GRE General Test flashcards

A text completion strategy where the blank is filled with a word that expresses an idea opposite to one already presented in the sentence, often signaled by contrast words.

• Look for words like 'however', 'but', 'clashes with'.
• The blank will complete the contrasting idea.
• Helps distinguish between abstract and practical concepts.

Memory trick: When 'but' or 'however' appears, expect a flip!

Choosing an abstract noun that accurately describes a complex relationship, concept, or state of being presented in the sentence.

• Abstract nouns represent ideas, qualities, or concepts.
• Context is crucial for distinguishing subtle differences between similar abstract nouns.
• Consider the overall theme and implications of the sentence.

Memory trick: Abstract Nouns Define the Invisible Dynamics.

Selecting an adjective that accurately describes a noun based on the surrounding context and tone of the sentence.

• Adjectives modify nouns, providing more detail.
• Consider the connotations (positive/negative) of the adjective.
• Ensure the adjective enhances the meaning of the sentence.

Memory trick: The Adjective Paints the Noun's Picture.

Adjusting the dimensions of an object (like an image) proportionally to maintain its original shape without distortion.

• Ratio of width to height remains constant.
• Calculate the scaling factor for one dimension.
• Apply the same scaling factor to all other dimensions.

Memory trick: Find the factor for one, apply to the other, new dimensions are won!

A measure of the relative growth of a quantity, expressed as a percentage of the original quantity.

• Calculated as (New Value - Original Value) / Original Value * 100%
• Used to show how much a quantity has grown.
• Essential for analyzing growth rates in various fields.

Memory trick: New-Old over Old, then multiply by 100, the change is bold!

Using a given scale to convert a measurement from a model or drawing to its actual size, and then converting units if necessary.

• Scale factor 1:N means 1 unit on drawing = N units in real life.
• To find actual size, multiply drawing size by N.
• 1 meter = 100 centimeters.

Memory trick: Scale Up, Then Convert Down: Multiply by scale first, then divide for units.

Using ratios to determine an unknown quantity when a known relationship between two quantities is given.

• Ratios can be written as fractions: a/b = c/d.
• Cross-multiplication is used to solve proportions: ad = bc.
• Ensure units are consistent when setting up proportions.

Memory trick: Ratio's Rule: Set up the fractions, then cross-multiply to solve.

The area of a triangle can be calculated if the lengths of two sides and the measure of the included angle (Side-Angle-Side) are known.

• Formula: Area = (1/2)ab\(\sin(C)\)
• a and b are the lengths of the two sides.
• C is the measure of the angle included between sides a and b.

Memory trick: Half-AB-Sine-C: Remember the formula for side-angle-side area.

Calculating a rate per single unit of quantity, then using that rate to determine a total for a different quantity, often involving unit conversions.

• Unit rate = Total Quantity / Total Units.
• Conversion factor for hours to minutes is 60 minutes/hour.
• Ensure all calculations are performed with consistent units or convert at the appropriate step.

Memory trick: Rate First, Then Convert: Find the rate per unit, then scale and change units.

Solving problems by establishing a constant ratio (unit rate) between two quantities and using it to find an unknown quantity.

• Identify the given ratio (e.g., cups per serving).
• Determine the unit rate (quantity per 1 unit).
• Multiply the unit rate by the desired total units.

Memory trick: Find the unit for one, then scale it up, your recipe's done!

When a constant is added to or subtracted from each value in a dataset, the mean changes by that constant. When each value is multiplied or divided by a constant, the mean changes by that constant factor.

• If x' = x + c, then mean' = mean + c.
• If x' = x * c, then mean' = mean * c.
• These properties simplify calculations for transformed datasets.

Memory trick: Mean's Mirror: Whatever you do to each number, the mean does too.

The median is the middle value in an ordered data set. For an odd number of data points, it's the single middle value. For an even number, it's the average of the two middle values.

• Always order data before finding the median.
• Outliers have less impact on the median than on the mean.
• The median divides the data set into two equal halves.

Memory trick: Order numbers, find the middle path.

Applying multiple percentage increases or decreases sequentially to a value, where each subsequent change is based on the new current value.

• Changes are multiplicative, not additive.
• Order of operations matters.
• Final value = Initial Value * (1 ± r1) * (1 ± r2) * ...

Memory trick: Multiply by (1+gain), then by (1-loss), for the final value, without cross!

Calculating the total time required for a task based on a given rate, and then converting that time into a different unit (e.g., minutes to hours).

• Units must be consistent for calculations.
• Total quantity / Rate = Total time.
• Conversion factors (e.g., 60 minutes = 1 hour) are essential.

Memory trick: Total entries by rate, then minutes to hours, don't be late!

The volume of a cylinder is the amount of space it occupies, calculated by multiplying the area of its circular base by its height.

• Formula: V = \(\pi r^2 h\)
• r is the radius of the base, h is the height (or length) of the cylinder.
• Diameter is twice the radius (d = 2r).

Memory trick: Radius First, Then Pi-R-Squared-H: Find the radius, then apply the volume formula.

Applying a given ratio to a total quantity to find the proportional amount of one part of the ratio.

• Ratios express the relationship between two or more quantities.
• They can be written as fractions, with a colon, or with the word 'to'.
• To apply a ratio, set up a proportion or multiply the ratio fraction by the total.

Memory trick: Ratio's Rate, Total's Fate: Multiply to get the correct count.

Solving a problem that involves calculating a percentage increase and then applying that new value in further calculations.

• Often requires sequential calculations.
• First, find the new value after the percentage change.
• Then, use this new value in subsequent steps.

Memory trick: First the boost, then the week; production numbers we seek!

Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal amount and also on the accumulated interest of previous periods.

• Simple Interest Formula: I = P * R * T
• Compound Interest Formula: A = P * (1 + R)^T (where A is total amount, I = A - P)
• Compound interest generally yields more over longer periods due to interest on interest.

Memory trick: Simple's Steady, Compound's Climb: Calculate each path, then find the gap.

A quantity is subjected to multiple percentage decreases, where each subsequent decrease is applied to the already reduced amount.

• To decrease by P percent, multiply by (1 - P/100).
• For successive decreases, multiply by the factor (1 - P/100) repeatedly.
• The order of application for successive percentage changes does not matter.

Memory trick: Reduce and Repeat: Apply the reduction factor multiple times to the current value.

Reducing a quantity by a certain percentage, where the decrease is calculated based on the original quantity.

• To decrease by P percent, calculate P/100 * Original Value.
• New Value = Original Value - (P/100 * Original Value).
• Alternatively, New Value = Original Value * (1 - P/100).

Memory trick: Original Minus Percent: Subtract the percentage portion from the starting amount.

When a quantity increases by a certain percentage over multiple periods, the increase in each period is applied to the new, larger base from the previous period.

• To increase by P percent, multiply by (1 + P/100).
• For n periods, the final value = Initial Value * (1 + P/100)^n.
• This is a form of exponential growth.

Memory trick: Grow by Factor, Power by Time: Find the growth factor, then raise it to the number of periods.

Determining the average of a dataset after a new data point is added or removed.

• Sum of all values is crucial.
• Total count of values changes when a new point is added.
• New average = (Old Sum + New Value) / (Old Count + 1).

Memory trick: Old sum, new value, divide by new count, the new average you've found!

The process by which a quantity decreases by a constant factor (usually 1/2) over equal intervals of time.

• Formula: N(t) = N0 * (1/2)^(t/T), where N0 is initial amount, t is total time, T is half-life period.
• Each half-life period reduces the quantity by half.
• Common in radioactive decay and medication breakdown.

Memory trick: Divide by two, each cycle through, till total time is due!

Exponential growth describes a quantity that increases by a constant factor over equal time intervals.

• Formula: N(t) = N0 * (factor)^(t/T_interval)
• N0 is initial quantity, factor is growth multiplier, t is total time, T_interval is time for one growth cycle.
• In this case, factor is 3, T_interval is 2 hours.

Memory trick: Intervals Count, Factor Power: Find how many times it grows, then raise the factor to that power.

Growth that is calculated on the initial principal and also on the accumulated interest or growth from previous periods.

• Formula: P(1 + r)^n, where P is principal, r is rate, n is periods.
• Leads to exponential increase over time.
• Common in finance, biology, and population studies.

Memory trick: Principal plus rate, to the power of time, watch your growth climb!

For a data set with an even number of values, the median is the average of the two middle values after the data has been ordered from least to greatest.

• Data must be ordered.
• Identify the two central values.
• Calculate their arithmetic mean.

Memory trick: Even Median's Average: Order the numbers, find the two middle ones, then average them out!

The arithmetic mean, or average, is a measure of central tendency calculated by summing all values in a dataset and dividing by the number of values.

• Most common type of average.
• Sensitive to outliers (extreme values).
• Represents the 'equal distribution' value if all items were the same.

Memory trick: Central Tendency: Think of finding the 'heart' of your data.

To find a percentage of a quantity, convert the percentage to a decimal or fraction and multiply it by the quantity.

• Percentage means 'out of one hundred'.
• To convert a percentage to a decimal, divide by 100.
• To find the remaining percentage, subtract the given percentage from 100%.

Memory trick: Good parts always make for happy machines.

Comparing compound interest involves calculating the future value of an investment under different compounding frequencies and annual interest rates, then finding the difference.

• Compound Interest Formula: A = P(1 + r/n)^(nt).
• A = future value, P = principal, r = annual interest rate (decimal), n = number of times compounded per year, t = time in years.
• Higher compounding frequency (n) generally leads to slightly higher returns for the same nominal rate.

Memory trick: Calculate each option, then find their difference.

Linear decrease describes a quantity that reduces by a fixed amount over equal intervals of time or another variable.

• Involves a constant rate of reduction.
• Can be modeled by a linear equation: Final = Initial - (Rate × Time).
• Distinguished from exponential decay where the reduction is proportional to the current amount.

Memory trick: Constant Change: Think of a steady drip reducing a bucket's water level.