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 Problem Solving

## 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

## Solid Geometry – Sectors cones

A sector of a circle of radius 5 cm is recast into a right circular cone of height 4 cm. What is the volume of the cone so formed? Explanation: A sector of a circle with radius 5 cm will look something like this. When recast into a right-circular cone of height 4 cm it will look something like this. Hence, the radius of the sector becomes the … [Read more...] about Solid Geometry – Sectors cones

## 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