# Monthly Archives: January 2018

## Set of Primes

Let be the set of primes that divide . What is the largest integer so that the set of primes that divides is equal to ? Source: NCTM Mathematics Teacher, August 2006 Solution The next prime greater than is . … Continue reading

## Largest 4-digit Integer x

Consider the equation . Find the largest four-digit integer for which there is an integer so that the pair is a solution. Source: NCTM Mathematics Teacher, August 2006 Solution For to be an integer, must be a multiple of . … Continue reading

## Two Defective Tiles

An -by–ft area has been tiled with -foot-square tiles. Two of the tiles were defective. What is the probability that the two defective tile share an edge? Source: NCTM Mathematics Teacher, August 2006 Solution Area Vertical shared edges Horizontal shared … Continue reading

## Choosing an Integer

An experiment consists of choosing with replacement an integer at random among the numbers from to inclusive. If we let denote a number that is an integral multiple of and denote a number that is not an integral multiple of … Continue reading

## Shift Left

Given the equation , find an equation whose roots are each less than the roots of the given equation. Source: NCTM Mathematics Teacher, August 2006 Solution If we graph the given equation as a function , we see that it … Continue reading

## Tangent Circles

Consider the circles that have radii and are tangent to the line at the point . Find the sum of the coordinates of the centers of the circles. Source: NCTM Mathematics Teacher, August 2006 Solution For the two circles to … Continue reading

## Father and Son Eat Together

A father and son eat meals together. If the son eats twice as fast as the father and the father eats a meal in minutes, how many meals can the son eat in hours? Source: NCTM Mathematics Teacher, August 2006 … Continue reading