GMAT Focus Edition flashcards

Bin width, also known as interval width, is the size of each category or interval when grouping continuous data into bins for analysis or visualization (e.g., histograms).

• Calculated as (Max Value - Min Value) / Number of Bins.
• All bins typically have the same width.
• Choosing appropriate bin width is important for data representation.

Memory trick: Range Divided by Bins, Width Defined.

Quadratic equations (ax^2 + bx + c = 0) arise in geometry when dealing with areas or volumes where dimensions are related in a way that involves squares of variables.

• Often involve finding dimensions (length, width, radius).
• Solutions may yield a positive and negative root, only positive is usually valid.
• Can be solved by factoring, quadratic formula, or completing the square.

Memory trick: Geometry's Dimensions Lead to Quadratic Solutions.

Bayes' Theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. It calculates conditional probability.

• P(A|B) = [P(B|A) * P(A)] / P(B)
• P(B) is often calculated using the law of total probability.
• Used to update beliefs based on new evidence.

Memory trick: Prior Beliefs Updated by Evidence.

The overall percentage change in a value after multiple sequential percentage increases or decreases.

• Changes are applied sequentially to the current value.
• Not a simple addition/subtraction of percentages.
• Can be calculated as (Final Value / Initial Value - 1) * 100%.

Memory trick: First, find the 'new now' then apply the 'next then'.

When multiple entities work together, their combined rate is the sum of their individual rates, assuming they work independently.

• Individual rates must be calculated first.
• Rates are typically expressed as 'amount per unit time'.
• Combined rate is simply the sum of individual rates.

Memory trick: Add their speeds to get the team's total sprint.

If an event can occur in 'm' ways, and a second independent event can occur in 'n' ways, then the two events can occur in m * n ways.

• Used to find the total number of possible outcomes.
• Applies when selections are independent.
• Involves multiplication of the number of choices for each step.

Memory trick: Multiply options like building a meal, piece by piece.

If (A + B) is divisible by N, and B is divisible by N, then A must also be divisible by N. This principle is key for Data Sufficiency problems involving divisibility.

• If a sum/difference of two numbers is divisible by N, and one number is divisible by N, the other must also be divisible by N.
• This extends to remainders: if A = qN + r and B = pN, then A+B = (q+p)N + r, so (A+B) has the same remainder as A when divided by N.
• Crucial for determining divisibility of an unknown variable.

Memory trick: If the sum shares a trait, and one part has it, the other part must too.

When multiple entities (people, machines, etc.) work together on a task, their individual work rates are added to find the combined work rate. The time taken is then total work divided by the combined rate.

• Rates are additive when working together.
• Work = Rate × Time.
• Time = Work / Combined Rate.

Memory trick: Rates Add Up, Work Gets Done Faster.

A combination is a selection of items from a larger set where the order of selection does not matter.

• Used when order of selection is irrelevant.
• Formula: C(n, k) = n! / (k! * (n-k)!).
• Distinguished from permutations where order matters.

Memory trick: Combinations: just a group, no seating chart. Permutations: specific order matters.

Binomial probability calculates the likelihood of a specific number of successes in a fixed number of independent trials, given a constant probability of success for each trial.

• Fixed number of trials (n).
• Each trial has only two possible outcomes (success/failure).
• Probability of success (p) is constant for each trial.
• Trials are independent.

Memory trick: Count the chances for exact hits in a set number of tries.

The present value of a bond is the sum of the present values of its future coupon payments and its face value at maturity, discounted at the market interest rate.

• Bonds are valued by discounting future cash flows.
• Cash flows include periodic coupon payments and the face value at maturity.
• The discount rate used is the market interest rate (yield to maturity) for similar bonds.

Memory trick: Bonds' worth is found by bringing future money back home.

Solving real-world problems by translating them into two or more linear equations and finding the values of the variables that satisfy all equations simultaneously.

• Define variables for unknown quantities.
• Formulate equations based on the problem's conditions.
• Use substitution or elimination methods to solve the system.
• Often involves rates, quantities, costs, or mixtures.

Memory trick: Read, define, equation-ize, then solve and verify the prize.

The algebraic identity a^2 - b^2 = (a - b)(a + b) is often useful in Data Sufficiency problems, especially when one of the factors (a+b or a-b) is provided or can be derived.

• Factoring a difference of squares simplifies expressions.
• Can connect seemingly unrelated equations.
• Useful in problems involving sums and differences of variables.

Memory trick: Look for squares; they often hide a useful sum and difference.

A quick and simple rule to estimate the number of years required for an investment to triple in value.

• Years to triple ≈ 114 / (annual interest rate as a whole number).
• Similar to the Rule of 72 but for tripling instead of doubling.
• Provides a reasonable approximation for GMAT purposes, especially when options are spaced out.

Memory trick: 114 on top, rate below, for tripling, that's how you know!

Calculating the total output when multiple entities (machines, people) work together, by summing their individual rates.

• Individual rates must be in the same units (e.g., units/hour).
• Combined rate = sum of individual rates.
• Total work = combined rate × time.

Memory trick: Find each rate alone, then sum them up, and multiply by time to fill the cup.

The probability of an event occurring given that another event has already occurred, where the first event changes the conditions for the second event (e.g., by reducing the sample space).

• The denominator (total possible outcomes) decreases after each draw.
• The numerator (favorable outcomes) also decreases if the drawn item is of that type.
• Calculated by multiplying the probabilities of successive events.

Memory trick: Each pick changes the 'pie' for the next slice.

The effective annual interest rate (EAR) is the actual annual rate of return earned or paid on an investment or loan, taking into account the effect of compounding interest.

• EAR accounts for compounding frequency.
• It allows comparison of investments with different compounding periods.
• EAR is always greater than or equal to the nominal rate if compounding occurs more than once a year.

Memory trick: Effective Rates Make All Investments Clearer.

A quick and simple rule to estimate the number of years required to double an investment or the interest rate needed for an investment to double in a given number of years.

• Years to double ≈ 72 / (annual interest rate as a whole number).
• Interest rate ≈ 72 / (years to double).
• Works best for interest rates between 6% and 10% but is a useful approximation for GMAT.

Memory trick: 72 on top, time or rate below, for doubling, that's how you know!

Successive percentage changes are applied one after another, with each subsequent change based on the new, adjusted value.

• Changes are multiplicative, not additive.
• Order of application does not affect the final result.
• To find the final value, multiply the original value by (1 +/- %change1) * (1 +/- %change2) etc.

Memory trick: Each discount takes a bite from what's left, not the original pie.

A counting technique that finds the number of elements in the union of two sets by summing the sizes of the individual sets and subtracting the size of their intersection.

• Formula: |A U B| = |A| + |B| - |A ∩ B|.
• Used to avoid double-counting elements that are common to both sets.
• Often applied in probability and set theory problems.

Memory trick: Total = A + B - Both + Neither.

Two quantities are in direct proportion with a power if one quantity varies directly as a power (square, cube, etc.) of the other, meaning their ratio is a constant (y = kx^n).

• Expressed as y = kx^n, where k is the constant of proportionality.
• As x increases, y increases (or decreases if n is negative).
• Finding 'k' is crucial to solve for unknown values.

Memory trick: Constant K Links Powerful Proportions.

Problems involving combining two or more substances with different concentrations to achieve a desired final concentration or quantity.

• Set up equations for total quantity and total amount of solute.
• Often involves solving a system of two linear equations.
• Concentration is (amount of solute / total quantity).

Memory trick: Two equations, two unknowns, total volume and total 'stuff' combine.

A weighted average is an average where some values contribute more than others to the final mean. Each value is multiplied by a weight, and the sum of these products is divided by the sum of the weights.

• Used when data points have different levels of importance.
• Formula: (Σ(value × weight)) / (Σweights).
• Common in calculating GPA, course grades, or financial metrics.

Memory trick: Weights Matter for the True Average.

For a discrete random variable representing the number of successes in 'n' trials, where the probability of success in a single trial is 'p', the expected value (mean) is E(X) = np.

• Represents the average outcome over many trials.
• Not necessarily an outcome that will occur on any single trial.
• Used in probability and statistics for predictions.

Memory trick: Expect N-P to Predict Outcomes.

Exponential growth with a constant doubling time means a quantity consistently doubles over fixed intervals. The formula is N = N₀ * 2^(t/T), where N₀ is initial quantity, t is total time, and T is doubling time.

• Growth is multiplicative, not additive.
• Doubling periods must be calculated first.
• Can be modeled by N = N₀ * 2^n, where n is the number of doubling periods.

Memory trick: Doubling time means hitting 'times two' over and over.

To count the number of integers in an inclusive range from 'a' to 'b' (where 'a' and 'b' are integers and a ≤ b), the formula is b - a + 1.

• Applies to consecutive integers.
• The '+ 1' accounts for including both the start and end numbers.
• Useful for problems involving sequences, raffle tickets, or page numbers.

Memory trick: End Minus Start Plus One is Done.

Calculating the amount of space occupied by a three-dimensional cylindrical object.

• Formula for cylinder volume: V = πr²h, where r is radius and h is height.
• Units of volume are cubic units (e.g., m³).
• Often combined with rate problems to find time to fill/empty.

Memory trick: Volume is pie-R-squared-H, then time is volume over flow rate.

When adding a number to an integer, the remainder of the sum when divided by N is equal to the remainder of (original remainder + added number) when divided by N.

• If n = qN + r, then n + x = qN + r + x.
• The new remainder is the remainder of (r + x) when divided by N.
• Useful for quickly determining remainders of modified numbers.

Memory trick: Just add the remainders, then re-divide if needed.

Linear equations are algebraic equations where each term is either a constant or the product of a constant and a single variable (e.g., ax + b = c). Word problems require translating real-world scenarios into these equations.

• Involve a constant rate of change.
• Often represent total cost, distance, or production.
• Steps include defining variables, setting up the equation, and solving.

Memory trick: Variables Create Equations, Solutions Emerge.

An average that takes into account the relative importance or frequency (weights) of each value in the data set.

• Each value is multiplied by its corresponding weight.
• The sum of these products is divided by the sum of the weights.
• Often used in probability (total probability), finance, and mixtures.

Memory trick: Weight times value, sum them all, then divide by total weight's call.

A theorem that provides a unique solution (modulo the product of the moduli) to a system of simultaneous congruences.

• Involves finding a number that leaves specific remainders when divided by different numbers.
• Often solved by listing possibilities or using number theory principles.
• The smallest positive integer is usually sought.

Memory trick: List, check, intersect: find the number that fits all remainder rules.

A phenomenon where a quantity increases by a fixed factor (e.g., triples) over a constant time interval, leading to rapid growth.

• Nt = N0 * (growth factor)^(t/doubling_time)
• For tripling, growth factor is 3.
• The exponent represents the number of tripling periods.

Memory trick: Count the 'tripling' steps, then multiply by the factor each time!

If two integers are divisible by a number, their sum and difference are also divisible by that number. Conversely, if a sum/difference and one of the integers are divisible, the other integer is too.

• If x is divisible by d and y is divisible by d, then (x + y) is divisible by d.
• If x is divisible by d and y is divisible by d, then (x - y) is divisible by d.
• If (x + y) is divisible by d and x is divisible by d, then y must be divisible by d.

Memory trick: Think of multiples: if parts make a multiple, the missing piece must too!

A method of determining the total cost of an item or service by considering different cost components, each multiplied by its respective rate or weight, then summed.

• Allows for combining diverse cost factors into a single metric.
• Useful for comparing alternatives with different cost structures.
• Requires accurate unit costs for each component.

Memory trick: Every minute, every liter, adds to the bill, make it fitter.

A statement that describes the unique benefits customers can expect from a product or service, often highlighting how it solves a problem or improves their situation, and why it is superior to alternatives.

• Communicates clear benefits to the target audience.
• Often emphasizes tangible gains or avoided pains.
• Must be compelling and differentiate from competitors.

Memory trick: More for less relative, makes the upgrade imperative.

The process of determining the overall monetary gain from sales by multiplying total revenue by the profit margin, or by multiplying sales volume by average selling price and then by the profit margin.

• Total Revenue = Sales Volume * Average Selling Price.
• Profit = Total Revenue * Profit Margin (as a decimal).
• Crucial for evaluating the financial performance of different product lines or business segments.

Memory trick: Volume times price times margin, reveals the profit's origin.

A calculation that takes into account the varying degrees of importance or frequency of the numbers in a data set, typically by multiplying each value by its corresponding weight before summing (for average) or comparing (for product).

• Weights can be percentages, frequencies, or other measures of importance.
• Used to create a more representative overall measure.
• Ensures that more significant factors contribute proportionally more to the final result.

Memory trick: Connect the dots, solve the plot, from two charts a new insight is got.

The process of determining the absolute number of interactions (engagements) with content by multiplying the total audience reached by the engagement rate (percentage of audience that interacted).

• Engagement Rate = (Engaged Users / Total Reach) * 100%.
• Engaged Users = Total Reach * (Engagement Rate / 100).
• A higher engagement rate does not always mean a higher total number of engaged users if reach is low.

Memory trick: Reach multiplied by rate, determines engagement's fate.

The process of comparing line items in financial statements, or other data sets, to derive insights into performance, efficiency, or risk by expressing one value in relation to another.

• Ratios simplify complex data into comparable metrics.
• They highlight relationships between different variables.
• Context is crucial for interpreting ratio results.

Memory trick: Workforce per dollar, a project's true collar.

The process of determining the percentage of users who complete a desired action (e.g., purchase, sign-up) out of the total number of users who had the opportunity to complete that action.

• Conversion Rate = (Conversions / Total Visitors) * 100%.
• Conversions = Total Visitors * (Conversion Rate / 100).
• A key metric for measuring marketing and sales effectiveness.

Memory trick: Visitors times rate, seals the purchase fate.

A type of question that tests the ability to determine whether given information (usually in the form of two statements) is sufficient to answer a question, without necessarily solving the problem completely.

• Focus on sufficiency, not on finding the answer.
• Evaluate each statement independently first.
• Then consider both statements together if neither is sufficient alone.

Memory trick: Quality is defects per unit, not just the total loot.

In Data Sufficiency, a statement about 'better risk-adjusted return' directly implies a higher ratio of return to risk. This metric is crucial for investors aiming to maximize returns while controlling for risk.

• Often represented by the Sharpe Ratio or similar metrics.
• Higher values indicate more return per unit of risk.
• A direct comparison of this metric is sufficient to answer questions about 'maximizing return for a given risk'.

Memory trick: Risk-adjusted return is key, for balanced prosperity.

A measure of return that considers the amount of risk taken to achieve that return, often calculated as a ratio of return to a risk metric like standard deviation.

• Higher ratio indicates better performance.
• Standard deviation is a common measure of risk.
• Useful for comparing investments with different risk profiles.

Memory trick: ROI's shield protects against SD.

To determine which of two quantities (A/B vs C/D) is greater, one typically needs information about both the numerators and denominators. Knowing only about numerators or only about denominators is usually insufficient.

• If A>C and B<D, the comparison of A/B vs C/D is ambiguous without specific values.
• If A>C and B>D, the comparison is also ambiguous.
• Both components of the ratio are generally needed for a conclusive comparison.

Memory trick: Efficiency is adoption for every dollar spent.

A derived metric that normalizes a total value by dividing it by the number of units or individuals associated with that value, providing an average per item or person.

• Helps in comparing efficiency or value across different scales.
• Common examples include revenue per customer, cost per unit, profit per employee.
• Requires clear definition of 'unit' and 'total value'.

Memory trick: Divide sales by customers, see who truly hustles.

Disputing that a specific cause is responsible for an observed effect, often by introducing a more direct or significant alternative cause that occurred concurrently.

• Questions the 'why' behind an outcome.
• Often involves identifying a confounding event or variable.
• Focuses on whether the claimed cause is truly the primary driver.

Memory trick: Don't credit the new tool if someone else is pulling the strings.

Questioning whether data or findings from one context are relevant or generalizable to a different, specific situation or target group.

• Focuses on differences between the study population/conditions and the target population/conditions.
• Highlights issues of representativeness or external validity.
• Undermines recommendations based on misapplied evidence.

Memory trick: Don't cross a bridge if it's built for a different river.

Disputing the practical importance or meaningfulness of a statistically significant finding, especially when the effect size or definition of 'significant' is trivial.

• Goes beyond statistical significance to real-world impact.
• Often involves scrutinizing the definition of key terms or outcomes.
• Argues that the observed effect, though real, is not important enough.

Memory trick: Don't just count the points; see if they actually make a difference.

Questioning whether a proposed action will achieve its specifically stated effect to the degree claimed, often by highlighting a disproportionate impact or minor contribution.

• Focuses on the magnitude or significance of the claimed outcome.
• Often involves numerical or proportional information.
• Challenges the 'noticeable' or 'significant' aspect of a claim.

Memory trick: Don't just hit the target; make sure your arrow actually moves it.

Bolstering a causal argument by showing that other potential influencing variables (confounding factors) have been accounted for or minimized.

• Increases confidence that the observed effect is due to the proposed cause.
• Reduces the possibility of alternative explanations.
• Often involves experimental controls or statistical adjustments for known variables.

Memory trick: Clear the fog around the path to see the true direction.

Providing evidence that directly undermines the proposed primary cause while simultaneously supporting an alternative explanation.

• Simultaneously weakens one hypothesis and strengthens another.
• Often involves showing the proposed primary cause is absent or weak where the effect is strong.
• Requires careful comparison of conditions.

Memory trick: If the usual suspect is innocent, look for the less obvious culprit.

Questioning the reliability or appropriateness of the method used to measure a key variable, thereby invalidating any conclusions drawn from those measurements.

• Focuses on the data collection process itself.
• Highlights flaws in the chosen benchmark or instrument.
• Directly impacts the soundness of the evidence presented.

Memory trick: If your ruler is bent, all your measurements will be wrong.

Enhancing the validity of a causal argument by demonstrating that other potential influencing factors were accounted for or eliminated.

• Reduces the likelihood of confounding variables.
• Makes the observed effect more attributable to the proposed cause.
• Often involves explicit mention of experimental controls or statistical adjustments.

Memory trick: To make your chain strong, remove all rust and test each link.

Providing additional information that clarifies or reinforces the plausible pathway through which a proposed cause leads to its effect.

• Explains *how* the cause brings about the effect.
• Adds detail or a missing link to the causal chain.
• Makes the causal relationship more believable.

Memory trick: Show exactly how the gears turn to make the clock tick.

Data Sufficiency questions ask whether the provided statements offer enough information to answer a specific question, often involving comparing rates or ratios.

• Focus on sufficiency, not on actually solving the problem.
• Evaluate each statement independently first, then together if needed.
• A statement is sufficient if it unequivocally answers the question (yes or no).

Memory trick: Is it enough? That's the only question. Don't solve, just verify sufficiency.

A per-unit metric expresses a quantity or value in relation to a single unit of another quantity, often used to compare efficiency or cost.

• Calculated by dividing a total quantity by the number of units.
• Examples include cost per item, time per task, or revenue per customer.
• Essential for performance analysis and benchmarking.

Memory trick: Efficiency is all about how much you get per unit of effort or time.

A product calculation involves multiplying two or more numbers together to find their product, often used to combine different metrics into a single score.

• The result of multiplication is called the product.
• Used in various fields, including scoring systems, area calculations, and financial modeling.
• Different from a sum (addition) or a ratio (division).

Memory trick: When scores multiply, the impact grows quickly.

Data Sufficiency questions involving linear regression models typically test whether the equation of the line (slope and intercept) is provided or can be derived to make predictions.

• Linear equation: y = mx + b, where 'm' is the slope (rate of change) and 'b' is the y-intercept.
• R-squared measures how well the model fits the data, but doesn't give the prediction formula itself.
• To predict a change in 'y' given a change in 'x', the slope 'm' is crucial.

Memory trick: To predict, you need the 'rules' of the relationship, not just how strong it is.

A weighted average is an average in which each value contributes differently to the final average, based on a specific weight or frequency.

• Used when some data points are more important or occur more frequently than others.
• Calculated by summing the product of each value and its weight, then dividing by the sum of the weights.
• Common in statistics, finance, and survey analysis.

Memory trick: To find the true average, consider how much each part 'weighs' in.

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

• Interest is reinvested and earns interest itself.
• Formula: A = P(1 + r/n)^(nt), where A = future value, P = principal, r = annual interest rate, n = number of times interest is compounded per year, t = number of years.
• Crucial for long-term investment growth.

Memory trick: Calculating compound returns needs careful attention to principal and interest.