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

# GRE Arithmetic Theory & Practice Questions

## 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

## GRE Quant |Probability Maximum & Minimum

A medium difficulty GRE Quant Sample Question in Probability. Ms Li works at an office where the work timing is from 9:00 AM to 6:00 PM. 25% of a year she goes late to office and 35% of a year she leaves early from office. If P is the probability that she works at office the entire day then (a) 0.25 ≤ P ≤ 0.35(b) 0.25 ≤ P ≤ 0.65(c) 0.4 ≤ P ≤ 0.65(d) 0.35 ≤ P ≤ 0.4(e) 0.35 ≤ … [Read more...] about GRE Quant |Probability Maximum & Minimum

## Numerical entry – Number Properties

If a + b=ab and a, b are natural numbers then how many pairs of (a, b) are there? Answer: 1 pair – (2, 2) Explanation a + b = ab ab – a – b = 0 ab – a – b + 1 = 1 (a – 1)(b – 1) = 1 Now, for this to be true, given that a and b are natural numbers a – 1 = b – 1 = 1. i.e., 1 x 1 = 1 Therefore, a = 2 and b = 2. … [Read more...] about Numerical entry – Number Properties

## Numeric Entry – Probability, Number Properties

A four-digit number is to be formed with the digits {0, 1, 2, 3, 4, 5} without repetition. What is the probability that this number will leave a remainder 2 when divided by 9? Answer: 0.14 Explanation Required probability = (number of four digit numbers that leave a remainder 2 when divided by 9) / (total number of four digit numbers that can be formed) If a … [Read more...] about Numeric Entry – Probability, Number Properties