# Monthly Archives: February 2018

## Largest Product

If , what arrangement of whole numbers , and into a three-digit and a two-digit number will produce the greatest product? Use each digit only once. Source: NCTM Mathematics Teacher, August 2006 Solution Let and be the two numbers. is … Continue reading

## Difference of Cubes

Suppose that and are two real numbers such that and . Find . Source: NCTM Mathematics Teacher, August 2006 Solution Substitute the value of and Substitute the value of Answer:

## Rationalize Denominators

Find so that . Source: NCTM Mathematics Teacher, August 2006 Solution Rationalize the denominators Multiply both sides by Cancel the opposite terms and , and , etc. Answer:

## Remainder of Sum of Factorials

What is the remainder when is divided by ? Source: NCTM Mathematics Teacher, August 2006 Solution divided by leaves a remainder of . is a multiple of so will have the same remainder as . Likewise, , etc. are multiples … Continue reading

## Partition of Integers

Among all collections, , of positive integers whose sum is , what is the largest product that the integers in can form? Source: NCTM Mathematics Teacher, August 2006 Solution Our first attempt at making the largest product is to write … Continue reading

## Three Numbers in Geometric Progression

If the product of three numbers in geometric progression is and their sum is , find the largest of the three numbers. Source: NCTM Mathematics Teacher, August 2006 Solution We assume that the three numbers are not consecutive but in … Continue reading

## Consecutive Remainders

What is the smallest positive integer that when divided by , and leaves the remainders , and , respectively? Source: NCTM Mathematics Teacher, August 2006 Solution If leaves a remainder of , the possible values of are . The integers … Continue reading

## Divisible by 3 or 7

Find the number of four-digit positive integers divisible by or . Source: NCTM Mathematics Teacher, August 2006 Solution Consider , the set of four-digit positive integers divisible by and , the set of four-digit positive integers divisible by . The … Continue reading

## Area of Trapezoid

In a trapezoid with parallel to , the diagonals intersect at point . The area of triangle is , and the area of triangle is . Find the area of the trapezoid. Source: NCTM Mathematics Teacher, August 2006 Solution Draw … Continue reading