# Tag Archives: integers

## Smallest Quantity

If and , which of the following is never greater than any of the others? (a) (b) (c) (d) (c) Source:NCTM Mathematics Teacher, September 2006 Solution Suppose and (a) (b) (c) (d) (e) (a),(d),(e) have the smallest value Suppose and … Continue reading

## Values of Integers

If and are integers such that , what are the possible values of ? (a) only (b) only (c) only multiples of (d) any integer (e) none of these Source: NCTM Mathematics Teacher, September 2006 Solution Let be an integer … Continue reading

## TV Game Show

On a television show, a player receives points for answering an easy question and points for a hard one. What is the largest integer that cannot be a contestant’s total score of the game? Source: NCTM Mathematics Teacher, October 2006 … Continue reading

## Multiple of 3

If is an integer, show why must be a multiple of . Source: NCTM Mathematics Teacher, October 2006 Solution which is a rational number. Clearly, for to be an integer must be a multiple of . Answer: Shown in solution

## Largest of Five Integers

A set contains five integers. When distinct elements of this set are added together, two at a time, the complete list of different possible sums is , and . What is the largest of the five integers in the set? … Continue reading

## Four Numbers

The numbers , and are such that the sum of any one of them and the product of the other three is equal to . If , and , find . Source: NCTM Mathematic Teacher, January 2006 Solution There are … Continue reading

## Find All Integers

Find all integers such that is also an integer. Source: NCTM Mathematics Teacher, December 2005 SOLUTION The expression is an integer if is a divisor of . The divisors of are: Eight integers make the expression also an integer. Answer: 8

## Integral Points

A point is called integral if both and are integers. How many points on the graph of are integral points? Source: NCTM Mathematics Teacher, November 2006 SOLUTION Divide by , Divide by Divide by , no solution , duplicate solution … Continue reading

## Divide in Half

Divide in Half How many ordered pairs of integers satisfy ? Source: NCTM Mathematics Teacher 2006 SOLUTION For to be an integer must divide evenly. ordered pairs satisfy the requirement: , and . But, I don’t know how to prove … Continue reading

## Sum of Alternating Integers

What is the value of (alternating signs for each term)? Source: NCTM Mathematics Teacher 2006 SOLUTION The sum consists of additions of a positive and a negative integer each resulting in Answer: