Problem SolvingFebruary 2013

2/4/13 Find F!

Using the equations below, find the value of F if A is 5.

2/5/13 How Long?

How long will it take a two-mile-long train going 12 mph to get completely through a mile-long tunnel?

2/6/13 What’s Next?

Determine the next two numbers in the pattern below:

31, 62, 93, 25, 56, 87, __, __,

2/7/13 Reverse & Add

If you find the sum of any two-digit number and the number formed by reversing its digits, the resulting value is always divisible by what two positive whole numbers?

14 +41 = ?

2/8/13 Kids!

At 12 Noon, the principal sent home 1/3 of the students plus 6. At 1 PM, she counted the remaining students and sent home 1/4 of them. At 2 PM, she sent home the last 21 students. How many students were originally in school that day?

2/11 Mean & Median

The mean of three numbers is 10, and their median is 10.3. If the difference between the largest and the smallest of the three numbers is 2, what are the three numbers?

2/12/13 Who Am I?

I am the smallest counting number that is divisible by the first ten composite numbers. Who am I?

2/13/13 Unshaded!

The diagram below contains two shaded circles that have a wire wrapped around them. The area of each shaded circle is 9π square inches. What is the total area of the unshaded section in the diagram that is enclosed by the wire?

2/14 Find the Length

One-sixth of a steel beam of a bridge is in cement below the bed of a river. Two-fifths of the beam is in the water, and 78 feet of the beam are above the water. How long is the steel beam?

2/15/13 Make 1 Move!

Make the equation below a true statement by repositioning one and only one digit in the equation. You cannot add or delete any mathematical symbol or move the – or = signs.

26 – 63 = 1

2/25 Jason’s Wardrobe

Jason has 6 pairs of pants, 10 shirts, 2 belts, and 4 neckties. Assume that wearing a tie and a belt is optional.

How many different outfits can Jason make from his wardrobe?

2/26/13 Find a & b

Find the values of a and b so that 8 is both the mean and median of this set of numbers:

{a, b, 10, 7, 11}

2/27/13 Multiply!

Without rearranging any digits, insert one multiplication symbol (×) into the following expression to obtain the greatest possible product:

1 2 3 4 5

2/28/13 Solve this!

Find the values of the positive numbers a and b, given that a is 8 times the size of b and the reciprocal of ab is 1 less than 3.

Problems adapted from...

Problems adapted from NCTM’s Math Teaching in the Middle School

Menu of Problems November 2007 & March 2008