Placement Aptitude (Quant, Logical, Verbal) Module 11 – Series, analogies and coding
Analogies and odd one out
Name the relationship in word, number and letter analogies, pick the odd one out by the most specific shared property, and put words in logical order.
What you will learn
- Identify the relationship in a word analogy with a bridge sentence, keeping the order of the given pair
- Find the rule of a number or letter analogy that fits every pair given
- Choose the odd one out by the most specific property the other items share
- Order words along a named scale or process, and pick the essential part of a thing
What you’ll learn
What you will learn
- Identify the relationship in a word analogy with a bridge sentence, keeping the order of the given pair
- Find the rule of a number or letter analogy that fits every pair given
- Choose the odd one out by the most specific property the other items share
- Order words along a named scale or process, and pick the essential part of a thing
On this page
An analogy question gives a pair such as DOCTOR : HOSPITAL and asks which word relates to a third word in the same way. The method is to state the relationship in one exact sentence, a bridge sentence: One short, exact sentence that states how the two words of an analogy's given pair are related, in their order, so that it can be tried on every option., “a doctor works in a hospital”, and try that sentence on every option: a teacher works in a school. In an odd one out question, also called classification: The question type also called odd one out: every item but one shares a property, and the item without that property is the answer., all the items but one share a property; find the property, and the item without it is the odd one out. When two properties each leave out a different item, choose the more specific one, the property fewer things have. Number and letter analogies hide a rule instead of a meaning, and the rule must fit every pair given. GATE’s General Aptitude syllabus lists analogy, and AMCAT’s lists analogy and classification.
A bridge sentence names the relationship exactly
A bridge sentence must be exact enough that only one option fits. “A doctor is linked to a hospital” lets every option in, while “a doctor works in a hospital” admits only the place where a teacher works. Keep the order of the given pair: DOCTOR : HOSPITAL runs from worker to workplace, so the answer must too. The diagram adds what to do when two fit, or none:
The bridge-sentence method for analogies
Text description of the diagram
The first box says: say how the given pair is related. The example is DOCTOR : HOSPITAL, and the sentence is "a doctor works in a hospital".
An arrow leads to the second box: try the sentence on every option. The example asks TEACHER : ?, with the options school, student, chalk and book.
Three arrows leave the second box, one for each outcome. If one option fits, that is the answer, here school. If two fit, sharpen the sentence and try again. If none fits, name another relationship.
Eight kinds cover most items:
- Worker and tool. TAILOR : NEEDLE, a tailor works with a needle.
- Worker and workplace. CHEF : KITCHEN, a chef works in a kitchen.
- Part and whole. PETAL : FLOWER, a petal is part of a flower.
- Material and product. MILK : CHEESE, cheese is made from milk.
- Kind and class. COBRA : SNAKE, a cobra is a kind of snake.
- Degree. TIRED : EXHAUSTED, exhausted is very tired.
- Young and adult. FOAL : HORSE, a foal is a young horse.
- Opposites. ANCIENT : MODERN, ancient is the opposite of modern.
Step through PILOT : COCKPIT :: SURGEON : ? and its four options:
The drawing shows the whole scene; its 5 steps are listed below.
Every step as text
- The given pair. The pair runs from a worker to a place, a pilot and the cockpit. The answer must run the same way, from SURGEON to a place, so the order is fixed before any option is read.
- A first sentence. 'A pilot works in a cockpit' names the relationship, worker and workplace, but not how precisely the place is meant.
- Every option. Tried on all four options, the sentence lets two in. A surgeon works in a hospital and in an operating theatre; a scalpel is a tool and a patient a person, so they drop out.
- Sharpen it. The cockpit is not the whole aircraft but the room where the pilot's work is done. 'A surgeon works in the room where the work is done' fits only one option.
- The answer. OPERATING THEATRE. The hospital is the whole building, the match for the whole aircraft, which is too wide.
The sharper sentence left OPERATING THEATRE, the room where a surgeon’s work is done; the hospital is the whole building, too wide.
Checkpoint
Check: Bridge sentences, in the pair's order
A number rule must fit every pair given
Number analogies hide a rule f, written a : f(a), and the rule must fit every pair given. 4 : 63 fits both n³ − 1 and 4n² − 1, so a fair item adds a second pair or offers options that only one rule produces. Step through the item 2 : 7 :: 4 : 63 :: 6 : ?, one rule at a time:
The drawing shows the whole scene; its 5 steps are listed below.
Every step as text
- One pair. Start with 4 : 63. Two simple rules turn 4 into 63, n³ − 1, which gives 64 − 1, and 4n² − 1, which gives 4 × 16 − 1.
- The cube rule. Under n³ − 1, the answer for 6 would be 6³ − 1 = 215.
- The square rule. Under 4n² − 1, the answer for 6 would be 4 × 36 − 1 = 143. One pair, two rules, two different answers.
- The second pair. Test both rules on 2 : 7. n³ − 1 gives 8 − 1 = 7, which fits; 4n² − 1 gives 4 × 4 − 1 = 15, which does not.
- The answer. Only n³ − 1 fits every pair given, so 6 : 215. A rule that fits one pair is only a candidate until every other pair agrees.
The second pair kept n³ − 1 and ruled out the other, so the answer is 6³ − 1 = 215. Letter analogies work on positions, A = 1 to Z = 26: ACE : BDF moves every letter 1 place, so GIK : HJL, and DOG : GRJ moves every letter 3 places, so CAT : FDW. When a shift is not obvious, write the positions under the letters: DOG is 4, 15, 7 and GRJ is 7, 18, 10, three more each.
Checkpoint
Check: Number and letter rules that fit every pair
The odd one out lacks the most specific shared property
Look for the property that every item but one shares. In 2, 3, 5, 9, 11 two properties compete: all but 9 are prime, and all but 2 are odd. Choose the more specific property, the one fewer things have. The program counts how many numbers from 1 to 1,000 have each of nine properties, then lists every property that leaves out exactly one number of three sets:
# Odd one out in a set of numbers: find every property that all the numbers but one share. When two properties pick
# different numbers, prefer the more specific one, the property that fewer numbers have (counted from 1 to 1,000).
from math import isqrt
def is_cube(n):
r = round(n ** (1 / 3))
return any((r + d) ** 3 == n for d in (-1, 0, 1))
PROPERTIES = {"cubes": is_cube, "squares": lambda n: isqrt(n) ** 2 == n, "multiples of 7": lambda n: n % 7 == 0,
"primes": lambda n: n > 1 and all(n % q for q in range(2, isqrt(n) + 1)),
"multiples of 5": lambda n: n % 5 == 0, "multiples of 4": lambda n: n % 4 == 0,
"multiples of 3": lambda n: n % 3 == 0, "even": lambda n: n % 2 == 0, "odd": lambda n: n % 2 == 1}
HOW_MANY = {name: sum(map(has, range(1, 1001))) for name, has in PROPERTIES.items()}
print("Numbers from 1 to 1,000 with each property:")
for name, count in HOW_MANY.items():
print(f" {name}: {count}")
for numbers in ([2, 3, 5, 9, 11], [27, 64, 125, 144, 343], [21, 35, 49, 63, 80]):
print(", ".join(map(str, numbers)))
found = []
for name, has in PROPERTIES.items():
lacking = [n for n in numbers if not has(n)]
if len(lacking) == 1:
found.append((HOW_MANY[name], name, lacking[0]))
print(f" all but {lacking[0]} are {name} ({HOW_MANY[name]} of 1,000)")
count, name, odd = min(found)
print(f" → {odd}, by the most specific property ({name})")Output
Numbers from 1 to 1,000 with each property: cubes: 10 squares: 31 multiples of 7: 142 primes: 168 multiples of 5: 200 multiples of 4: 250 multiples of 3: 333 even: 500 odd: 500 2, 3, 5, 9, 11 all but 9 are primes (168 of 1,000) all but 2 are odd (500 of 1,000) → 9, by the most specific property (primes) 27, 64, 125, 144, 343 all but 144 are cubes (10 of 1,000) → 144, by the most specific property (cubes) 21, 35, 49, 63, 80 all but 80 are multiples of 7 (142 of 1,000) all but 80 are odd (500 of 1,000) → 80, by the most specific property (multiples of 7)
Recorded with Python 3.14.8 on macOS 26 arm64. To run it yourself: mise exec python@3.14.8 -- python3 odd_one_out.py
Runs on this device, in your browser. The first run downloads Python (about 13.5 MB), which is kept for the next runs.
Your run, in this browser
From 1 to 1,000 there are 168 primes but 500 odd numbers, so the odd one out is 9; when two properties disagree, the rarer one decides. Word sets work the same way: in HAMMER, SAW, CHISEL, NAIL, DRILL four are tools, and a nail is what a hammer drives, so NAIL is the odd one out. Prefer a property of meaning to one of spelling, such as first letters, unless no meaning splits the set. In APPLE, MANGO, POTATO, BANANA, GRAPE, APPLE is the only word that starts with a vowel, but POTATO is the only vegetable, and meaning comes first.
Thesaurus (Synonyms & Antonyms) Check what each word of an analogy means, with synonyms and opposites grouped by sense, before you settle on a bridge sentence.Checkpoint
Check: The most specific shared property
Order follows a named scale, and an essential part cannot be left out
Word-order items arrange words along a process or a scale: VILLAGE, TOWN, CITY, STATE, COUNTRY grows in size, and BIRTH, CHILDHOOD, ADULTHOOD, OLD AGE follows a life. Name the scale or the process first; each word then has one place on it. Step through EXAMINATION, ADMISSION, RESULT, LECTURE in the order a student meets them:
The drawing shows the whole scene; its 5 steps are listed below.
Every step as text
- Name the process. Before ordering anything, name the process the words belong to, a course from joining it to finishing it. Without a named process, two orders can both seem to make sense.
- First. Nothing in the course can happen before the student is admitted, so ADMISSION comes first.
- Second. Lectures teach what the course covers, and they come before the course is examined, so LECTURE is second.
- Third. The EXAMINATION tests what the lectures taught, so it follows them.
- Last. A RESULT reports the examination, so it can only come last. The order is ADMISSION, LECTURE, EXAMINATION, RESULT.
Once the process was named, each word had one place in it. An essential-part item asks what a thing cannot exist without: a bicycle needs wheels, but not a bell. Ask whether the thing would still be itself without the option; if it would, that option is not essential. Run that test on every option, not only the first that seems right.
Checkpoint
Check: Logical order and essential parts
Practise: analogies, odd ones out and order
The exercise picks the odd number out, trying the properties from the most specific. Then come untimed questions on all four ideas, the weakest first.
Exercise · Easy · Python
Find the odd number out by the most specific property
PROPERTIES lists nine properties of whole numbers, from the most specific (the one that fewest numbers from 1 to 1,000 have, cubes) to the least specific (even and odd). Write odd_one_out(numbers) for a list of five different positive whole numbers. Go through PROPERTIES in order and stop at the first property that every number but one has. Return a tuple of the number without it and the property's name, for example (9, "prime") for [2, 3, 5, 9, 11]. Return None when no property leaves out exactly one number.
Going in this order is the lesson's rule for competing properties: in [2, 3, 5, 9, 11], "odd" also leaves out one number, 2, but "prime" comes first because fewer numbers are prime.
Starter code · odd.py
from math import isqrt
def is_cube(n):
"""Exact for every whole number up to a million: the rounded cube root, cubed, gives n back only for cubes."""
return round(n ** (1 / 3)) ** 3 == n
# From the most specific property to the least: how many numbers from 1 to 1,000 have each one.
PROPERTIES = [
("cube", is_cube), # 10
("square", lambda n: isqrt(n) ** 2 == n), # 31
("multiple of 7", lambda n: n % 7 == 0), # 142
("prime", lambda n: n > 1 and all(n % q for q in range(2, isqrt(n) + 1))), # 168
("multiple of 5", lambda n: n % 5 == 0), # 200
("multiple of 4", lambda n: n % 4 == 0), # 250
("multiple of 3", lambda n: n % 3 == 0), # 333
("even", lambda n: n % 2 == 0), # 500
("odd", lambda n: n % 2 == 1), # 500
]
def odd_one_out(numbers):
"""(number, property) for the first property that all the numbers but one have, or None."""
# Replace this line with your code.
return NoneThe sample tests · test_odd.py
from odd import odd_one_out
def test_prime_beats_odd():
"""Two properties compete: prime is the more specific"""
assert odd_one_out([2, 3, 5, 9, 11]) == (9, "prime")
def test_cubes():
"""144 is a square but not a cube"""
assert odd_one_out([27, 64, 125, 144, 343]) == (144, "cube")
def test_squares():
"""50 sits between the squares 49 and 64"""
assert odd_one_out([16, 36, 49, 50, 81]) == (50, "square")
def test_multiples_of_7():
"""Every number but 50 is a multiple of 7"""
assert odd_one_out([14, 28, 35, 49, 50]) == (50, "multiple of 7")
def test_multiples_of_5():
"""41 is prime, but so is no other number here"""
assert odd_one_out([10, 20, 35, 41, 55]) == (41, "multiple of 5")
def test_multiples_of_4():
"""22 is even but not a multiple of 4"""
assert odd_one_out([4, 8, 12, 16, 22]) == (22, "multiple of 4")
def test_multiples_of_3():
"""14 is the only number not divisible by 3"""
assert odd_one_out([3, 6, 9, 12, 14]) == (14, "multiple of 3")
def test_even():
"""11 is the only odd number"""
assert odd_one_out([2, 4, 6, 8, 11]) == (11, "even")
def test_odd():
"""10 is the only even number; 1 is neither prime nor composite"""
assert odd_one_out([1, 3, 5, 7, 10]) == (10, "odd")
def test_no_odd_one_out():
"""Every number is a multiple of 3, and no property leaves out exactly one"""
assert odd_one_out([3, 6, 9, 12, 15]) is NoneA hint
For each (name, has) pair in PROPERTIES, build the list of numbers without the property, [n for n in numbers if not has(n)]. If that list has exactly one number, you have the answer; otherwise move on to the next property.
Results of the sample tests
| Test | Result | Details |
|---|
What your code printed
The sample tests run on this device, in your browser (Pyodide): nothing is sent to mysmartcopilot.com. The first run downloads Python (about 13.5 MB), which is kept for the next runs. A check in your browser is feedback for you, not proof that the code is right for every input.
Practice that adapts to you
Practise this lesson
16 questions about 6 ideas of this lesson. Each answer is explained at once, and what you get right is kept in this browser.
Ten word analogies and number rules, worked with every option Pro: opens with a Pro, Premium or Ultimate pass
Analogy items are won by ruling out options for a stated reason, not by a feeling that one word goes best. This part works ten original word analogies option by option, measures how many number rules one pair allows, and works letter and pair formats.
In this part:
- Ten word analogies, each with its bridge sentence and the options it rules out
- How many rules one number pair allows, measured on 167 rules
- Letter analogies and choose-the-pair items, worked
1 runnable example (Python) · about 4 minutes
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Classification and word order in depth, six traps and a timed set Pro: opens with a Pro, Premium or Ultimate pass
Odd-one-out items go wrong when two properties compete or when a property belongs to one item by chance, and order items go wrong when two orders both make sense. This part measures how often properties compete, works the hard cases, reproduces six traps and ends with eight timed items.
In this part:
- Competing properties, measured on 142,506 sets
- Word classification when meanings compete, worked
- Word order and essential parts, worked
- Six traps, each reproduced
- Eight items in ten minutes
- Each answer, with its working
1 runnable example (Python) · about 5 minutes
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Interview questions
-
Fresher · Warm-up
What is a bridge sentence in an analogy question, and why does it help?
A bridge sentence states how the two words of the given pair are related, in one short, exact sentence that uses both of them: for SCALPEL : SURGEON, “a surgeon cuts with a scalpel”. You then put the third word into the same sentence and see which option completes it: “a carpenter cuts with a saw”. It helps in three ways. It makes you name the relationship instead of matching words by feel. It keeps the pair's order, tool then worker, so you do not pick an option that runs the other way. And when two options fit, it shows what to fix: make the sentence more specific until only one does.
-
Fresher to mid
An analogy item reads BOOK : LIBRARY :: PAINTING : ? and offers GALLERY, MUSEUM, ARTIST and FRAME. Two options seem to fit. Which is the intended answer, how do you defend it, and how would you repair the item?
-
Fresher to mid
In the set 2, 7, 11, 13, 15, one candidate picks 2 as the odd one out and another picks 15. Who is right, how do you defend the choice, and how would you change the set so that only one answer fits?
-
Fresher to mid
An item reads 6 : 35 :: 8 : ? and gives no other pair. Three candidates answer 63, 47 and 45, and each shows a rule. Who is right, and what should the item have included?
Key takeaways
- State the pair’s relationship in one exact bridge sentence and try it on every option, keeping the pair’s order.
- A number rule must fit every pair given, because one pair alone can fit several rules with different answers.
- The odd one out lacks the property all the others share, and when two properties compete, the rarer one decides.
- A word-order item follows one named scale or process, and an essential part is one the thing cannot exist without.
Terms in this lesson
- bridge sentence
- One short, exact sentence that states how the two words of an analogy's given pair are related, in their order, so that it can be tried on every option.
- classification
- The question type also called odd one out: every item but one shares a property, and the item without that property is the answer.
References
- GATE General Aptitude syllabus (analytical aptitude: logic, analogy) (Indian Institute of Technology Madras)
- AMCAT syllabus: Logical Ability (analogy and classification pattern recognition, logical word sequence) (AMCAT)
- A000720: the number of primes up to n (The OEIS Foundation)
- odometer (Oxford Learner's Dictionaries, Oxford University Press)
- curator (Oxford Learner's Dictionaries, Oxford University Press)
- prune (Oxford Learner's Dictionaries, Oxford University Press)
- bronze (Oxford Learner's Dictionaries, Oxford University Press)
- emu (Oxford Learner's Dictionaries, Oxford University Press)
- entomology (Oxford Learner's Dictionaries, Oxford University Press)
- gallery (Oxford Learner's Dictionaries, Oxford University Press)
- museum (Oxford Learner's Dictionaries, Oxford University Press)
- math: isqrt (Python Software Foundation)
- itertools: combinations (Python Software Foundation)
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