Using GMAT Divisibility Rules to Answer Quant Questions Faster

GMAT Divisibility Rules to Answer Quant Questions Faster: Divisibility rules play a crucial role in effective GMAT preparation. These rules enhance candidates’ problem-solving efficiency. Additionally, understanding divisibility shortcuts allows candidates to quickly rule out wrong answers and elect the correct one. Therefore, it is recommended to master these rules.

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Understanding GMAT Divisibility Rules to Answer Quant Questions

• Divisible by 0 : No number can be divided by 0.
• Divisible by 2 : If the last digit of a given number is 0, 2, 4, 6, or 8, the number is divisible by 2.
• Divisible by 3 : A number is divisible by 3 if the sum of its digits is divisible by 3. For example, numbers like 342, 999, etc., are divisible by 3 because 3+4+2= 9, 9+9+9=27. Both these numbers are divisible by 3, so the actual number will also be divisible by 3.
• Divisible by 4 : If the last two digits of a number form a number divisible by 4, the entire number is divisible by 4. For example, 5020 ends in 20, which is divisible by 4.
• Divisible by 5 : If the last digit is either 0 or 5, the number is divisible by 5.
• Divisible by 6 : A number divisible by both 2 and 3 is also divisible by 6.
• Divisible by 7 : For divisibility by 7, it's usually best to perform the actual division as the formulas are complex.
• Divisible by 8 : If a number is even and its last three digits are divisible by 8, the number itself will be divisible by 8. For example, 5,160 is divisible by 8 because 160/8 equals 20.
• Divisible by 9 : A number is divisible by 9 if the sum of its digits is divisible by 9. For example, 244575 follows this rule as the sum of its digits is 27, which is divisible by 9.
• Divisible by 10 : If the last digit of a number is 0, it is divisible by 10.
• Divisible by 11 : If the difference between the sum of the digits in odd positions and the sum of the digits in even positions is divisible by 11, the number is divisible by 11 and 0. For example, 9592 is divisible by 11 because (9-5+9-2=11), which is divisible by 11.
• Divisible by 12 : If a number is divisible by both 3 and 4, it is also divisible by 12.

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Prime Number Divisibility in GMAT

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Divisibility Problems With Remainder in GMAT

• Grasp the Problem: Start by identifying the key elements in the question. These include the dividend, the divisor, and the remainder.
• Perform the Division: Carry out the division to find how many times the divisor fits into the dividend and note the remainder. For example, in the equation 88 ÷ 6, 5 fits into 88 three times (14), leaving a remainder of 4.
• Use Modular Arithmetic (if applicable): In some cases, using modular arithmetic can simplify the divisibility process. For instance, writing 88 ≡ 4 (mod 6) means that 88 leaves a remainder of 4 when divided by 6.
• Identify Patterns: Remainder problems involving large numbers depend on recognizing patterns. Identifying these problems can help candidates solve complex problems more easily.

Benefits of Answering Divisibility Problems in GMAT

Simplifying Complex Calculations

Spotting Numerical Patterns

Minimising Calculation Errors

Boosting Efficiency