GMAT Quantitative Reasoning key terms

A whole number with no fractional or decimal part, such as -3, 0, or 17. Integers can be positive, negative, or zero, and they are closed under addition, subtraction, and multiplication.

The property that one integer can be divided by another with a remainder of zero. Knowing divisibility rules for numbers like 2, 3, 5, and 9 lets you test factors quickly without long division.

An integer greater than 1 whose only positive divisors are 1 and itself, such as 2, 3, 5, 7, and 11. The number 1 is not prime, and 2 is the only even prime.

Writing a positive integer as a product of prime numbers, for example 60 = 2 x 2 x 3 x 5. This form makes it easy to find greatest common factors, least common multiples, and the count of divisors.

The largest positive integer that divides each number in a set evenly. For 18 and 24, the greatest common factor is 6. It is found by comparing the shared prime factors of the numbers.

The smallest positive integer that is a multiple of each number in a set. For 4 and 6, the least common multiple is 12. It is useful for adding fractions and solving repeating-event problems.

The amount left over after dividing one integer by another when the division is not exact. For example, 17 divided by 5 gives a quotient of 3 and a remainder of 2.

A comparison of two quantities by division, often written as a fraction or with a colon. A ratio of 3 to 4 means the first quantity is three-fourths the size of the second.

An equation stating that two ratios are equal, such as 3/4 = 9/12. Solving a proportion usually means cross-multiplying to find an unknown value in one of the ratios.

A ratio expressed as a part per hundred. For instance, 25 percent means 25 out of every 100, or one quarter of a whole, and is written as 0.25 in decimal form.

The difference between a new value and an original value, divided by the original value and expressed as a percent. A positive result is an increase; a negative result is a decrease.

The sum of a set of values divided by the number of values. For 4, 6, and 11, the average is 7. The mean is affected by every value in the set, including outliers.

The middle value of a set when the values are arranged in order. If the set has an even number of values, the median is the average of the two middle values.

An average in which each value counts according to an assigned weight rather than equally. It equals the sum of each value times its weight, divided by the total of the weights.

A measure of how spread out a set of values is around its mean. A larger standard deviation means values are more dispersed; a smaller one means they cluster near the mean.

The difference between the largest and smallest values in a data set. It is a simple measure of spread but depends only on the two extreme values.

A letter or symbol that stands for an unknown or changing quantity in an expression or equation. For example, in 3x + 5 = 20, the letter x is the variable.

A mathematical phrase combining numbers, variables, and operations without an equals sign, such as 2x + 7. An expression can be simplified or evaluated but not solved.

A statement that two expressions are equal, joined by an equals sign. Solving an equation means finding the value or values of the variable that make the statement true.

An equation in which each variable appears to the first power, so its graph is a straight line. A typical form is y = mx + b, where m is the slope and b is the y-intercept.

An equation of the form ax squared plus bx plus c equals zero, where a is not zero. Its solutions, called roots, can be found by factoring, completing the square, or the quadratic formula.

Rewriting an expression as a product of simpler expressions, such as turning x squared minus 9 into (x - 3)(x + 3). Factoring is a key method for solving polynomial equations.

A statement comparing two expressions that are not necessarily equal, using symbols such as less than, greater than, or their or-equal-to forms. Multiplying or dividing by a negative number reverses the direction of the inequality.

The distance of a number from zero on the number line, always non-negative. The absolute value of both 5 and -5 is 5, and equations involving it often have two solutions.

A rule that assigns exactly one output value to each input value. For example, f(x) = 2x + 1 gives a single result for every number substituted for x.

A measure of how steep a line is, equal to the change in y divided by the change in x between two points. A horizontal line has slope zero, and a vertical line has undefined slope.

The point where a line crosses the vertical axis, occurring where x equals zero. In the form y = mx + b, the value b is the y-intercept.

A relationship in which one quantity is a constant multiple of another, written y = kx. As one quantity increases, the other increases proportionally, and the graph passes through the origin.

A number written above and to the right of a base that tells how many times the base is multiplied by itself. In 2 to the fourth power, 2 is the base and 4 is the exponent.

A number that, when multiplied by itself, gives a specified value. The square root of 49 is 7, and every positive number has two square roots, one positive and one negative.

A closed three-sided polygon whose interior angles always add to 180 degrees. Triangles are classified by side lengths as equilateral, isosceles, or scalene, and by angles as acute, right, or obtuse.

The rule that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. It is written as a squared plus b squared equals c squared.

The longest side of a right triangle, located opposite the right angle. Its length can be found from the two shorter sides using the Pythagorean theorem.

Triangles with equal corresponding angles and proportional corresponding side lengths. Their matching sides share a constant ratio, which allows unknown lengths to be calculated.

The set of all points in a plane at a fixed distance, called the radius, from a central point. Its circumference equals 2 times pi times the radius, and its area equals pi times the radius squared.

The distance from the center of a circle to any point on the circle. It is half the diameter, and it appears in both the circumference and area formulas.

The measure of the surface enclosed by a two-dimensional figure, expressed in square units. Common formulas include length times width for rectangles and one-half base times height for triangles.

The measure of the three-dimensional space occupied by a solid, expressed in cubic units. For a rectangular box it equals length times width times height.

A grid formed by a horizontal x-axis and a vertical y-axis that intersect at the origin. Each point is located by an ordered pair (x, y) giving its horizontal and vertical positions.

A ratio that compares quantities with different units, such as miles per hour or cost per item. Rate problems often use the relationship distance equals rate times time.

A word problem about two or more agents completing a task together at different rates. Rates are added, so the combined rate is the sum of the individual rates.

A word problem combining two or more substances with different concentrations to form a new mixture. The total amount of each component before and after mixing is conserved.

Interest calculated only on the original principal, using the formula interest equals principal times rate times time. It does not compound, so the yearly interest amount stays constant.

Interest calculated on both the original principal and previously earned interest, so the balance grows faster over time. The formula is principal times (1 plus rate) raised to the number of periods.

A question format asking whether the given statements provide enough information to answer a question, without requiring the actual numeric answer. The focus is on determining sufficiency, not solving fully.

A condition that provides enough information to determine exactly one answer to the question asked. If a statement allows more than one possible answer, it is not sufficient.

One of the two labeled pieces of information supplied in a data sufficiency problem. Each statement is considered separately, and the two are combined only if neither alone is sufficient.

A single case that shows a general claim is false. In data sufficiency, finding two different values that both satisfy a statement proves that statement is not sufficient.

A strategy of substituting convenient numbers for variables to test whether an answer choice or statement holds. Choosing values such as 2, 0, and a fraction helps reveal special cases.