This GRE® quant practice question tests your understanding of properties of triangles in Geometry. Concepts tested include properties of right triangles, orthocenter and circumcenter of triangles. Also, basic properties of coordinate geometry including coordinates of mid point of a line segment, equation of a line, computing intercepts of a line and distance between two points … [Read more...] about Geometry Triangles – Circumcentre, Orthocentre

# GRE Problem Solving

## GRE Hard Math – Permutation Combination

In how many rearrangements of the word SCINTILLATING will no two 'I' come together?Explanation:Let us consider the following arrangement without the three I’s._S_C_N_T_L_L_A_T_N_G_No two I’s would come together if the I’s are placed in the blanks. So, the question boils down to first finding out the number of ways in which three blanks can be chosen out of 11 blanks. This can … [Read more...] about GRE Hard Math – Permutation Combination

## GRE Geometry – same base, same height

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 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 Practice: Chess Board Probability

What is the probability that two squares(smallest dimension) selected randomly from a chess board have only one common corner?Explanation:From the diagram you see that considering the top two rows, there are 14 ways of choosing two squares with just one common corner.Like wise rows (2, 3), (3, 4)…….(7, 8) can be considered. Therefore, number of ways = 14 x 7 = … [Read more...] about GRE Practice: Chess Board Probability