Number System & Simplification

Number system is the cheapest scoring block in any quantitative paper, because almost every question is answered by a divisibility rule or a remainder trick rather than by long arithmetic. If you are calculating for more than a few seconds here, you have missed the shortcut.

Don't read this page — work through it. Each block asks you to commit to an answer before it tells you anything.

Start here: what do you already know?

Number system — true or false?

6 statements · 10s each

The divisibility rules that pay

Divisor	Test
2	Last digit is even
3	Digit sum divisible by 3
4	Last two digits form a multiple of 4
5	Ends in 0 or 5
6	Passes both the 2 and 3 tests
8	Last three digits form a multiple of 8
9	Digit sum divisible by 9
11	Alternating digit sums differ by 0 or a multiple of 11

Sort the numbers by divisibility

Is each number divisible by 3?

0/6

1007

Which group does it belong to?

Commit to the answer

Compute, then check

1/4

What is the HCF of 12 and 18?

118

Method, in order

How to attack a number-system question

1/5

1. Try a divisibility rule first

Before dividing anything, check the digit sum and last digits. Most questions are designed around one rule.

Match the rule to its divisor

Divisor → Test

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Pick from the left

Quick reference

Carry these into the exam

Exam tip: LCM × HCF = product of the numbers appears in some form almost every year. If a question gives you three of those four values, the fourth is a single division away.

Test yourself

Check your understanding

1 of 6

Which of these numbers is divisible by 4?