An equilateral triangle and a parallelogram lie on the same base and between the same parallel lines. The area of the parallelogram is 200*root(3) sq cm. What is the length of the side of the triangle?Explanation: Two triangles with the same base and between the same parallel lines will have equal areas. Likewise, a triangle and a parallelogram with the same base and between … [Read more...] about GRE Geometry – same base, same height

# GRE Problem Solving

## GRE Geometry – Planet Circles

Consider a planet P1 (like earth) that is spherical in shape. It has an atmospheric layer around it that also takes the same shape as that of the planet. An adventurist launches a rocket from a neighboring planet P2 to this planet P1. The rocket cuts the atmospheric layer at point A, grazes the planet P1 and goes out of the atmospheric layer at point B. If AB = 100 km, what is … [Read more...] about GRE Geometry – Planet Circles

## GRE Algebra – Word Problems

When four is added to six times a number and the result squared, the result obtained is four times the square of the sum of the number and its next multiple. What is the number?Explanation:The question can be directly converted to an equation as follows.Let ‘n’ be the number.(4 + 6n)2= 4(n + 2n)222(2 + 3n)2 = 4(3n)24 + 12n + 9n2= 9n2n = … [Read more...] about GRE Algebra – Word Problems

## GRE Geometry – Chords and Circles

A, B and C are three points on a circle. AB, BC and AC are three chords where AB = AC. If the maximum length of BC is 10 cm, what is the area of triangle ABC? Explanation: If BC, which is a chord, should have the maximum length then it should be the diameter. And since angle(BAC) is the angle subtended by the diameter at the circumference, it should be 90 degrees. And we … [Read more...] about GRE Geometry – Chords and Circles

## Algebra – Inequalities and Exponents

Solve: (a) 7^(4-16x) > 1 (b) 2/(x-1) < 1 (a) For any a^b > 1, if a > 1 then b should be greater than 0. Hence 4 – 16x > 0 Therefore, x<1/4. (b) 2/(x-1) < 1 2/(x-1) - 1< 0 [2-(x-1)]/(x-1) < 0 (3-x)/(x-1) < 0 (x-3)/(x-1) > 0 Hence ‘x’ lies outside the roots ‘1’ and ‘3’. Therefore, x € (-∞ , 1) U (3, ∞) … [Read more...] about Algebra – Inequalities and Exponents