# Tag Archives: absolute value

## Cottages on a Straight Road

There are four cottages on a straight road. The distance between Ted’s and Alice’s cottages is km. Both Bob’s and Carol’s cottages are twice as far from Alice’s as they are from Ted’s. Find the distance between Bob’s and Carol’s … Continue reading

## 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

## Absolute Value Function

What is the area of the region bounded by the graph of ? Source: NCTM Mathematics Teacher, October 2006 Solution If and If and If and If and The four graphs intersect and form a square of side length . … Continue reading

## Distance From Zero

Find the product of all real values of that satisfy the equation . Source: NCTM Mathematics Teacher, January 2006 SOLUTION One way to interpret the absolute values and is to think of them as the distances from point to point … Continue reading

## Absolute Value

How many different real-valued pairs satisfy this system of two equations? Source: NCTM Mathematics Teacher, November 2006 SOLUTION Suppose Substitute the value of into Eq. or We have two pairs and . Suppose Substitute the value of into Eq. or … Continue reading

## Square Root Function

How many positive real numbers are solutions to ? Source: NCTM Mathematics Teacher, November 2006 SOLUTION The graphs of the two functions and show two intersection points There are two solutions to . Answer:

## Distance Between Two Points

If two points are selected at random from the interval , what is the probability that the distance between them is less than one fourth? Source: NCTM Mathematics Teacher, February 2006 SOLUTION Consider two points and on the interval. Create … Continue reading

## Nine Dates

Choose any square of nine dates from a month in a calendar. What is the absolute value of the difference of the products of the dates in the opposite corners? Source: NCTM Mathematics Teacher, February 2006 SOLUTION Let represent the … Continue reading

## Absolute Difference

To answer this puzzler, you must provide the absolute value of the difference of the values determined in part 1 and part 2. Part 1: Determine the least positive integer by which can be multiplied so that the product is … Continue reading

## M and N

and are positive integers and neither of [them] are divisible by . If the product of and equals , find the absolute value of the difference of and . Source: mathcontest.olemiss.edu 10/8/2012 SOLUTION Since and are not divisible by , neither of … Continue reading