8 directors, the vice chairman and the chairman are to be seated around a circular table. If the chairman should sit between a director and the vice chairman, in how many ways can they be seated? Answer: 8! * 2 Explanation: Let us consider the vice chairman and the chairman together as one entity. Hence, 8 directors + this entity can be arranged circularly in (9-1)! ways. … [Read more...] about Permutation Rearrangement

# GRE Arithmetic Theory & Practice Questions

## Number Properties – Factorial & Remainders

If p = 1! + (2x2!) + (3x3!) + (4x4!)...... + (10x10!), what is the remainder when p+2 is divided by 11!? Answer: 1 Explanation: p = 1! + (2x2!) + (3x3!) + (4x4!)...... + (10x10!) p = (1x1!) + (2x2!) + (3x3!) + (4x4!)...... + (10x10!) But, (1x1!) = 2! – 1! (2x2!) = 3! – 2! (3x3!) = 4! – 3! And so on. Hence, p = 2! – 1! + 3! – 2! + 4! – 3! + 5! – 4! + 6! – 5! + 7! – 6! … [Read more...] about Number Properties – Factorial & Remainders

## Statistics – Mean, Median, Range

The maximum mark in an examination is 100 and the minimum is 0. The average mark of seven students such that no two of them have scored the same marks is 88. If the median score is 92 and all the marks are integers, what is the maximum possible difference between the largest and the smallest mark obtained by these seven students? Answer: 54 Explanation: Average mark of … [Read more...] about Statistics – Mean, Median, Range

## Arithmetic and Geometric Progressions

The second, the first and the third term of an A.P whose common difference is non zero form a G.P in that order. Find its common ratio. Answer: -2 Explanation: Let the terms in GP be a, ar, ar2. Hence the terms ar, a and ar2 are in AP. Therefore, a – ar = ar2– a ‘a’ cannot be 0. Hence, 1 – r = r2 – 1 r2 + r -2 = 0 (r + 2)(r – 1) = 0 Now r cannot be ‘1’ … [Read more...] about Arithmetic and Geometric Progressions

## Number Properties – Divisibility Basics

If n is a natural number what is the remainder when (23*35*57*79)^n is divided by 2? Answer: 1 Explanation: 23, 35, 57, 79 are all odd numbers. The product of any number of odd numbers will also be an odd number and an odd number raised to any power will again be an odd number. When an odd number is divided by 2 the remainder is 1. If n is a natural number what is the … [Read more...] about Number Properties – Divisibility Basics