SPI Reasoning · Free notes

Classification: SPI Reasoning

Classification has 6 questions in the SPI bank, all from the 2022 paper, and every one asks for the odd number or the odd set of numbers among four options. Three options share a rule and one breaks it. The work is quick once you know your primes, squares and cubes by heart, and the two HARD questions only ask you to look inside each set and test how its numbers are linked.

The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.

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Subtopic notes

Odd One Out
6 questions
Three of the four options share a rule and one breaks it. Find the rule from the options, test it on each, and the one that fails is the answer.

Formula & revision sheet

1 formulas · 1 reference tables · 6 gotchas across all subtopics — the exam-eve cheat-sheet

Odd One Out

Formulas (1)

The rule inside a pair or set · Common links in a set $b = a^2,\; b = a^3,\; b = a^2 \pm 1,\; c = a \times b,\; c = a \div b$

Reference tables (1)

Number facts to test first5 rows

Property	Numbers to know	Quick test
Primes up to 100	2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97	Divide by 2, 3, 5, 7 for numbers under 100 51 = 3 × 17, 57 = 3 × 19 and 91 = 7 × 13 look prime but are not.
Perfect squares	121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 625, 900, 1024	Find the squares on either side
Perfect cubes	1, 8, 27, 64, 125, 216, 343, 512, 729, 1000	Learn them to 10 cubed
Even numbers	Last digit 0, 2, 4, 6 or 8	Look at the last digit
Digit sum	Add the digits: 5742 gives 18	Same digit sum is a common shared rule

Try the quick tests in this order: even or odd, prime, square or cube, digit sum.

Watch out for (6)

Stopping at the first rule you see
→ Find the rule three options share
Testing only some options
→ Find the rule three options share
Calling an odd number prime on sight
→ Number facts to test first
Missing a second rule
→ Number facts to test first
Finding a rule that fits two options only
→ The rule inside a pair or set
Missing a near miss
→ The rule inside a pair or set

Question weightage by concept

3 concepts · 6 questions — where the marks actually sit, so you know what to drill first

Odd One Out6 questions · 100%

Concept	Qs	Share
Number facts to test first	3	50%
The rule inside a pair or set	3	50%
Find the rule three options sharefoundation	—	—

Test yourself on a real paper

Sit a past SPI paper, timed and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Sit an SPI past paper