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

## 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

## Permutation Combination – chess board

How many squares are there on a chess board? P.S. No, the answer is not 64 Explanation: Of course, as you might think, aren’t there only 8 x 8 = 64 squares on a chess board? Well, no. All these 64 squares are squares of 1 block. However, one can notice that there are squares of 4 blocks too i.e., 7 x 7 = 49. Likewise, until the largest square which is the chess board … [Read more...] about Permutation Combination – chess board

## 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

## Quantitative Comparison – Number Properties

N is the smallest number that has 7 factors.Quantity A: Number of factors that sqrt(N) has.Quantity B: Number of factors that N-2 has.Explanation:A number with 7 factors will be of the form a6.N is given to be the smallest such number. Hence N = 26.Quantity A:Sqrt(N) = 23and this has 4 factors.Quantity B:N – 2 = 26 – 2 = 64 – 2 = 62 = 2 * 31 and this has 4 factors.Therefore, … [Read more...] about Quantitative Comparison – Number Properties