-of-intensity analogy, not a category one.
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Exam strategy

Six tips that hold in the AAI ATC hall

State the rule in wordsOne sentence, before you read a single option.
Use both given pairsThe exam supplies two examples so you can confirm. Use them.
Root after addingThe rule people skip, and the one AAI used in 2021.
Triads anchor on the firstTwo arrows from the first number. Never a chain.
Rotation means same lettersAny option that reorders the interior is wrong on sight.
Compute the last letterWrong options in letter analogies usually differ only at the end.
Quick revision

Chapter summary sheet

Letter analogyFind the shift on letter one, confirm on the last, then apply.
2025 Shift 1PARENTS → TEVIRXW is +4 throughout; PROUDLY → TVSYHPC with a wrap.
Number pairsAdd, multiply, square, root-after-adding, digits, factors.
2021 Shift 315 : 5 means add 10 and take the root, so 26 gives 6.
TriadsBoth relations start from the first number.
2021 Shift 3(18, 6, 36) is ÷3 and ×2, matching (24, 8, 48).
RotationFront letter moves to the back. No other change is allowed.
2025 Shift 2NAMASTE → AMASTEN → MASTENA, so CURTAIN → URTAINC → RTAINCU.
Meaning analogiesName the relationship precisely enough that one option survives.

↓ Free download — Analogy question PDF

Practice covering all five analogy types, with a printable alphabet-position strip and ruled working space for your letter and number arithmetic. Print it, solve it, keep it.

End of chapter

Comprehensive assessment

Multiple choice and assertion–reason, building in difficulty. Full solutions are in the downloadable PDF above.

A · Multiple choice questions

1. TOWER is related to VQYGT. In the same way RADAR is related to?
2. PARENTS : TEVIRXW :: PROUDLY : ? PYQ 2025 · Shift 1
3. FLIGHT : UORTSG :: PILOT : ?
4. 7 : 49 :: 11 : ?
5. 15 : 5 :: 26 : ? PYQ 2021 · Shift 3
6. 63 : 8 :: 143 : ?
7. Which set matches (12, 4, 24)?
8. Which set matches (18, 6, 36)? PYQ 2021 · Shift 3
9. Which set matches (7, 50, 12)?
10. RADAR – ADARR – DARRA. Which follows the same logic?
11. NAMASTE – AMASTEN – MASTENA. Which follows the same logic? PYQ 2025 · Shift 2
12. SIGNAL – LANGIS – ANGISL. Which follows the same logic?
13. Pilot : Aircraft :: Driver : ?
14. Wing : Aircraft :: Rudder : ?
15. Drizzle : Downpour :: Breeze : ?

B · Assertion and reason

16. Assertion: A letter analogy should be confirmed on both given pairs before it is applied. Reason: The second pair exists so that a misread letter in the first can be caught.
17. Assertion: In a rotation analogy, any option that reorders interior letters can be rejected immediately. Reason: Rotation moves letters without altering their relative order.
18. Assertion: A number triad should be described as a chain from first to second to third. Reason: Chains are faster to test against four options than two separate relations.
19. Assertion: If a plain square root fails on a number pair, adding a constant first is worth testing. Reason: AAI used exactly this construction in the 2021 paper.
20. Assertion: In a meaning analogy, a relationship sentence true for two options is good enough. Reason: Word analogies always have more than one defensible answer.
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Three more marks. Nine reasoning topics left.

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