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Digits & Number Properties for CAT: Formulas, Weightage & Question Types

Digit-position puzzles, reversed numbers and digit sums of huge numbers.

Digits & Number Properties formula sheet

Everything CAT needs from Digits & Number Properties, in one place. Bookmark it for revision; the lesson in the app explains where each line comes from and when to reach for it.

Everything for this chapter, in one place.

Place value — the one tool

A two-digit number10a+b10a + b
A three-digit number100a+10b+c100a + 10b + c
A four-digit number1000a+100b+10c+d1000a + 100b + 10c + d
The leading digitis never 0
Each digitis an integer from 0 to 9

Reversal

Two digits, reversed minus original9(b−a)9(b-a)
Three digits, reversed minus original99(c−a)99(c-a) — the middle digit never matters
So a reversal differenceis always a multiple of 9, or of 99
A palindromereads the same both ways

Digit sums and divisibility

Divisible by 3 or 9the digit sum is
Divisible by 11the alternating digit sum is
Divisible by 4the last two digits form a multiple of 4
Divisible by 8the last three digits do
Divisible by 2, 5, 10decided by the last digit alone

Big powers, written out

2a×5b2^a \times 5^b with a>ba>b=2a−b×10b= 2^{a-b} \times 10^{b} — a short number followed by bb zeros
10n−k10^n - ka run of 9s followed by the digits of 10m−k10^m - k
So a digit sumcomes from the shape of the number, never from multiplying it out

Counting with digit conditions

All digits distinct, 3-digit9×9×89 \times 9 \times 8
Product of digits is non-zerono digit may be 0
Mean of a symmetric familythe mean of each digit position, recombined

Magic square, 3×33\times3 with 1–9

Every line sums to15
The centreis always 5

The 5 Digits & Number Properties question types CAT repeats

Past CAT papers return to the same few shapes. Learn to recognise them and most questions become a known routine.

  1. 01

    Digit-position equations

  2. 02

    Reversing the digits

  3. 03

    Counting numbers with a digit property

  4. 04

    The digit sum of a huge number

  5. 05

    A magic square

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Digits & Number Properties in CAT: quick answers

How many Digits & Number Properties questions come in CAT Quant?
About 0.5 questions in a 22-question Quant section, worth roughly 1 marks. Digits & Number Properties appeared in 10 of the 24 CAT papers from 2017 to 2025, 12 questions in all, which ranks it 20 of 25 Quant chapters.
Are Digits & Number Properties questions in CAT MCQ or TITA?
58% of the Digits & Number Properties questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Digits & Number Properties questions does CAT ask?
CAT keeps returning to 5 question shapes in Digits & Number Properties: Digit-position equations; Reversing the digits; Counting numbers with a digit property; The digit sum of a huge number; A magic square.

More Number System for CAT