# Monthly Archives: August 2014

## Square Inside Square

In the diagram, two sets of parallel lines intersect to form a square. What is the area of the shaded region? Source: NCTM Mathematics Teacher 2006 SOLUTION By the Pythagorean theorem The two right triangles and are congruent by SAS. … Continue reading

## Radius of Tangent Circle

A circular arc centered at one vertex of a square of side length passes through two other vertices. A small circle is tangent to the large circle and to two sides of the square. What is the radius of the … Continue reading

## Colored Balls

A bowl contains colored balls: green, red, blue, yellow, black, and white. If you are blindfolded, what is the smallest number of balls you must pick to guarantee that you have at least balls of the same color? Source: NCTM … Continue reading

## Bead on a String

Joan holds a -inch long piece of light-weight string with a heavy bead on it. One end is in her right hand; the other is in her left hand. Initially, her hands are together. How many inches apart must she … Continue reading

## Filling a Square

The square shown here can be filled in so that each row and each column contains each of the numbers , and exactly once. What does equal? Source: NCTM Mathematics Teacher 2006 SOLUTION Fill in the fourth column: goes in … Continue reading

## Number of Square Units

What is the number of square units enclosed by the polygon ? Source: NCTM Mathematics Teacher 2006 SOLUTION Polygon encloses polygon . Number of square units inside polygon Number of square units inside polygon Number of square units inside polygon … Continue reading

## Class Average

Johnny was ill and had to take a test a day late. His raised the class average from to . How many students, including Johnny, took the test? Source: NCTM Mathematics Teacher 2006 SOLUTION Let represent the scores of the … Continue reading

## Profit or Loss

A used car salesman sold two cars and received for each car. One of these transactions yielded a percent profit for the dealer (compared to his purchase price), whereas the other amounted to a percent loss. What is the dealer’s … 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: