p, q and r are three points on the real number line where q = $latex \frac{2pr}{p+r}$. Quantity A: $latex \left | \frac{1}{p} - \frac{1}{r}\right |$ Quantity B: $latex \left | \frac{1}{q} - \frac{1}{p}\right |$ Explanation: q = $latex \frac{2pr}{p+r}$ qp + qr = 2pr Divide both sides of the equation by pqr (1/r) + (1/p) = (2/q) [(1/r) + (1/p)]/2 = … [Read more...] about Quantitative Comparison – Numberline, Absolute Value

# GRE Number Properties

## 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

## 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

## 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

## 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