Table of Contents
Key Takeaways:
• Remainder GMAT questions test how well you understand division and modular arithmetic.
• Understand the concept of remainders and their importance in GMAT quantitative questions
• Learn key formulas and properties of remainders to solve problems quickly
• Practice with sample problems to reinforce your understanding and improve your speed
Mastering the GMAT's quantitative section requires a solid grasp of fundamental mathematical concepts, including the often-overlooked topic of remainders. While seemingly simple, remainder problems can be deceptively challenging and frequently appear on the GMAT, testing your ability to think critically and solve problems efficiently. This guide will equip you with the essential strategies and techniques to confidently tackle remaining GMAT questions, helping you boost your GMAT score and move closer to your goal of attending a top business school.
What Are Remainder Questions on the GMAT?
Remainder GMAT questions test your ability to handle division problems where the result is not a whole number, focusing on the leftover, or remainder, after division. For example, in a division of 25 by 7, the quotient is 3, and the remainder is 4. These types of problems can appear in both the problem-solving and data sufficiency sections of the GMAT.
Remainder GMAT problems often follow a predictable pattern, known as the remainder cycle. For instance, when dividing by a number like 7, possible remainders are 0 to 6, repeating in a cycle as numbers increase. This cycle helps simplify calculations and identify patterns that lead to the correct answers without going through full division.
Common Tips:
- The Euclidean algorithm helps solve remainder problems by expressing a division equation in the form
x = y × q + r, wherexis the dividend,yis the divisor,qis the quotient, andris the remainder. - Shortcut: For divisors like 10 or 100, the remainder is simply the last digit(s) of the dividend.
Remainder Examples:
| Dividend | Divisor | Quotient | Remainder |
|---|---|---|---|
| 25 | 7 | 3 | 4 |
| 50 | 6 | 8 | 2 |
| 83 | 9 | 9 | 2 |
How to Solve Remainder Problems: Step-by-Step Guide
To solve remainder problems on the GMAT, understanding the basic concepts of division is crucial. A remainder is the number left over after dividing one integer by another when they don't divide evenly. Here's a step-by-step approach to solve such problems:
Step 1: Identify Key Terms
In any remainder problem, three key terms are involved:
- Dividend (x): The number to be divided.
- Divisor (y): The number you are dividing by.
- Quotient (q): The result of the division.
- Remainder (r): What is left after dividing.
The formula to express this is: x = y × q + r where r (remainder) is always less than the divisor y.
Step 2: Apply the Formula
When solving, first use the formula to break down the division. For instance, if the problem states "When x is divided by y, the remainder is r," apply the formula to calculate the quotient (q) and remainder (r). Practice helps to master this equation setup quickly during remainder GMAT problems.
Step 3: Use the Remainder Cycle
Certain divisors create patterns, or remainder cycles. For example, when dividing by 7, the possible remainders are 0 through 6, repeating as numbers increase. Recognizing these cycles can help simplify remainder GMAT questions.
Step 4: Work with Decimals
Sometimes, remainder problems are presented with decimals. In such cases, convert the decimal into a remainder by multiplying the decimal portion by the divisor.
Remainder Cycle: How Numbers Repeat
In remainder problems, the concept of the remainder cycle is crucial for solving questions efficiently. When you divide numbers by a fixed divisor, the possible remainders repeat in a predictable pattern. For example, when dividing numbers by 7, the remainders will always be within the range of 0 to 6, and the pattern repeats as the dividend increases. Recognizing these cycles allows you to quickly identify remainders without doing complex division every time.
This cyclical behavior is particularly useful in remainder GMAT problems, where time is limited, and recognizing patterns can save valuable seconds
Example: For divisor 7:
- 1 ÷ 7 = 0 remainder 1
- 8 ÷ 7 = 1 remainder 1
- 15 ÷ 7 = 2 remainder 1
This pattern continues, cycling through possible remainders from 0 to 6.
Note: To know the latest exam structure & updates, click here: GMAT Question Paper Pattern 2024
Common Types of Remainder Problems in the GMAT Quant Section
Remainder problems are a key focus in the GMAT Quant section, appearing frequently in problem-solving and data sufficiency questions. These problems assess how well you can manage integer division, leaving a remainder. Understanding the types of remainder problems helps in efficiently tackling them during the test. Here's a breakdown of the common types:
1. Basic Remainder Problems
These problems ask for the remainder when one number is divided by another. For instance, when you divide 25 by 7, the quotient is 3, and the remainder is 4. This type is the simplest form of remainder GMAT problems.
2. Remainders and Ratios
This type integrates ratios into remainder questions. You may need to figure out the remainder when one integer is divided by another, often hidden within complex word problems. Recognizing this type helps solve remainder GMAT Quantitative Reasoning Sample questions more easily.
3. Division of Variables
In this scenario, you're often given variables and asked to compute the remainder after division. Algebraic manipulation is essential here, making these problems a bit more complex.
4. Min/Max Remainders
These problems deal with finding the minimum or maximum remainder when numbers are divided by specific divisors. A good grasp of remainder cycles helps in solving these efficiently.
Example Table:
| Type of Problem | Example Problem | Solution Approach |
|---|---|---|
| Basic Remainder Problem | 25 ÷ 7, remainder? | Quotient is 3, remainder is 4 |
| Remainders and Ratios | If \( s/t = 64.12 \), what is the remainder? | Use decimal part to find remainder |
| Division of Variables | If \( n^2 \div 12 \), remainder? | Use algebra to solve for remainder |
| Min/Max Remainders | Smallest positive remainder when \( n \div 5 \)? | Analyze divisors and apply the remainder cycle |
Mastering these common types of remainder GMAT problems will improve your efficiency and accuracy, enhancing your performance on the Quant section.
For more in detailed infirmarion, click here: GMAT Question Patterns: Remainders | GMAT Club
Remainder Theorems and Key Formulas for GMAT Success
Remainders play a crucial role in GMAT quant questions, especially when dealing with integers that don’t divide evenly. Understanding remainder theorems and key formulas can make solving these problems faster and more efficient, helping you boost your score.
Remainder Theorem:
The remainder theorem is based on the concept that if a number x is divided by a divisor d, then the division can be expressed as: x = d × q + r Where:
- x is the dividend
- d is the divisor
- q is the quotient
- r is the remainder
In GMAT Quantitative Algebra Syllabus problems, it’s important to note that the remainder r must always be less than the divisor d. This theorem is foundational when solving remainder GMAT questions involving integer properties.
Key Formulas:
1. Euclidean Division Algorithm: This formula expresses division as x = d × q + r. For example, dividing 25 by 7 gives a quotient of 3 and a remainder of 4, which can be represented as: 25 = 7 × 3 + 4.
2. Remainder Cycles: When dividing by certain numbers, the remainders repeat in a predictable cycle. For example, dividing by 7 gives remainders ranging from 0 to 6, repeating with each successive multiple of 7.
3. Modulo Operation: The modulo operation is a shortcut to find remainders. For example, x mod d gives the remainder when x is divided by d. In remainder GMAT questions, recognizing when to apply this can save time.
Example Table:
| Formula | Description | Example |
|---|---|---|
| Euclidean Division Algorithm | Expresses division with quotient and remainder | 25 = 7 × 3 + 4 |
| Remainder Cycle | Remainders repeat in a cycle when dividing by certain numbers | Dividing by 7 gives remainders 0 to 6 |
| Modulo Operation | Shortcut to calculate remainders | 25 mod 7 = 4 |
Mastering these theorems and formulas will help you efficiently solve remainder GMAT problems and tackle complex questions with confidence. By using shortcuts like the modulo operation and recognizing remainder cycles, you can save time on test day.
Top Tips to Ace Remainder Questions in GMAT Quant
Remainder problems on the GMAT Quant section can be tricky, but with the right approach, you can solve them quickly and accurately. Here are some tips to help you ace remainder questions:
1. Understand the Basics
Ensure you understand the core concept of remainders—how a number is divided, and what is left over. The formula to remember is: x = y × q + r where x is the dividend, y is the divisor, q is the quotient, and r is the remainder. The remainder is always less than the divisor.
2. Look for Patterns
In many remainder GMAT problems, recognizing patterns can help. For instance, if you're dividing by 7, the possible remainders range from 0 to 6, and this cycle repeats. Understanding how these cycles work can save you time.
3. Use Smart Number Plugging
When working with variables, plug in simple numbers to test your equations. This strategy helps you visualize the remainder and find the answer quickly. For instance, in some cases, plugging in values that satisfy the given conditions simplifies complex questions.
4. Know the Common Shortcuts
Some remainder problems allow for shortcuts. For example, dividing a number by 10 means the remainder is simply the last digit. Similarly, dividing by 100 gives the last two digits as the remainder. These small hacks can save valuable time during the test.
Example Table:
| Tip | Explanation | Example |
|---|---|---|
| Recognize Remainder Cycles | Identify repeating cycles in division | Dividing by 7 yields remainders 0-6 |
| Use Number Plugging | Simplify problems by plugging in values | Plugging in x = 14, y = 3 |
| Apply Shortcuts | Use quick tricks like last digit for remainder | 57 ÷ 10 → remainder 7 |
By mastering these tips, you can tackle any remainder GMAT question with confidence, saving time and improving accuracy on the Quant section.
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Conclusion
To excel at remainder GMAT questions, focus on mastering key concepts like division patterns and shortcuts. By applying these strategies and practicing regularly, you can efficiently solve remainder problems, saving valuable time during the test. Incorporating these skills will improve both your confidence and your overall Quant score on the GMAT.
