GMAT Quantitative Reasoning flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Divisibility by 3

An integer is divisible by 3 exactly when the sum of its digits is divisible by 3. Example: 4,821 has digit sum 15, so it is divisible by 3.

LCM and GCF product

For positive integers a and b, the least common multiple times the greatest common factor equals the product a times b. Example: LCM(6,8)=24 and GCF(6,8)=2, product 48 = 6 x 8.

Combined percent change

Successive percent changes multiply as factors. A 25% increase followed by a 20% decrease gives 1.25 x 0.80 = 1.00, so the net change is zero percent.

Count of evenly spaced terms

For a sequence with first term a, last term L, and constant step d, the number of terms is (L - a)/d + 1. Example: 5, 10, ..., 50 has (50-5)/5 + 1 = 10 terms.

Prime testing bound

To decide whether n is prime, test only primes up to the square root of n. If none divides n, then n is prime. Example: test 2, 3, 5, 7 for n = 53.

Negative exponent rule

For nonzero x and positive integer a, x raised to the negative a equals 1 divided by x raised to the a. Example: 2^(-3) = 1/8.

Quadratic formula

For ax^2 + bx + c = 0 with a not zero, the solutions are x = [-b plus or minus the square root of (b^2 - 4ac)] divided by 2a.

Discriminant meaning

The value b^2 - 4ac for a quadratic. Positive gives two distinct real roots, zero gives one repeated real root, and negative gives no real roots.

Sum and product of roots

For ax^2 + bx + c = 0, the two roots sum to -b/a and multiply to c/a. Example: x^2 - 5x + 6 = 0 has roots 2 and 3, sum 5, product 6.

Difference of squares

The identity a^2 - b^2 = (a - b)(a + b). It factors quickly and also shows that the product of two numbers differing by 2 is one less than the middle square.

Perpendicular slope relation

Two nonvertical lines are perpendicular exactly when their slopes multiply to -1. Example: slopes 3/4 and -4/3 are perpendicular. Horizontal and vertical lines are also perpendicular.

Absolute value inequality split

For k greater than zero, the inequality |x| < k means -k < x < k, while |x| > k means x > k or x < -k. The equation |x| = k gives x = k or x = -k.

Parallel lines condition

Two nonvertical lines are parallel exactly when they have equal slopes and different y-intercepts. Equal slopes with equal intercepts describe the same line, giving infinitely many solutions.

Exponential decay formula

A quantity starting at P and decreasing by rate r each period equals P(1 - r)^t after t periods. Example: 500 at 10% decay for 2 years gives 500(0.9)^2 = 405.

Pythagorean common triples

Right triangles with integer sides include 3-4-5, 5-12-13, 8-15-17, and 7-24-25, plus any integer multiple of these, such as 6-8-10.

45-45-90 triangle ratio

An isosceles right triangle has legs in ratio 1:1 and hypotenuse equal to leg times the square root of 2. Example: legs 5 give hypotenuse 5 sqrt(2).

30-60-90 triangle ratio

Sides opposite 30, 60, and 90 degrees are in ratio 1 : sqrt(3) : 2. The hypotenuse is twice the shortest side, and the middle side is shortest times sqrt(3).

Polygon interior angle sum

A polygon with n sides has interior angles summing to (n - 2) x 180 degrees. Example: a hexagon has 4 x 180 = 720 degrees.

Similar figure scaling

If two similar figures have corresponding lengths in ratio k, their areas are in ratio k^2 and their volumes in ratio k^3. Doubling lengths multiplies area by 4.

Inscribed angle theorem

An angle inscribed in a circle measures half the arc it intercepts. A triangle inscribed in a semicircle therefore has a right angle at the circumference.

Circle equation standard form

A circle centered at (h, k) with radius r satisfies (x - h)^2 + (y - k)^2 = r^2. Example: center (2, -1), radius 3 gives (x-2)^2 + (y+1)^2 = 9.

Combined work rate

When two workers complete a job in times t1 and t2 alone, together they finish in time t satisfying 1/t = 1/t1 + 1/t2. Example: 4 and 6 hours give 2.4 hours.

Mixture concentration equation

Mixing volume A at concentration a with volume B at concentration b gives final concentration (Aa + Bb)/(A + B). Total solute is conserved across the mix.

Weighted average formula

The weighted average equals the sum of each value times its weight, divided by the total weight. It always lies between the smallest and largest values used.

Compound interest formula

A = P(1 + r/n)^(nt), where P is principal, r the annual rate, n the compounding periods per year, and t the number of years.

Two-set inclusion-exclusion

For two overlapping groups, total = A + B - both + neither. The overlap is subtracted once because it was counted in both A and B.

Consecutive integer product

The product of any k consecutive integers is divisible by k factorial. Example: any three consecutive integers multiply to a multiple of 6.

Data sufficiency choice C

Choice C applies when the two statements together determine a unique answer, but neither statement alone is sufficient. Both must be used jointly.

Data sufficiency choice D

Choice D applies when each statement independently provides enough information to answer the question. Neither statement is needed to supplement the other.

Sufficiency requires uniqueness

A statement is sufficient only if it yields exactly one possible value for the target quantity. Two or more possible values make the statement insufficient.

Independent statement evaluation

Evaluate each data sufficiency statement separately against the question stem. Never use information from one statement while judging the other.

Yes/no sufficiency test

For a yes/no question, a statement is sufficient only if it forces a definite yes or a definite no. If both outcomes remain possible, the statement is insufficient.