GMAT® Word List

Adaptive Testing Format

The GMAT employs an adaptive testing model for the Data Insights, Verbal Reasoning, and Quantitative Reasoning sections where each question’s difficulty is dynamically adjusted based on the candidate’s previous responses. A correct answer leads to a more challenging question while an incorrect answer results in an easier one, thereby quickly homing in on the candidate’s true ability level.

Key Benefits

• Precision: The tailored adjustment of question difficulty rapidly zeroes in on the candidate’s skill level, ensuring a precise measurement of ability.
• Efficiency: By matching each question to the candidate’s performance, the test requires fewer questions to reliably assess capability, reducing overall testing time without compromising accuracy.
• Personalization: The adaptive format creates a unique testing trajectory for each candidate, offering a more individualized and relevant evaluation experience.
• Enhanced Validity: Continuous adjustment of difficulty minimizes the effects of random guessing, leading to a more valid assessment of one’s quantitative, verbal, and data reasoning skills.

This approach ensures that the GMAT is both a rigorous and efficient tool for accurately gauging a candidate’s abilities across all sections.

Aggregation involves combining multiple pieces of data to form a summary statistic.

Examples of Aggregation:

• Sum: Total of a set of numbers.
• Average (Mean): Overall central tendency.
• Count: The number of data points.

Usage: Aggregated data simplifies complex data sets, making trends and comparisons clearer.

Tip: Be aware of what is being aggregated to avoid misleading conclusions.

Simplifying Algebraic Expressions

When simplifying algebraic expressions, you typically combine like terms and apply the distributive property.

• Combining Like Terms: Identify terms with the same variable parts and add or subtract their coefficients. For example, in the expression \(\mathrm{3\,x+2\,x}\), the like terms combine to give \(\mathrm{(3+2)\,x=5\,x}\).
• Distributive Property: Multiply each term inside a parenthesis by the term outside. For instance, in the expression \(\mathrm{a\, (b+c)}\), applying the distributive property results in \(\mathrm{a\,b+a\,c}\).
• Example: Simplify \(\mathrm{2\, (3\,x+4)+5\,x}\): First, distribute to get \(\mathrm{6\,x+8+5\,x}\) and then combine like terms \(\mathrm{6\,x+5\,x=11\,x}\). The simplified expression is \(\mathrm{11\,x+8}\).

Combining these techniques makes it easier to solve and manipulate algebraic expressions in various GMAT problems.

Step 1: Simplify the Equation

Expand any parentheses and combine like terms so that both sides of the equation are in their simplest form.

Step 2: Group Like Terms

Use addition or subtraction to shift all terms containing \(\mathrm{x}\) to one side and all constant terms to the opposite side.

Step 3: Isolate the Variable

Divide or multiply both sides of the equation by the coefficient of \(\mathrm{x}\) to solve for \(\mathrm{x}\).

Step 4: Check the Solution

Substitute the value found for \(\mathrm{x}\) back into the original equation to confirm its correctness.

Main Methods for Solving Quadratic Equations

• Factoring: Write the quadratic in the form \( ax^2 + bx + c = 0 \) and express it as a product of two binomials. This method is best used when the factors are easy to identify and the quadratic factors neatly.
• Completing the Square: Transform the quadratic into the form \( a(x - h)^2 = k \). This method is useful for deriving the vertex form of the quadratic and when the equation does not factor cleanly.
• Quadratic Formula: Use the formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). This is the most general method and works for any quadratic equation, regardless of whether it factors.
• Graphing: Plot the quadratic function and determine the x-intercepts. This method provides a visual representation and can be useful for understanding the behavior of the quadratic.

How to Decide Which Method to Use

• If the coefficients are simple and the quadratic factors easily, factoring is quick and efficient.
• If you need the vertex form or the quadratic does not factor neatly, completing the square can be advantageous.
• If an exact solution is required or when dealing with more complex coefficients, the quadratic formula is the best choice.
• If you wish to understand the graphical interpretation of the quadratic, graphing can provide useful insights, although it might be less precise for finding exact solutions.

Substitution Method

• This method involves solving one equation for one variable (e.g., \(\mathrm{y}\) in terms of \(\mathrm{x}\)) and substituting the result into the other equation. It is best used when one of the equations is already solved or can be easily manipulated to isolate a variable.

Elimination Method

• In the elimination method, equations are added or subtracted (possibly after multiplying by suitable constants) to cancel one of the variables. This method is effective when the coefficients of the variable to be eliminated are easy to align, making the process straightforward.

Graphing Method

• Graphing involves plotting each equation on the coordinate plane and finding the point of intersection. Although less precise for obtaining exact answers, it offers a visual verification of the solution. This method is useful when an approximate solution is acceptable or when visual interpretation aids understanding.

Matrix Methods (Cramer’s Rule and Inverse Matrix Method)

• These techniques are typically applied to systems with more than two variables. Cramer’s Rule employs determinants to solve for each variable, while the Inverse Matrix Method uses the inverse of the coefficient matrix. They are best used when the system is larger or when a systematic approach is desired, though they are less common on the GMAT where systems tend to be small and can often be solved using substitution or elimination.

Choosing a method depends on the system’s structure: use substitution when a variable is easily isolated, elimination when coefficients are conducive to cancellation, graphing when a visual solution is helpful, and matrix techniques for systematic handling of larger systems.

Inequality Direction Change:

When you multiply or divide both sides of an inequality by a negative number, the direction of the inequality is reversed.

Example: If mathrm{A} < mathrm{B}, then multiplying by -1 gives -mathrm{A} > -mathrm{B}.

Key Strategies for Analyzing Trends in Table Columns

• Examine Column Headings and Units: Ensure you understand what each column measures and the units used, as this context is critical for trend analysis.
• Check for Consistency and Missing Data: Look for any inconsistencies or gaps in the data that could affect trend interpretation.
• Identify Time or Sequence Order: Determine if the table represents a time series or sequential order, which will guide your trend analysis.
• Compute Differences and Percent Changes: Calculate the differences or percent changes between successive entries to quantify any upward or downward trends.
• Look for Patterns and Outliers: Analyze the data for consistent patterns, cycles, or anomalies that stand out from the normal trend.
• Cross-compare with Other Columns: Compare trends in one column with related columns to identify correlations or divergences in data behavior.
• Verify Statistical Significance: Where applicable, use statistical measures or tests to confirm whether observed trends are significant.

Conclusion: A systematic approach that incorporates these strategies will help in accurately interpreting trends and making informed decisions based on the table data.

Scatter Plot Analysis

Scatter plots display data points for two variables, allowing quick visual assessment of relationships. By plotting the data, you can detect trends such as upward or downward patterns, assess the correlation between the variables, and pinpoint outliers that deviate from the overall pattern.

• Identifying Trends: Examine whether the points form a pattern. An upward-sloping cluster suggests a positive trend, while a downward-sloping one indicates a negative trend. Sometimes, a curved pattern may hint at non-linear relationships.
• Assessing Correlations: Use a trend line or compute statistical measures. A tight grouping of points around a regression line shows a strong correlation, whether positive or negative. The strength is often quantified by correlation coefficients.
• Spotting Outliers: Look for data points that stand apart from the main cluster. These anomalies can signal errors in data collection or unique observations that might need special attention.

Analyzing scatter plot data in these ways is crucial for GMAT Data Insights questions, as it enables evaluators to understand relationships, verify assumptions, and make data-driven decisions.

Steps to Analyze Supporting Details

• Contextualize the Detail: Understand where the supporting detail fits within the overall argument and what claim it is intended to bolster.
• Assess Relevance: Evaluate whether the detail directly addresses the argument's central claim or only provides background information. Determine if the detail is necessary or supplementary.
• Examine the Connection: Analyze how the detail reinforces the argument. Consider if it provides evidence, illustrates a point, or offers a counterexample that the argument addresses.
• Check for Assumptions and Logical Flow: Identify any underlying assumptions that link the supporting detail to the argument. Verify if the detail logically follows and if any gaps weaken the connection.
• Consider the Credibility: Evaluate the source or basis of the supporting detail. Credible and specific evidence typically strengthens the argument more than vague or anecdotal details.

Application in GMAT Questions

• Focus on how each detail impacts the reasoning behind the argument.
• Use these steps in critical reasoning sections to dissect why certain details are included and how they function in reinforcing or weakening the argument.

Overview

Divisibility rules and factorization strategies simplify arithmetic problem‐solving by reducing complex calculations into manageable parts. They help identify whether a number is divisible by another without performing full division and enable restructuring numbers into their prime factors for subsequent operations.

Key Benefits

• Simplification: Divisibility rules such as those for 2, 3, 5, and 7 quickly indicate if a number can be factored by a smaller number, eliminating unnecessary calculations.
• Efficient Factoring: Using prime factorization transforms a number into its building blocks, making it easier to compare common factors or simplify fractions. For instance, expressing a number as \(\mathrm{p_1\,p_2\,\ldots\,p_n}\) can reveal cancellations or further divisibility.
• Problem Breakdown: Factorization provides a systematic method to decompose larger problems into simpler sub-problems, which is particularly useful in time-limited contexts like the GMAT.
• Error Reduction: By employing divisibility tests and factorization, one minimizes computational mistakes and streamlines the process of identifying viable solution pathways.

Conclusion

Overall, by incorporating divisibility rules and factorization strategies, arithmetic problem-solving becomes more direct and less error-prone, enabling quicker identification of potential solution paths in GMAT quantitative contexts.

Key Rules for Integer Arithmetic Operations

Addition and Subtraction:

• When adding two integers with the same sign, add their absolute values and keep the common sign.
• For integers with different signs, subtract the smaller absolute value from the larger and assign the sign of the integer with the greater absolute value.
• Subtraction is equivalent to adding the opposite; that is, \(\mathrm{a} - \mathrm{b} = \mathrm{a} + (-\mathrm{b})\).

Multiplication and Division:

• If both integers have the same sign, the product or quotient is positive.
• If the integers have opposite signs, the product or quotient is negative.
• Division follows the same rules as multiplication; note that division by zero is undefined.

Additional Concepts:

• Adhere to the order of operations (parentheses, exponents, multiplication and division, addition and subtraction).
• Multiplication distributes over addition: \(\mathrm{a}\cdot(\mathrm{b}+\mathrm{c}) = \mathrm{a}\cdot\mathrm{b} + \mathrm{a}\cdot\mathrm{c}\).
• The commutative and associative properties apply to both addition and multiplication.

Percent Calculations Using Arithmetic Methods

Percent means per hundred. To work with percents arithmetically, you first convert the percent into a decimal by dividing by 100, then multiply the decimal by the quantity involved.

Steps:

• Conversion: Convert a percent, say \(X\,\%\), into decimal form by computing \(X/100\). For example, \(30\,\%\) becomes \(30/100 = 0.30\).
• Multiplication: Multiply the decimal by the number you are evaluating. For instance, \(30\,\%\) of a number \(N\) is \(N\times(30/100)\).

Examples:

• To calculate \(20\,\%\) of \(50\): Convert \(20\,\%\) to \(20/100 = 0.20\), then compute \(50\times0.20 = 10\).
• To determine \(150\,\%\) of \(80\): Convert to \(150/100 = 1.50\), then calculate \(80\times1.50 = 120\).

Adjusting Values by a Percent:

To increase a number \(A\) by \(X\,\%\), compute \(A\times(1+X/100)\); to decrease \(A\) by \(X\,\%\), compute \(A\times(1-X/100)\). For example, increasing \(100\) by \(15\,\%\) gives \(100\times(1+15/100)=100\times1.15=115\).

This method is widely used on the GMAT, especially in quantitative reasoning, where accurately converting percents and performing multiplication is essential.

Understanding Ratios and Proportions

Ratios are comparisons between two quantities, while proportions state that two ratios are equal. They are powerful tools in solving arithmetic problems because they allow us to scale quantities up or down and find missing values.

• Setting Up Equations: Express the problem as a ratio and set it equal to another ratio. For example, if the ratio of apples to oranges is given as \(\mathrm{3\,:\,4}\) and you have a certain number of apples, you can set up the proportion \(\frac{\mathrm{3}}{\mathrm{4}} = \frac{\mathrm{apples}}{\mathrm{oranges}}\) to solve for the unknown quantity.
• Cross Multiplication: Once a proportion is established, you can cross multiply to create an equation that is easier to solve. For instance, if \(\frac{\mathrm{a}}{\mathrm{b}} = \frac{\mathrm{c}}{\mathrm{d}}\), then \(\mathrm{a}\times\mathrm{d}=\mathrm{b}\times\mathrm{c}\).
• Scaling Quantities: Ratios help in scaling problems. For example, if a recipe ratio is known and you need to adjust the serving size, you can determine the proportional amount of each ingredient through multiplication.
• Real-World Applications: Many arithmetic problems involving speed, distance, or mixtures use ratios and proportions. For instance, if a car travels \(\mathrm{60\,miles}\) in \(\mathrm{1\,hour}\), you can use a proportion to find out how far it travels in another time period.

Summary

Ratios and proportions allow you to create a direct relationship between quantities. By setting up a proportion and using cross multiplication, you can solve for unknown values in a straightforward manner. This method is widely applicable in various arithmetic problems found in the GMAT, particularly in the Quantitative Reasoning section.