SNAP Number System and Simplification formula sheet, free to download as a 5-page PDF. Number System questions sit inside SNAP's 20-question Quant, DI and DS section, and this sheet takes roughly eight minutes to work through, so it belongs in your final revision.

The sheet covers all five formula groups in real notation, and a concept video walks through the same rules with worked examples.

Built for revision, so every line trades explanation for speed. Read the working behind each formula in the full Number System and Simplification notes before leaning on this sheet.

Number System Formula for SNAP: Divisibility Rules and HCF-LCM

Two rules cover most divisibility questions in SNAP's Quant section:

Formula: Divisible by 3/9 if the digit sum is divisible by 3/9. Divisible by 11 if (sum of digits at odd places) minus (sum at even places) is 0 or a multiple of 11.

2145 has digit sum 12, so it's divisible by 3 but not 9. Checking the 11-rule: (2+4) − (1+5) = 0, so 2145 is also divisible by 11.

HCF and LCM are linked by one relation that saves a full factorisation:

Formula: HCF × LCM = Product of the two numbers

Two numbers with HCF 4 and LCM 48 must multiply to 4 × 48 = 192, useful even when the two numbers themselves aren't given.

Remainder and Cyclicity Formula for SNAP Quantitative Aptitude

Large exponents in a remainder question are never meant to be divided directly − they're meant to be reduced using a cycle:

Formula: To find the remainder of a^n divided by d, reduce a modulo d first, then use the cycle length of that reduced base's powers

The remainder of 7^100 divided by 5: powers of 7 mod 5 cycle as 2, 4, 3, 1 (length 4). Since 100 divided by 4 leaves remainder 0, the answer matches the 4th term in the cycle, which is 1.

The same cycle logic gives the unit digit of a large power directly:

Formula: Unit digits of powers of 2, 3, 7, 8 cycle every 4 terms; powers of 4, 9 cycle every 2; powers of 0, 1, 5, 6 never change

The unit digit of 23^47: the base ends in 3, whose cycle is 3, 9, 7, 1 (length 4). Since 47 divided by 4 leaves remainder 3, the answer is the 3rd term in the cycle, which is 7.

Simplification Formula for SNAP: The BODMAS Order

Every simplification question follows one fixed order, and skipping a step out of turn is the most common way marks are lost here:

Formula: Brackets, then Of, then Division and Multiplication (left to right), then Addition and Subtraction (left to right)

20 − 4 × 3 + 6 ÷ 2 works out to 20 − 12 + 3 = 11. Division and multiplication share one pass in the order they appear, and neither one automatically goes before the other.

Number System Concept Video for SNAP with Solved Examples

Source: Mathological

How to Revise Number System and Simplification Before SNAP

The closing page repeats every formula in one table, each checked against real numbers.

  • Cover the formula column and reproduce it from the quantity name
  • Memorise the divisibility rules through 11 cold, since there's no time to re-derive them in the exam
  • Find the cycle length before touching any large exponent, for both remainders and unit digits
  • Practice BODMAS on strings with mixed operators until the order is automatic

SNAP Number System and Simplification Formula Sheet FAQs

Ques. What is the fastest way to check divisibility by 11?

Ans. Subtract the sum of digits at even places from the sum of digits at odd places. If the result is 0 or a multiple of 11, the number is divisible by 11.

Ques. How do I find the unit digit of a number raised to a large power?

Ans. Find the cycle length of the base's last digit (4 for 2, 3, 7, 8; 2 for 4, 9; 1 for 0, 1, 5, 6), divide the exponent by that cycle length, and match the remainder to the corresponding term in the cycle.

Ques. What is the relation between HCF and LCM?

Ans. HCF multiplied by LCM always equals the product of the two numbers. This lets you find one value if the other three are known.

Ques. In BODMAS, does division always come before multiplication?

Ans. No. Division and multiplication are done in the order they appear, left to right, not division first every time. The same applies to addition and subtraction.

Ques. Can the PDF be downloaded for free?

Ans. Yes. All 5 pages can be read on this page or downloaded at no cost, so it can be printed or kept on a phone for last-minute revision.