GRE resources

Solves a quantity comparison using the signs of xy and xy squared, showing x must be positive and y negative without solving exactly, to prove one quantity is always greater.

Solves a system of linear equations asked for an expression like x plus y, using the combination method of adding or subtracting equations. Shows why subtracting the right side works since both equal the same value.

Primes greater than 2 are all odd, and odd plus odd is even, so the possible sum of two of them is found by ruling out answer choices, without adding any up.

A repeating sequence of five numbers is summed over its first 25 terms by spotting the five-term repeat and summing just one cycle first.

A nested radical expression simplifies step by step, using the cube root of 8 and rewriting the square root of a power as half its exponent to reach a final value of 2.

Works through finding a two-digit integer whose units digit doubles its tens digit and which is also a multiple of 9, then checks answer choices against its multiples.

A multi-step percent problem finds one person's pay as a percent of another's after a raise, solved by plugging in 100 for the base wage instead of using variables.

A composite function problem shows how to solve the interior function first, then feed its output into the exterior function. Comparing f(g(4)) with g(f(4)) demonstrates how swapping the order changes the result.

Solves a combinations problem of choosing 4 books from 7, using three questions: how many decisions, how many options per decision, and whether order matters, dividing out arrangements that count the same group twice.

Finds the 12th digit after the decimal in 4 divided by 11 by spotting the repeating 0.3636 pattern rather than relying on a calculator.

A power expression with 81 and 9 gets rewritten in base three, then power-of-a-power, product, and quotient rules simplify it step by step to 3 to the fifth.

A rooster-to-hen ratio problem is solved two ways: setting up an algebraic fraction equation, then rethinking the ratio as equally sized groups to find the totals.

Squaring a binomial with square roots gets FOILed term by term, combining radicals like root 16x times root x into 4x, to simplify down to 9x, then checked by plugging in a test value for x.

Tackles a quantity comparison by plugging in integers for x, testing whether the range of x, x squared, x cubed and x fourth power falls between 253 and 1,297 to see if x could equal 5.

Solves a multi-triangle diagram by chaining supplementary angles, vertical angles, and the triangle angle sum to find two unknown angles, then compares one to half the other.

A final grade is found by multiplying midterm, final exam, and practice set scores by their given weights, then summing the results. Weights must total 100%, and the answer is rounded to the nearest whole number.